engineering.jsonl

{"answer": "The moment is 300 N·m.", "choices": {"A": "200 N·m", "B": "300 N·m", "C": "400 N·m", "D": "350 N·m"}, "id": "eng_0001", "kind": "multiple_choice", "lang": "en", "question": "Force 150 N acts at 2 m from a pivot. What is the moment?", "steps": ["F = 150 N, d = 2 m.", "M = Fd = 300 N·m.", "Select option B (300 N·m)."], "subject": "engineering", "text": "Answer: 300 N·m.\nSteps:\n1. F = 150 N, d = 2 m.\n2. M = Fd = 300 N·m.\n3. Select option B (300 N·m).\nAnswer: (B)", "topic": "statics"}
{"answer": "The specific volume is 1 m³/kg.", "choices": null, "id": "eng_0002", "kind": "worked_example", "lang": "en", "question": "Gas fills 4 m³ with mass 4 kg. What is the specific volume?", "steps": ["V = 4 m³, m = 4 kg.", "v = V/m = 1 m³/kg.", "Result 1 m³/kg."], "subject": "engineering", "text": "Answer: 1 m³/kg.\nSteps:\n1. V = 4 m³, m = 4 kg.\n2. v = V/m = 1 m³/kg.\n3. Result 1 m³/kg.", "topic": "thermodynamics"}
{"answer": "Odpor je 5 Ω.", "choices": null, "id": "eng_0003", "kind": "worked_example", "lang": "cs", "question": "Napětí 15 V žene 3 A. Jaký je odpor?", "steps": ["V = 15 V, I = 3 A.", "R = V/I = 5 Ω.", "Result 5 Ω."], "subject": "engineering", "text": "Answer: 5 Ω.\nSteps:\n1. V = 15 V, I = 3 A.\n2. R = V/I = 5 Ω.\n3. Result 5 Ω.", "topic": "circuits"}
{"answer": "Settling time is about 9 s.", "choices": null, "id": "eng_0004", "kind": "worked_example", "lang": "en", "question": "Time constant 3 s. What is 5% settling time?", "steps": ["τ = 3 s.", "ts ≈ 3τ = 9 s.", "Result 9 s."], "subject": "engineering", "text": "Answer: 9 s.\nSteps:\n1. τ = 3 s.\n2. ts ≈ 3τ = 9 s.\n3. Result 9 s.", "topic": "control"}
{"answer": "Outlet velocity is 6 m/s.", "choices": {"A": "4 m/s", "B": "6 m/s", "C": "8 m/s", "D": "10 m/s"}, "id": "eng_0005", "kind": "multiple_choice", "lang": "en", "question": "Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 3 m/s. What is outlet velocity?", "steps": ["A1v1 = 0.02×3 m³/s.", "v2 = 6 m/s.", "Select option B (6 m/s)."], "subject": "engineering", "text": "Answer: 6 m/s.\nSteps:\n1. A1v1 = 0.02×3 m³/s.\n2. v2 = 6 m/s.\n3. Select option B (6 m/s).\nAnswer: (B)", "topic": "fluids"}
{"answer": "The strain is 200 microstrain.", "choices": {"A": "100 microstrain", "B": "200 microstrain", "C": "300 microstrain", "D": "400 microstrain"}, "id": "eng_0006", "kind": "multiple_choice", "lang": "en", "question": "Bar 1000 mm stretches 0.2 mm. What is the strain?", "steps": ["ΔL = 0.2 mm, L = 1000 mm.", "ε = 200 microstrain.", "Select option B (200 microstrain)."], "subject": "engineering", "text": "Answer: 200 microstrain.\nSteps:\n1. ΔL = 0.2 mm, L = 1000 mm.\n2. ε = 200 microstrain.\n3. Select option B (200 microstrain).\nAnswer: (B)", "topic": "materials"}
{"answer": "Max friction is 200 N.", "choices": {"A": "250 N", "B": "150 N", "C": "200 N", "D": "300 N"}, "id": "eng_0007", "kind": "multiple_choice", "lang": "en", "question": "Normal force 400 N, friction coefficient 0.5. What is max friction?", "steps": ["μ = 0.5 (dimensionless), N = 400 N.", "F = μN = 200 N.", "Select option C (200 N)."], "subject": "engineering", "text": "Answer: 200 N.\nSteps:\n1. μ = 0.5 (dimensionless), N = 400 N.\n2. F = μN = 200 N.\n3. Select option C (200 N).\nAnswer: (C)", "topic": "statics"}
{"answer": "První zákon říká, že energie se zachovává: teplo je práce plus vnitřní energie.", "choices": null, "id": "eng_0008", "kind": "concept", "lang": "cs", "question": "Co je první zákon termodynamiky?", "steps": ["Teplo v J.", "Práce v J.", "Vnitřek drží."], "subject": "engineering", "text": "Answer: Zachování energie.\nSteps:\n1. Teplo v J.\n2. Práce v J.\n3. Vnitřek drží.", "topic": "thermodynamics"}
{"answer": "The tap voltage is 7 V.", "choices": null, "id": "eng_0009", "kind": "worked_example", "lang": "en", "question": "Divider with two 1000 Ω resistors fed 14 V. What is the tap voltage?", "steps": ["Vin = 14 V, halves.", "Vout = 7 V.", "Result 7 V."], "subject": "engineering", "text": "Answer: 7 V.\nSteps:\n1. Vin = 14 V, halves.\n2. Vout = 7 V.\n3. Result 7 V.", "topic": "circuits"}
{"answer": "Feedback control measures output and corrects input to track a setpoint.", "choices": null, "id": "eng_0010", "kind": "concept", "lang": "en", "question": "What is feedback control?", "steps": ["Sense output.", "Compare target.", "Drive error down."], "subject": "engineering", "text": "Answer: Measure and correct.\nSteps:\n1. Sense output.\n2. Compare target.\n3. Drive error down.", "topic": "control"}
{"answer": "Density is mass per unit volume, in kilograms per cubic metre.", "choices": null, "id": "eng_0011", "kind": "concept", "lang": "en", "question": "What is density?", "steps": ["kg over m³.", "Water 1000.", "Steel 7850."], "subject": "engineering", "text": "Answer: Mass per volume.\nSteps:\n1. kg over m³.\n2. Water 1000.\n3. Steel 7850.", "topic": "fluids"}
{"answer": "Thermal stress is 36 MPa.", "choices": null, "id": "eng_0012", "kind": "worked_example", "lang": "en", "question": "Steel bar (E = 200 GPa, α = 12e-6/K) cools 15 K constrained. What thermal stress arises?", "steps": ["E = 200 GPa, ΔT = 15 K.", "σ = EαΔT = 36 MPa.", "Result 36 MPa."], "subject": "engineering", "text": "Answer: 36 MPa.\nSteps:\n1. E = 200 GPa, ΔT = 15 K.\n2. σ = EαΔT = 36 MPa.\n3. Result 36 MPa.", "topic": "materials"}
{"answer": "The vertical component is 120 N.", "choices": null, "id": "eng_0013", "kind": "worked_example", "lang": "en", "question": "Force 150 N pulls at a 3-4-5 angle. What is the vertical component?", "steps": ["F = 150 N, sin = 4/5.", "Fy = 0.8×150 = 120 N.", "Result 120 N."], "subject": "engineering", "text": "Answer: 120 N.\nSteps:\n1. F = 150 N, sin = 4/5.\n2. Fy = 0.8×150 = 120 N.\n3. Result 120 N.", "topic": "statics"}
{"answer": "The work done is 120 kJ.", "choices": {"A": "100 kJ", "B": "120 kJ", "C": "140 kJ", "D": "160 kJ"}, "id": "eng_0014", "kind": "multiple_choice", "lang": "en", "question": "Gas expands at 200 kPa by 0.6 m³. What work is done?", "steps": ["p = 200 kPa, ΔV = 0.6 m³.", "W = pΔV = 120 kJ.", "Select option B (120 kJ)."], "subject": "engineering", "text": "Answer: 120 kJ.\nSteps:\n1. p = 200 kPa, ΔV = 0.6 m³.\n2. W = pΔV = 120 kJ.\n3. Select option B (120 kJ).\nAnswer: (B)", "topic": "thermodynamics"}
{"answer": "The power is 690 W.", "choices": {"A": "460 W", "B": "690 W", "C": "920 W", "D": "805 W"}, "id": "eng_0015", "kind": "multiple_choice", "lang": "en", "question": "A 230 V appliance draws 3 A. What is its power?", "steps": ["V = 230 V, I = 3 A.", "P = VI = 690 W.", "Select option B (690 W)."], "subject": "engineering", "text": "Answer: 690 W.\nSteps:\n1. V = 230 V, I = 3 A.\n2. P = VI = 690 W.\n3. Select option B (690 W).\nAnswer: (B)", "topic": "circuits"}
{"answer": "Integrační výstup je 15 V.", "choices": null, "id": "eng_0016", "kind": "worked_example", "lang": "cs", "question": "Chyba 2 jednotky trvá 15 s při Ki = 0,5 1/s. Jaký je integrační výstup?", "steps": ["e = 2 units, t = 15 s.", "u = 0.5×2×15 = 15 V.", "Result 15 V."], "subject": "engineering", "text": "Answer: 15 V.\nSteps:\n1. e = 2 units, t = 15 s.\n2. u = 0.5×2×15 = 15 V.\n3. Result 15 V.", "topic": "control"}
{"answer": "The exit velocity is 5 m/s.", "choices": null, "id": "eng_0017", "kind": "worked_example", "lang": "en", "question": "Tank head 1.25 m (take g = 10 m/s²). What is the Torricelli velocity?", "steps": ["h = 1.25 m, g = 10 m/s².", "v = √(2gh) = 5 m/s.", "Result 5 m/s."], "subject": "engineering", "text": "Answer: 5 m/s.\nSteps:\n1. h = 1.25 m, g = 10 m/s².\n2. v = √(2gh) = 5 m/s.\n3. Result 5 m/s.", "topic": "fluids"}
{"answer": "Příčná deformace je -420 mikrostrainu.", "choices": null, "id": "eng_0018", "kind": "worked_example", "lang": "cs", "question": "Tyč se natáhne o 1400 mikrostrainu, Poisson 0,3. Jaká je příčná deformace?", "steps": ["εa = 1400 microstrain, ν = 0.3.", "εt = −νεa = -420 microstrain.", "Result -420 microstrain."], "subject": "engineering", "text": "Answer: -420 microstrain.\nSteps:\n1. εa = 1400 microstrain, ν = 0.3.\n2. εt = −νεa = -420 microstrain.\n3. Result -420 microstrain.", "topic": "materials"}
{"answer": "The reaction at B is 400 N.", "choices": null, "id": "eng_0019", "kind": "worked_example", "lang": "en", "question": "Beam 6 m, load 600 N at 4 m from A. What is reaction at B?", "steps": ["F = 600 N, span 6 m.", "RB = 600×4/6 = 400 N.", "Result 400 N."], "subject": "engineering", "text": "Answer: 400 N.\nSteps:\n1. F = 600 N, span 6 m.\n2. RB = 600×4/6 = 400 N.\n3. Result 400 N.", "topic": "statics"}
{"answer": "A thermodynamic system is a defined region with a boundary exchanging heat, work, or mass.", "choices": null, "id": "eng_0020", "kind": "concept", "lang": "en", "question": "What is a thermodynamic system?", "steps": ["Boundary set.", "Exchanges cross.", "Rest surroundings."], "subject": "engineering", "text": "Answer: Defined region.\nSteps:\n1. Boundary set.\n2. Exchanges cross.\n3. Rest surroundings.", "topic": "thermodynamics"}
{"answer": "Total resistance is 500 Ω.", "choices": {"A": "400 Ω", "B": "600 Ω", "C": "500 Ω", "D": "550 Ω"}, "id": "eng_0021", "kind": "multiple_choice", "lang": "en", "question": "Resistors 100 Ω and 400 Ω in series. What is total resistance?", "steps": ["R1 = 100 Ω, R2 = 400 Ω.", "R = 500 Ω.", "Select option C (500 Ω)."], "subject": "engineering", "text": "Answer: 500 Ω.\nSteps:\n1. R1 = 100 Ω, R2 = 400 Ω.\n2. R = 500 Ω.\n3. Select option C (500 Ω).\nAnswer: (C)", "topic": "circuits"}
{"answer": "Zpětná vazba měří výstup a opravuje vstup ke splnění cíle.", "choices": null, "id": "eng_0022", "kind": "concept", "lang": "cs", "question": "Co je zpětná vazba?", "steps": ["Snímej výstup.", "Srovnej cíl.", "Tlač chybu dolů."], "subject": "engineering", "text": "Answer: Měř a oprav.\nSteps:\n1. Snímej výstup.\n2. Srovnej cíl.\n3. Tlač chybu dolů.", "topic": "control"}
{"answer": "Pressure is force per unit area, measured in pascals.", "choices": null, "id": "eng_0023", "kind": "concept", "lang": "en", "question": "What is pressure?", "steps": ["N over m².", "Pa unit.", "kPa handy."], "subject": "engineering", "text": "Answer: Force per area.\nSteps:\n1. N over m².\n2. Pa unit.\n3. kPa handy.", "topic": "fluids"}
{"answer": "Napětí je 40 MPa.", "choices": {"A": "30 MPa", "B": "50 MPa", "C": "40 MPa", "D": "60 MPa"}, "id": "eng_0024", "kind": "multiple_choice", "lang": "cs", "question": "Ocel (E = 200 GPa) při deformaci 200 mikrostrainu. Jaké je napětí?", "steps": ["E = 200 GPa, ε = 200 microstrain.", "σ = Eε = 40 MPa.", "Vyber možnost C (40 MPa)."], "subject": "engineering", "text": "Answer: 40 MPa.\nSteps:\n1. E = 200 GPa, ε = 200 microstrain.\n2. σ = Eε = 40 MPa.\n3. Vyber možnost C (40 MPa).\nAnswer: (C)", "topic": "materials"}
{"answer": "The balancing reaction is 400 N upward.", "choices": {"A": "450 N", "B": "350 N", "C": "500 N", "D": "400 N"}, "id": "eng_0025", "kind": "multiple_choice", "lang": "en", "question": "Downward forces 160 N and 240 N act on a beam. What upward reaction balances them?", "steps": ["F1 = 160 N, F2 = 240 N.", "R = 160+240 = 400 N.", "Select option D (400 N)."], "subject": "engineering", "text": "Answer: 400 N.\nSteps:\n1. F1 = 160 N, F2 = 240 N.\n2. R = 160+240 = 400 N.\n3. Select option D (400 N).\nAnswer: (D)", "topic": "statics"}
{"answer": "The zeroth law says bodies in mutual thermal equilibrium share the same temperature.", "choices": null, "id": "eng_0026", "kind": "concept", "lang": "en", "question": "What is the zeroth law?", "steps": ["A with C.", "B with C.", "A with B."], "subject": "engineering", "text": "Answer: Same temperature.\nSteps:\n1. A with C.\n2. B with C.\n3. A with B.", "topic": "thermodynamics"}
{"answer": "The leaving current is 8 A.", "choices": null, "id": "eng_0027", "kind": "worked_example", "lang": "en", "question": "Currents 2 A and 6 A enter a node. What current leaves?", "steps": ["I1 = 2 A, I2 = 6 A.", "I3 = 8 A.", "Result 8 A."], "subject": "engineering", "text": "Answer: 8 A.\nSteps:\n1. I1 = 2 A, I2 = 6 A.\n2. I3 = 8 A.\n3. Result 8 A.", "topic": "circuits"}
{"answer": "The D output is 8 V.", "choices": null, "id": "eng_0028", "kind": "worked_example", "lang": "en", "question": "Error jumps 0 to 40 units in 2 s with Kd = 0.4 s. What is the D output?", "steps": ["Slope = 40/2 units/s.", "u = 0.4×slope = 8 V.", "Result 8 V."], "subject": "engineering", "text": "Answer: 8 V.\nSteps:\n1. Slope = 40/2 units/s.\n2. u = 0.4×slope = 8 V.\n3. Result 8 V.", "topic": "control"}
{"answer": "Hustota je hmotnost na jednotku objemu, v kilogramech na metr krychlový.", "choices": null, "id": "eng_0029", "kind": "concept", "lang": "cs", "question": "Co je hustota?", "steps": ["kg na m³.", "Voda 1000.", "Ocel 7850."], "subject": "engineering", "text": "Answer: Hmotnost na objem.\nSteps:\n1. kg na m³.\n2. Voda 1000.\n3. Ocel 7850.", "topic": "fluids"}
{"answer": "Stress is internal force per unit area, measured in pascals or megapascals.", "choices": null, "id": "eng_0030", "kind": "concept", "lang": "en", "question": "What is stress?", "steps": ["N over m².", "MPa handy.", "Tension positive."], "subject": "engineering", "text": "Answer: Force per area.\nSteps:\n1. N over m².\n2. MPa handy.\n3. Tension positive.", "topic": "materials"}
{"answer": "Each end reaction is 400 N.", "choices": null, "id": "eng_0031", "kind": "worked_example", "lang": "en", "question": "Uniform beam weighs 800 N over 8 m. What is each end reaction?", "steps": ["W = 800 N, midspan 4 m.", "R = W/2 = 400 N.", "Result 400 N."], "subject": "engineering", "text": "Answer: 400 N.\nSteps:\n1. W = 800 N, midspan 4 m.\n2. R = W/2 = 400 N.\n3. Result 400 N.", "topic": "statics"}
{"answer": "The power is 200 W.", "choices": null, "id": "eng_0032", "kind": "worked_example", "lang": "en", "question": "Work 2000 J is done in 10 s. What is the power?", "steps": ["W = 2000 J, t = 10 s.", "P = W/t = 200 W.", "Result 200 W."], "subject": "engineering", "text": "Answer: 200 W.\nSteps:\n1. W = 2000 J, t = 10 s.\n2. P = W/t = 200 W.\n3. Result 200 W.", "topic": "thermodynamics"}
{"answer": "Ohm's law says voltage equals current times resistance, V equals IR.", "choices": null, "id": "eng_0033", "kind": "concept", "lang": "en", "question": "What is Ohm's law?", "steps": ["V in volts.", "I in amps.", "R in ohms."], "subject": "engineering", "text": "Answer: V equals IR.\nSteps:\n1. V in volts.\n2. I in amps.\n3. R in ohms.", "topic": "circuits"}
{"answer": "Settling time is about 12 s.", "choices": {"A": "8 s", "B": "12 s", "C": "16 s", "D": "20 s"}, "id": "eng_0034", "kind": "multiple_choice", "lang": "en", "question": "First-order system has time constant 3 s. What is 2% settling time?", "steps": ["τ = 3 s.", "ts ≈ 4τ = 12 s.", "Select option B (12 s)."], "subject": "engineering", "text": "Answer: 12 s.\nSteps:\n1. τ = 3 s.\n2. ts ≈ 4τ = 12 s.\n3. Select option B (12 s).\nAnswer: (B)", "topic": "control"}
{"answer": "Hydrostatic pressure grows with depth as rho g h in a resting fluid.", "choices": null, "id": "eng_0035", "kind": "concept", "lang": "en", "question": "What is hydrostatic pressure?", "steps": ["Depth in m.", "Times rho g.", "kPa gauge."], "subject": "engineering", "text": "Answer: Rho g h.\nSteps:\n1. Depth in m.\n2. Times rho g.\n3. kPa gauge.", "topic": "fluids"}
{"answer": "Strain is relative elongation, a dimensionless ratio often in microstrain.", "choices": null, "id": "eng_0036", "kind": "concept", "lang": "en", "question": "What is strain?", "steps": ["Delta L over L.", "No units.", "Micro scale."], "subject": "engineering", "text": "Answer: Relative stretch.\nSteps:\n1. Delta L over L.\n2. No units.\n3. Micro scale.", "topic": "materials"}
{"answer": "Moment dvojice je 270 N·m.", "choices": {"A": "270 N·m", "B": "300 N·m", "C": "240 N·m", "D": "330 N·m"}, "id": "eng_0037", "kind": "multiple_choice", "lang": "cs", "question": "Dvojice sil 90 N má rameno 3 m. Jaký je její moment?", "steps": ["F = 90 N, d = 3 m.", "M = Fd = 270 N·m.", "Vyber možnost A (270 N·m)."], "subject": "engineering", "text": "Answer: 270 N·m.\nSteps:\n1. F = 90 N, d = 3 m.\n2. M = Fd = 270 N·m.\n3. Vyber možnost A (270 N·m).\nAnswer: (A)", "topic": "statics"}
{"answer": "Účinnost je 13 %.", "choices": null, "id": "eng_0038", "kind": "worked_example", "lang": "cs", "question": "Motor změní 130 J z 1000 J tepla na práci. Jaká je účinnost?", "steps": ["W = 130 J, Q = 1000 J.", "η = W/Q = 13%.", "Result 13%."], "subject": "engineering", "text": "Answer: 13%.\nSteps:\n1. W = 130 J, Q = 1000 J.\n2. η = W/Q = 13%.\n3. Result 13%.", "topic": "thermodynamics"}
{"answer": "The equivalent is 25 Ω.", "choices": {"A": "30 Ω", "B": "20 Ω", "C": "35 Ω", "D": "25 Ω"}, "id": "eng_0039", "kind": "multiple_choice", "lang": "en", "question": "Two 50 Ω resistors in parallel. What is the equivalent?", "steps": ["R = 50 Ω each.", "Req = R/2 = 25 Ω.", "Select option D (25 Ω)."], "subject": "engineering", "text": "Answer: 25 Ω.\nSteps:\n1. R = 50 Ω each.\n2. Req = R/2 = 25 Ω.\n3. Select option D (25 Ω).\nAnswer: (D)", "topic": "circuits"}
{"answer": "The closed-loop gain is 0.8.", "choices": null, "id": "eng_0040", "kind": "worked_example", "lang": "en", "question": "Unity feedback loop, forward gain 4. What is the closed-loop gain?", "steps": ["K = 4 (dimensionless).", "T = K/(1+K) = 0.8 (dimensionless).", "Result 0.8 (dimensionless)."], "subject": "engineering", "text": "Answer: 0.8 (dimensionless).\nSteps:\n1. K = 4 (dimensionless).\n2. T = K/(1+K) = 0.8 (dimensionless).\n3. Result 0.8 (dimensionless).", "topic": "control"}
{"answer": "The mass flow is 4 kg/s.", "choices": null, "id": "eng_0041", "kind": "worked_example", "lang": "en", "question": "Water flows 4 L/s. What is the mass flow in kg/s?", "steps": ["Q = 4 L/s, ρ = 1000 kg/m³.", "ṁ = 4 kg/s.", "Result 4 kg/s."], "subject": "engineering", "text": "Answer: 4 kg/s.\nSteps:\n1. Q = 4 L/s, ρ = 1000 kg/m³.\n2. ṁ = 4 kg/s.\n3. Result 4 kg/s.", "topic": "fluids"}
{"answer": "Estimated strength is 560 MPa.", "choices": null, "id": "eng_0042", "kind": "worked_example", "lang": "en", "question": "Steel hardness 160 HB. Estimate tensile strength (UTS ≈ 3.5·HB).", "steps": ["Hardness = 160 HB.", "UTS ≈ 3.5×160 = 560 MPa.", "Result 560 MPa."], "subject": "engineering", "text": "Answer: 560 MPa.\nSteps:\n1. Hardness = 160 HB.\n2. UTS ≈ 3.5×160 = 560 MPa.\n3. Result 560 MPa.", "topic": "materials"}
{"answer": "Výslednice je 300 N.", "choices": {"A": "250 N", "B": "300 N", "C": "350 N", "D": "400 N"}, "id": "eng_0043", "kind": "multiple_choice", "lang": "cs", "question": "Na šroub působí 180 N na východ a 240 N na sever. Jaká je výslednice?", "steps": ["Fx = 180 N, Fy = 240 N.", "R = √(180²+240²) = 300 N.", "Vyber možnost B (300 N)."], "subject": "engineering", "text": "Answer: 300 N.\nSteps:\n1. Fx = 180 N, Fy = 240 N.\n2. R = √(180²+240²) = 300 N.\n3. Vyber možnost B (300 N).\nAnswer: (B)", "topic": "statics"}
{"answer": "The new volume is 5 m³.", "choices": null, "id": "eng_0044", "kind": "worked_example", "lang": "en", "question": "Gas 3 m³ at 300 K warms to 500 K at constant pressure. What is the new volume?", "steps": ["V1 = 3 m³, T1 = 300 K.", "V2 = 3×500/300 = 5 m³.", "Result 5 m³."], "subject": "engineering", "text": "Answer: 5 m³.\nSteps:\n1. V1 = 3 m³, T1 = 300 K.\n2. V2 = 3×500/300 = 5 m³.\n3. Result 5 m³.", "topic": "thermodynamics"}
{"answer": "Energy used is 600 Wh.", "choices": {"A": "600 Wh", "B": "500 Wh", "C": "700 Wh", "D": "650 Wh"}, "id": "eng_0045", "kind": "multiple_choice", "lang": "en", "question": "A 300 W bulb burns 2 h. How much energy is used?", "steps": ["P = 300 W, t = 2 h.", "E = Pt = 600 Wh.", "Select option A (600 Wh)."], "subject": "engineering", "text": "Answer: 600 Wh.\nSteps:\n1. P = 300 W, t = 2 h.\n2. E = Pt = 600 Wh.\n3. Select option A (600 Wh).\nAnswer: (A)", "topic": "circuits"}
{"answer": "Open loop runs blind while closed loop uses feedback to reject disturbances.", "choices": null, "id": "eng_0046", "kind": "concept", "lang": "en", "question": "How do open and closed loop differ?", "steps": ["No sensor open.", "Sensor closed.", "Robust closed."], "subject": "engineering", "text": "Answer: Blind versus sensing.\nSteps:\n1. No sensor open.\n2. Sensor closed.\n3. Robust closed.", "topic": "control"}
{"answer": "Pascal's law says pressure applied to enclosed fluid spreads undiminished.", "choices": null, "id": "eng_0047", "kind": "concept", "lang": "en", "question": "What is Pascal's law?", "steps": ["Push piston.", "All walls feel.", "Hydraulics use."], "subject": "engineering", "text": "Answer: Spreads everywhere.\nSteps:\n1. Push piston.\n2. All walls feel.\n3. Hydraulics use.", "topic": "fluids"}
{"answer": "Hooke's law says stress is proportional to strain in the elastic range.", "choices": null, "id": "eng_0048", "kind": "concept", "lang": "en", "question": "What is Hooke's law?", "steps": ["Sigma equals E.", "Epsilon small.", "Unload recovers."], "subject": "engineering", "text": "Answer: Stress tracks strain.\nSteps:\n1. Sigma equals E.\n2. Epsilon small.\n3. Unload recovers.", "topic": "materials"}
{"answer": "A force is a vector push or pull with magnitude and direction, measured in newtons.", "choices": null, "id": "eng_0049", "kind": "concept", "lang": "en", "question": "What is a force?", "steps": ["Magnitude in N.", "Direction matters.", "Adds by vectors."], "subject": "engineering", "text": "Answer: Vector in newtons.\nSteps:\n1. Magnitude in N.\n2. Direction matters.\n3. Adds by vectors.", "topic": "statics"}
{"answer": "The pressure is 700 kPa.", "choices": null, "id": "eng_0050", "kind": "worked_example", "lang": "en", "question": "Gas 7 m³ at 100 kPa is squeezed to 1 m³ at constant temperature. What is the pressure?", "steps": ["p1 = 100 kPa, V1 = 7 m³.", "p2 = 100×7 = 700 kPa.", "Result 700 kPa."], "subject": "engineering", "text": "Answer: 700 kPa.\nSteps:\n1. p1 = 100 kPa, V1 = 7 m³.\n2. p2 = 100×7 = 700 kPa.\n3. Result 700 kPa.", "topic": "thermodynamics"}
{"answer": "The voltage is 84 V.", "choices": {"A": "72 V", "B": "84 V", "C": "96 V", "D": "108 V"}, "id": "eng_0051", "kind": "multiple_choice", "lang": "en", "question": "Current 7 A flows through 12 Ω. What is the voltage?", "steps": ["I = 7 A, R = 12 Ω.", "V = IR = 84 V.", "Select option B (84 V)."], "subject": "engineering", "text": "Answer: 84 V.\nSteps:\n1. I = 7 A, R = 12 Ω.\n2. V = IR = 84 V.\n3. Select option B (84 V).\nAnswer: (B)", "topic": "circuits"}
{"answer": "Steady-state error is 10%.", "choices": {"A": "12%", "B": "8%", "C": "10%", "D": "15%"}, "id": "eng_0052", "kind": "multiple_choice", "lang": "en", "question": "Type-0 loop has position constant Kp = 9. What is step steady-state error?", "steps": ["Kp = 9 (dimensionless).", "ess = 100/10 = 10%.", "Select option C (10%)."], "subject": "engineering", "text": "Answer: 10%.\nSteps:\n1. Kp = 9 (dimensionless).\n2. ess = 100/10 = 10%.\n3. Select option C (10%).\nAnswer: (C)", "topic": "control"}
{"answer": "Dynamický tlak je 375 Pa.", "choices": null, "id": "eng_0053", "kind": "worked_example", "lang": "cs", "question": "Vzduch (ρ = 1,2 kg/m³) letí 25 m/s. Jaký je dynamický tlak?", "steps": ["ρ = 1.2 kg/m³, v = 25 m/s.", "q = ½ρv² = 375 Pa.", "Result 375 Pa."], "subject": "engineering", "text": "Answer: 375 Pa.\nSteps:\n1. ρ = 1.2 kg/m³, v = 25 m/s.\n2. q = ½ρv² = 375 Pa.\n3. Result 375 Pa.", "topic": "fluids"}
{"answer": "The mass is 39.25 kg.", "choices": null, "id": "eng_0054", "kind": "worked_example", "lang": "en", "question": "Steel part volume 0.005 m³ (ρ = 7850 kg/m³). What is its mass?", "steps": ["V = 0.005 m³, ρ = 7850 kg/m³.", "m = ρV = 39.25 kg.", "Result 39.25 kg."], "subject": "engineering", "text": "Answer: 39.25 kg.\nSteps:\n1. V = 0.005 m³, ρ = 7850 kg/m³.\n2. m = ρV = 39.25 kg.\n3. Result 39.25 kg.", "topic": "materials"}
{"answer": "The net moment is 1460 N·m clockwise.", "choices": null, "id": "eng_0055", "kind": "worked_example", "lang": "en", "question": "500 N at 4 m clockwise, 180 N at 3 m counter-clockwise. What is the net moment?", "steps": ["M1 = 500×4 = 2000 N·m.", "M2 = 180×3 = 540 N·m.", "Net 1460 N·m."], "subject": "engineering", "text": "Answer: 1460 N·m.\nSteps:\n1. M1 = 500×4 = 2000 N·m.\n2. M2 = 180×3 = 540 N·m.\n3. Net 1460 N·m.", "topic": "statics"}
{"answer": "Carnot efficiency is 50%.", "choices": {"A": "55%", "B": "45%", "C": "50%", "D": "60%"}, "id": "eng_0056", "kind": "multiple_choice", "lang": "en", "question": "Carnot engine between 300 K and 600 K. What is its efficiency?", "steps": ["Tc = 300 K, Th = 600 K.", "η = 1 − 300/600 = 50%.", "Select option C (50%)."], "subject": "engineering", "text": "Answer: 50%.\nSteps:\n1. Tc = 300 K, Th = 600 K.\n2. η = 1 − 300/600 = 50%.\n3. Select option C (50%).\nAnswer: (C)", "topic": "thermodynamics"}
{"answer": "The power is 1840 W.", "choices": {"A": "1610 W", "B": "2070 W", "C": "1840 W", "D": "1955 W"}, "id": "eng_0057", "kind": "multiple_choice", "lang": "en", "question": "A 230 V appliance draws 8 A. What is its power?", "steps": ["V = 230 V, I = 8 A.", "P = VI = 1840 W.", "Select option C (1840 W)."], "subject": "engineering", "text": "Answer: 1840 W.\nSteps:\n1. V = 230 V, I = 8 A.\n2. P = VI = 1840 W.\n3. Select option C (1840 W).\nAnswer: (C)", "topic": "circuits"}
{"answer": "The controller output is 40 V.", "choices": {"A": "30 V", "B": "50 V", "C": "60 V", "D": "40 V"}, "id": "eng_0058", "kind": "multiple_choice", "lang": "en", "question": "P-controller with Kp = 2 V/V sees error 20 units. What is the output?", "steps": ["Kp = 2 V/V, e = 20 units.", "u = Kp·e = 40 V.", "Select option D (40 V)."], "subject": "engineering", "text": "Answer: 40 V.\nSteps:\n1. Kp = 2 V/V, e = 20 units.\n2. u = Kp·e = 40 V.\n3. Select option D (40 V).\nAnswer: (D)", "topic": "control"}
{"answer": "Archimedes' principle says buoyancy equals the weight of displaced fluid.", "choices": null, "id": "eng_0059", "kind": "concept", "lang": "en", "question": "What is Archimedes' principle?", "steps": ["Volume under.", "Times rho g.", "Floats if light."], "subject": "engineering", "text": "Answer: Displaced weight.\nSteps:\n1. Volume under.\n2. Times rho g.\n3. Floats if light.", "topic": "fluids"}
{"answer": "Napětí je vnitřní síla na plochu, v pascalech či megapascalech.", "choices": null, "id": "eng_0060", "kind": "concept", "lang": "cs", "question": "Co je napětí v materiálu?", "steps": ["N na m².", "MPa šikovné.", "Tah kladný."], "subject": "engineering", "text": "Answer: Síla na plochu.\nSteps:\n1. N na m².\n2. MPa šikovné.\n3. Tah kladný.", "topic": "materials"}
{"answer": "Rameno je 14 m.", "choices": null, "id": "eng_0061", "kind": "worked_example", "lang": "cs", "question": "Moment 2100 N·m dělá síla 150 N. Jaké je rameno?", "steps": ["M = 2100 N·m, F = 150 N.", "d = M/F = 14 m.", "Result 14 m."], "subject": "engineering", "text": "Answer: 14 m.\nSteps:\n1. M = 2100 N·m, F = 150 N.\n2. d = M/F = 14 m.\n3. Result 14 m.", "topic": "statics"}
{"answer": "The heat required is 66.88 kJ.", "choices": {"A": "76.88 kJ", "B": "56.88 kJ", "C": "86.88 kJ", "D": "66.88 kJ"}, "id": "eng_0062", "kind": "multiple_choice", "lang": "en", "question": "2 kg of water warms by 8 K (c = 4.18 kJ/(kg·K)). How much heat?", "steps": ["m = 2 kg, ΔT = 8 K.", "Q = mcΔT = 66.88 kJ.", "Select option D (66.88 kJ)."], "subject": "engineering", "text": "Answer: 66.88 kJ.\nSteps:\n1. m = 2 kg, ΔT = 8 K.\n2. Q = mcΔT = 66.88 kJ.\n3. Select option D (66.88 kJ).\nAnswer: (D)", "topic": "thermodynamics"}
{"answer": "The stored charge is 3000 μC.", "choices": null, "id": "eng_0063", "kind": "worked_example", "lang": "en", "question": "Capacitor 300 μF charged to 10 V. What charge is stored?", "steps": ["C = 300 μF, V = 10 V.", "Q = CV = 3000 μC.", "Result 3000 μC."], "subject": "engineering", "text": "Answer: 3000 μC.\nSteps:\n1. C = 300 μF, V = 10 V.\n2. Q = CV = 3000 μC.\n3. Result 3000 μC.", "topic": "circuits"}
{"answer": "PID control sums proportional, integral, and derivative terms on the error.", "choices": null, "id": "eng_0064", "kind": "concept", "lang": "en", "question": "What is PID control?", "steps": ["P reacts now.", "I removes offset.", "D damps."], "subject": "engineering", "text": "Answer: P plus I plus D.\nSteps:\n1. P reacts now.\n2. I removes offset.\n3. D damps.", "topic": "control"}
{"answer": "The volume is 14 m³.", "choices": null, "id": "eng_0065", "kind": "worked_example", "lang": "en", "question": "Tank base area 2 m², depth 7 m. What is the water volume?", "steps": ["A = 2 m², h = 7 m.", "V = Ah = 14 m³.", "Result 14 m³."], "subject": "engineering", "text": "Answer: 14 m³.\nSteps:\n1. A = 2 m², h = 7 m.\n2. V = Ah = 14 m³.\n3. Result 14 m³.", "topic": "fluids"}
{"answer": "Elongation is 2.5 mm.", "choices": {"A": "3.5 mm", "B": "1.5 mm", "C": "4.5 mm", "D": "2.5 mm"}, "id": "eng_0066", "kind": "multiple_choice", "lang": "en", "question": "Force 25 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation?", "steps": ["F = 25 kN, L = 2 m.", "ΔL = FL/AE = 2.5 mm.", "Select option D (2.5 mm)."], "subject": "engineering", "text": "Answer: 2.5 mm.\nSteps:\n1. F = 25 kN, L = 2 m.\n2. ΔL = FL/AE = 2.5 mm.\n3. Select option D (2.5 mm).\nAnswer: (D)", "topic": "materials"}
{"answer": "The horizontal component is 240 N.", "choices": null, "id": "eng_0067", "kind": "worked_example", "lang": "en", "question": "Force 400 N pulls at a 3-4-5 angle. What is the horizontal component?", "steps": ["F = 400 N, cos = 3/5.", "Fx = 0.6×400 = 240 N.", "Result 240 N."], "subject": "engineering", "text": "Answer: 240 N.\nSteps:\n1. F = 400 N, cos = 3/5.\n2. Fx = 0.6×400 = 240 N.\n3. Result 240 N.", "topic": "statics"}
{"answer": "Internal energy rises 50 kJ.", "choices": {"A": "50 kJ", "B": "55 kJ", "C": "45 kJ", "D": "60 kJ"}, "id": "eng_0068", "kind": "multiple_choice", "lang": "en", "question": "System gains 90 kJ of heat and does 40 kJ of work. What is internal energy change?", "steps": ["Q = 90 kJ, W = 40 kJ.", "ΔU = Q−W = 50 kJ.", "Select option A (50 kJ)."], "subject": "engineering", "text": "Answer: 50 kJ.\nSteps:\n1. Q = 90 kJ, W = 40 kJ.\n2. ΔU = Q−W = 50 kJ.\n3. Select option A (50 kJ).\nAnswer: (A)", "topic": "thermodynamics"}
{"answer": "Total resistance is 1000 Ω.", "choices": {"A": "900 Ω", "B": "1100 Ω", "C": "1050 Ω", "D": "1000 Ω"}, "id": "eng_0069", "kind": "multiple_choice", "lang": "en", "question": "Resistors 100 Ω and 900 Ω in series. What is total resistance?", "steps": ["R1 = 100 Ω, R2 = 900 Ω.", "R = 1000 Ω.", "Select option D (1000 Ω)."], "subject": "engineering", "text": "Answer: 1000 Ω.\nSteps:\n1. R1 = 100 Ω, R2 = 900 Ω.\n2. R = 1000 Ω.\n3. Select option D (1000 Ω).\nAnswer: (D)", "topic": "circuits"}
{"answer": "P pushes with error, I clears steady offset, and D brakes on fast change.", "choices": null, "id": "eng_0070", "kind": "concept", "lang": "en", "question": "What do P, I, D terms do?", "steps": ["P gain now.", "I sums past.", "D rates change."], "subject": "engineering", "text": "Answer: Push clear brake.\nSteps:\n1. P gain now.\n2. I sums past.\n3. D rates change.", "topic": "control"}
{"answer": "Continuity says mass flow is constant, so area times velocity stays fixed.", "choices": null, "id": "eng_0071", "kind": "concept", "lang": "en", "question": "What is the continuity equation?", "steps": ["Narrow pipe.", "Faster flow.", "Q constant."], "subject": "engineering", "text": "Answer: Area times velocity.\nSteps:\n1. Narrow pipe.\n2. Faster flow.\n3. Q constant.", "topic": "fluids"}
{"answer": "Young's modulus is stiffness, stress over strain in gigapascals.", "choices": null, "id": "eng_0072", "kind": "concept", "lang": "en", "question": "What is Young's modulus?", "steps": ["Steel 200 GPa.", "Alu 70 GPa.", "Steeper stiffer."], "subject": "engineering", "text": "Answer: Stiffness slope.\nSteps:\n1. Steel 200 GPa.\n2. Alu 70 GPa.\n3. Steeper stiffer.", "topic": "materials"}
{"answer": "The moment is 800 N·m.", "choices": {"A": "700 N·m", "B": "900 N·m", "C": "800 N·m", "D": "850 N·m"}, "id": "eng_0073", "kind": "multiple_choice", "lang": "en", "question": "Force 400 N acts at 2 m from a pivot. What is the moment?", "steps": ["F = 400 N, d = 2 m.", "M = Fd = 800 N·m.", "Select option C (800 N·m)."], "subject": "engineering", "text": "Answer: 800 N·m.\nSteps:\n1. F = 400 N, d = 2 m.\n2. M = Fd = 800 N·m.\n3. Select option C (800 N·m).\nAnswer: (C)", "topic": "statics"}
{"answer": "The first law states energy is conserved: heat added equals internal rise plus work done.", "choices": null, "id": "eng_0074", "kind": "concept", "lang": "en", "question": "What is the first law of thermodynamics?", "steps": ["Heat in J.", "Work in J.", "Internal stores."], "subject": "engineering", "text": "Answer: Energy conserved.\nSteps:\n1. Heat in J.\n2. Work in J.\n3. Internal stores.", "topic": "thermodynamics"}
{"answer": "Ztrátový výkon je 120 W.", "choices": null, "id": "eng_0075", "kind": "worked_example", "lang": "cs", "question": "Proud 2 A odporem 30 Ω. Jaký je ztrátový výkon?", "steps": ["I = 2 A, R = 30 Ω.", "P = I²R = 120 W.", "Result 120 W."], "subject": "engineering", "text": "Answer: 120 W.\nSteps:\n1. I = 2 A, R = 30 Ω.\n2. P = I²R = 120 W.\n3. Result 120 W.", "topic": "circuits"}
{"answer": "PID regulace sčítá složky P, I a D z regulační odchylky.", "choices": null, "id": "eng_0076", "kind": "concept", "lang": "cs", "question": "Co je PID regulace?", "steps": ["P tlačí hned.", "I maže trvalou.", "D tlumí."], "subject": "engineering", "text": "Answer: P plus I plus D.\nSteps:\n1. P tlačí hned.\n2. I maže trvalou.\n3. D tlumí.", "topic": "control"}
{"answer": "The flow rate is 8 L/s.", "choices": {"A": "6 L/s", "B": "10 L/s", "C": "8 L/s", "D": "12 L/s"}, "id": "eng_0077", "kind": "multiple_choice", "lang": "en", "question": "Pipe area 20 cm², velocity 4 m/s. What is flow in litres per second?", "steps": ["A = 20 cm², v = 4 m/s.", "Q = Av = 8 L/s.", "Select option C (8 L/s)."], "subject": "engineering", "text": "Answer: 8 L/s.\nSteps:\n1. A = 20 cm², v = 4 m/s.\n2. Q = Av = 8 L/s.\n3. Select option C (8 L/s).\nAnswer: (C)", "topic": "fluids"}
{"answer": "The modulus is 62.1 GPa.", "choices": null, "id": "eng_0078", "kind": "worked_example", "lang": "en", "question": "Composite with fibre fraction 0.3 (Ef = 200 GPa, Em = 3 GPa). What is the modulus?", "steps": ["Vf = 0.3, Ef = 200 GPa.", "E = VfEf+VmEm = 62.1 GPa.", "Result 62.1 GPa."], "subject": "engineering", "text": "Answer: 62.1 GPa.\nSteps:\n1. Vf = 0.3, Ef = 200 GPa.\n2. E = VfEf+VmEm = 62.1 GPa.\n3. Result 62.1 GPa.", "topic": "materials"}
{"answer": "Max friction is 450 N.", "choices": {"A": "500 N", "B": "400 N", "C": "550 N", "D": "450 N"}, "id": "eng_0079", "kind": "multiple_choice", "lang": "en", "question": "Normal force 900 N, friction coefficient 0.5. What is max friction?", "steps": ["μ = 0.5 (dimensionless), N = 900 N.", "F = μN = 450 N.", "Select option D (450 N)."], "subject": "engineering", "text": "Answer: 450 N.\nSteps:\n1. μ = 0.5 (dimensionless), N = 900 N.\n2. F = μN = 450 N.\n3. Select option D (450 N).\nAnswer: (D)", "topic": "statics"}
{"answer": "Teplota je 87 °C.", "choices": null, "id": "eng_0080", "kind": "worked_example", "lang": "cs", "question": "Teplota je 360 K. Kolik je to stupňů Celsia?", "steps": ["T = 360 K.", "C = 360 − 273 = 87 °C.", "Result 87 °C."], "subject": "engineering", "text": "Answer: 87 °C.\nSteps:\n1. T = 360 K.\n2. C = 360 − 273 = 87 °C.\n3. Result 87 °C.", "topic": "thermodynamics"}
{"answer": "The current is 8 A.", "choices": null, "id": "eng_0081", "kind": "worked_example", "lang": "en", "question": "Voltage 48 V across 6 Ω. What is the current?", "steps": ["V = 48 V, R = 6 Ω.", "I = V/R = 8 A.", "Result 8 A."], "subject": "engineering", "text": "Answer: 8 A.\nSteps:\n1. V = 48 V, R = 6 Ω.\n2. I = V/R = 8 A.\n3. Result 8 A.", "topic": "circuits"}
{"answer": "Stability means bounded inputs give bounded outputs without runaway.", "choices": null, "id": "eng_0082", "kind": "concept", "lang": "en", "question": "What is stability?", "steps": ["Poles left.", "No blowup.", "Margin kept."], "subject": "engineering", "text": "Answer: Bounded stays bounded.\nSteps:\n1. Poles left.\n2. No blowup.\n3. Margin kept.", "topic": "control"}
{"answer": "The Reynolds number is 100000.", "choices": {"A": "75000 (dimensionless)", "B": "125000 (dimensionless)", "C": "150000 (dimensionless)", "D": "100000 (dimensionless)"}, "id": "eng_0083", "kind": "multiple_choice", "lang": "en", "question": "Water at 2 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number?", "steps": ["ρ = 1000 kg/m³, v = 2 m/s, D = 0.05 m.", "Re = ρvD/μ = 100000 (dimensionless).", "Select option D (100000 (dimensionless))."], "subject": "engineering", "text": "Answer: 100000 (dimensionless).\nSteps:\n1. ρ = 1000 kg/m³, v = 2 m/s, D = 0.05 m.\n2. Re = ρvD/μ = 100000 (dimensionless).\n3. Select option D (100000 (dimensionless)).\nAnswer: (D)", "topic": "fluids"}
{"answer": "The shear stress is 32 MPa.", "choices": null, "id": "eng_0084", "kind": "worked_example", "lang": "en", "question": "Shear force 16 kN on 500 mm² section. What is the shear stress?", "steps": ["F = 16 kN, A = 500 mm².", "τ = F/A = 32 MPa.", "Result 32 MPa."], "subject": "engineering", "text": "Answer: 32 MPa.\nSteps:\n1. F = 16 kN, A = 500 mm².\n2. τ = F/A = 32 MPa.\n3. Result 32 MPa.", "topic": "materials"}
{"answer": "The vertical component is 360 N.", "choices": null, "id": "eng_0085", "kind": "worked_example", "lang": "en", "question": "Force 450 N pulls at a 3-4-5 angle. What is the vertical component?", "steps": ["F = 450 N, sin = 4/5.", "Fy = 0.8×450 = 360 N.", "Result 360 N."], "subject": "engineering", "text": "Answer: 360 N.\nSteps:\n1. F = 450 N, sin = 4/5.\n2. Fy = 0.8×450 = 360 N.\n3. Result 360 N.", "topic": "statics"}
{"answer": "The temperature is 318 K.", "choices": {"A": "313 K", "B": "318 K", "C": "323 K", "D": "328 K"}, "id": "eng_0086", "kind": "multiple_choice", "lang": "en", "question": "Temperature is 45 °C. What is it in kelvin?", "steps": ["T = 45 °C.", "K = 45 + 273 = 318 K.", "Select option B (318 K)."], "subject": "engineering", "text": "Answer: 318 K.\nSteps:\n1. T = 45 °C.\n2. K = 45 + 273 = 318 K.\n3. Select option B (318 K).\nAnswer: (B)", "topic": "thermodynamics"}
{"answer": "The equivalent is 50 Ω.", "choices": {"A": "50 Ω", "B": "55 Ω", "C": "45 Ω", "D": "60 Ω"}, "id": "eng_0087", "kind": "multiple_choice", "lang": "en", "question": "Two 100 Ω resistors in parallel. What is the equivalent?", "steps": ["R = 100 Ω each.", "Req = R/2 = 50 Ω.", "Select option A (50 Ω)."], "subject": "engineering", "text": "Answer: 50 Ω.\nSteps:\n1. R = 100 Ω each.\n2. Req = R/2 = 50 Ω.\n3. Select option A (50 Ω).\nAnswer: (A)", "topic": "circuits"}
{"answer": "The total gain is 14.", "choices": {"A": "14 (dimensionless)", "B": "12 (dimensionless)", "C": "16 (dimensionless)", "D": "18 (dimensionless)"}, "id": "eng_0088", "kind": "multiple_choice", "lang": "en", "question": "Two series blocks have gains 2 and 7. What is the total gain?", "steps": ["K1 = 2, K2 = 7 (dimensionless).", "K = 14 (dimensionless).", "Select option A (14 (dimensionless))."], "subject": "engineering", "text": "Answer: 14 (dimensionless).\nSteps:\n1. K1 = 2, K2 = 7 (dimensionless).\n2. K = 14 (dimensionless).\n3. Select option A (14 (dimensionless)).\nAnswer: (A)", "topic": "control"}
{"answer": "Hydraulic power is 1962 W.", "choices": null, "id": "eng_0089", "kind": "worked_example", "lang": "en", "question": "Pump lifts 0.02 m³/s of water 10 m. What hydraulic power is needed?", "steps": ["Q = 0.02 m³/s, H = 10 m.", "P = ρgQH = 1962 W.", "Result 1962 W."], "subject": "engineering", "text": "Answer: 1962 W.\nSteps:\n1. Q = 0.02 m³/s, H = 10 m.\n2. P = ρgQH = 1962 W.\n3. Result 1962 W.", "topic": "fluids"}
{"answer": "Thermal stress is 108 MPa.", "choices": null, "id": "eng_0090", "kind": "worked_example", "lang": "en", "question": "Steel bar (E = 200 GPa, α = 12e-6/K) cools 45 K constrained. What thermal stress arises?", "steps": ["E = 200 GPa, ΔT = 45 K.", "σ = EαΔT = 108 MPa.", "Result 108 MPa."], "subject": "engineering", "text": "Answer: 108 MPa.\nSteps:\n1. E = 200 GPa, ΔT = 45 K.\n2. σ = EαΔT = 108 MPa.\n3. Result 108 MPa.", "topic": "materials"}
{"answer": "The balancing reaction is 650 N upward.", "choices": {"A": "650 N", "B": "700 N", "C": "600 N", "D": "750 N"}, "id": "eng_0091", "kind": "multiple_choice", "lang": "en", "question": "Downward forces 260 N and 390 N act on a beam. What upward reaction balances them?", "steps": ["F1 = 260 N, F2 = 390 N.", "R = 260+390 = 650 N.", "Select option A (650 N)."], "subject": "engineering", "text": "Answer: 650 N.\nSteps:\n1. F1 = 260 N, F2 = 390 N.\n2. R = 260+390 = 650 N.\n3. Select option A (650 N).\nAnswer: (A)", "topic": "statics"}
{"answer": "The second law says entropy of an isolated system never decreases and heat flows hot to cold.", "choices": null, "id": "eng_0092", "kind": "concept", "lang": "en", "question": "What is the second law of thermodynamics?", "steps": ["Hot to cold.", "No free lunch.", "Irreversible."], "subject": "engineering", "text": "Answer: Entropy never falls.\nSteps:\n1. Hot to cold.\n2. No free lunch.\n3. Irreversible.", "topic": "thermodynamics"}
{"answer": "The resistance is 11 Ω.", "choices": null, "id": "eng_0093", "kind": "worked_example", "lang": "en", "question": "Voltage 33 V drives 3 A. What is the resistance?", "steps": ["V = 33 V, I = 3 A.", "R = V/I = 11 Ω.", "Result 11 Ω."], "subject": "engineering", "text": "Answer: 11 Ω.\nSteps:\n1. V = 33 V, I = 3 A.\n2. R = V/I = 11 Ω.\n3. Result 11 Ω.", "topic": "circuits"}
{"answer": "Stabilita znamená, že omezený vstup dá omezený výstup.", "choices": null, "id": "eng_0094", "kind": "concept", "lang": "cs", "question": "Co je stabilita systému?", "steps": ["Póly vlevo.", "Bez úletu.", "Rezerva drží."], "subject": "engineering", "text": "Answer: Omezené drží.\nSteps:\n1. Póly vlevo.\n2. Bez úletu.\n3. Rezerva drží.", "topic": "control"}
{"answer": "The buoyant force is 58860 N.", "choices": {"A": "58860 N", "B": "49050 N", "C": "68670 N", "D": "78480 N"}, "id": "eng_0095", "kind": "multiple_choice", "lang": "en", "question": "A hull displaces 6 m³ of water. What is the buoyant force?", "steps": ["V = 6 m³, ρ = 1000 kg/m³.", "F = ρgV = 58860 N.", "Select option A (58860 N)."], "subject": "engineering", "text": "Answer: 58860 N.\nSteps:\n1. V = 6 m³, ρ = 1000 kg/m³.\n2. F = ρgV = 58860 N.\n3. Select option A (58860 N).\nAnswer: (A)", "topic": "fluids"}
{"answer": "Deformace je poměrné prodloužení, bezrozměrné, často v mikrostrainu.", "choices": null, "id": "eng_0096", "kind": "concept", "lang": "cs", "question": "Co je deformace (strain)?", "steps": ["Delta L lomeno L.", "Bez jednotek.", "Mikro škála."], "subject": "engineering", "text": "Answer: Poměrné protažení.\nSteps:\n1. Delta L lomeno L.\n2. Bez jednotek.\n3. Mikro škála.", "topic": "materials"}
{"answer": "Síla je vektor s velikostí a směrem, měří se v newtonech.", "choices": null, "id": "eng_0097", "kind": "concept", "lang": "cs", "question": "Co je síla?", "steps": ["Velikost v N.", "Směr platí.", "Sčítá vektory."], "subject": "engineering", "text": "Answer: Vektor v newtonech.\nSteps:\n1. Velikost v N.\n2. Směr platí.\n3. Sčítá vektory.", "topic": "statics"}
{"answer": "The specific volume is 4 m³/kg.", "choices": null, "id": "eng_0098", "kind": "worked_example", "lang": "en", "question": "Gas fills 16 m³ with mass 4 kg. What is the specific volume?", "steps": ["V = 16 m³, m = 4 kg.", "v = V/m = 4 m³/kg.", "Result 4 m³/kg."], "subject": "engineering", "text": "Answer: 4 m³/kg.\nSteps:\n1. V = 16 m³, m = 4 kg.\n2. v = V/m = 4 m³/kg.\n3. Result 4 m³/kg.", "topic": "thermodynamics"}
{"answer": "Kirchhoff's current law says currents entering a node equal those leaving it.", "choices": null, "id": "eng_0099", "kind": "concept", "lang": "en", "question": "What is Kirchhoff's current law?", "steps": ["Sum in amps.", "In equals out.", "Charge conserves."], "subject": "engineering", "text": "Answer: Currents balance.\nSteps:\n1. Sum in amps.\n2. In equals out.\n3. Charge conserves.", "topic": "circuits"}
{"answer": "The error is 35 units.", "choices": null, "id": "eng_0100", "kind": "worked_example", "lang": "en", "question": "Setpoint 350 units, measurement 315 units. What is the error?", "steps": ["r = 350 units, y = 315 units.", "e = r−y = 35 units.", "Result 35 units."], "subject": "engineering", "text": "Answer: 35 units.\nSteps:\n1. r = 350 units, y = 315 units.\n2. e = r−y = 35 units.\n3. Result 35 units.", "topic": "control"}
{"answer": "Bernoulli's equation trades pressure, velocity, and height energy along a streamline.", "choices": null, "id": "eng_0101", "kind": "concept", "lang": "en", "question": "What is Bernoulli's equation?", "steps": ["Fast means low p.", "High means low v.", "Steady ideal."], "subject": "engineering", "text": "Answer: Energy tradeoff.\nSteps:\n1. Fast means low p.\n2. High means low v.\n3. Steady ideal.", "topic": "fluids"}
{"answer": "Příčná deformace je -780 mikrostrainu.", "choices": null, "id": "eng_0102", "kind": "worked_example", "lang": "cs", "question": "Tyč se natáhne o 2600 mikrostrainu, Poisson 0,3. Jaká je příčná deformace?", "steps": ["εa = 2600 microstrain, ν = 0.3.", "εt = −νεa = -780 microstrain.", "Result -780 microstrain."], "subject": "engineering", "text": "Answer: -780 microstrain.\nSteps:\n1. εa = 2600 microstrain, ν = 0.3.\n2. εt = −νεa = -780 microstrain.\n3. Result -780 microstrain.", "topic": "materials"}
{"answer": "The reaction at B is 1000 N.", "choices": null, "id": "eng_0103", "kind": "worked_example", "lang": "en", "question": "Beam 6 m, load 1500 N at 4 m from A. What is reaction at B?", "steps": ["F = 1500 N, span 6 m.", "RB = 1500×4/6 = 1000 N.", "Result 1000 N."], "subject": "engineering", "text": "Answer: 1000 N.\nSteps:\n1. F = 1500 N, span 6 m.\n2. RB = 1500×4/6 = 1000 N.\n3. Result 1000 N.", "topic": "statics"}
{"answer": "The work done is 220 kJ.", "choices": {"A": "200 kJ", "B": "240 kJ", "C": "220 kJ", "D": "260 kJ"}, "id": "eng_0104", "kind": "multiple_choice", "lang": "en", "question": "Gas expands at 200 kPa by 1.1 m³. What work is done?", "steps": ["p = 200 kPa, ΔV = 1.1 m³.", "W = pΔV = 220 kJ.", "Select option C (220 kJ)."], "subject": "engineering", "text": "Answer: 220 kJ.\nSteps:\n1. p = 200 kPa, ΔV = 1.1 m³.\n2. W = pΔV = 220 kJ.\n3. Select option C (220 kJ).\nAnswer: (C)", "topic": "thermodynamics"}
{"answer": "Ohmův zákon říká, že napětí je proud krát odpor, U rovná IR.", "choices": null, "id": "eng_0105", "kind": "concept", "lang": "cs", "question": "Co je Ohmův zákon?", "steps": ["U ve voltech.", "I v ampérech.", "R v ohmech."], "subject": "engineering", "text": "Answer: U rovná IR.\nSteps:\n1. U ve voltech.\n2. I v ampérech.\n3. R v ohmech.", "topic": "circuits"}
{"answer": "Ustálená hodnota je 30 jednotek.", "choices": {"A": "25 units", "B": "30 units", "C": "35 units", "D": "40 units"}, "id": "eng_0106", "kind": "multiple_choice", "lang": "cs", "question": "Soustava K/(10s+1) s K = 30 dostane jednotkový skok. Jaká je ustálená hodnota?", "steps": ["DC gain K = 30 (dimensionless).", "Step final = 30 units.", "Vyber možnost B (30 units)."], "subject": "engineering", "text": "Answer: 30 units.\nSteps:\n1. DC gain K = 30 (dimensionless).\n2. Step final = 30 units.\n3. Vyber možnost B (30 units).\nAnswer: (B)", "topic": "control"}
{"answer": "Přetlak je 68.67 kPa.", "choices": {"A": "63.67 kPa", "B": "68.67 kPa", "C": "73.67 kPa", "D": "78.67 kPa"}, "id": "eng_0107", "kind": "multiple_choice", "lang": "cs", "question": "Hloubka vody je 7 m. Jaký je přetlak?", "steps": ["ρ = 1000 kg/m³, h = 7 m.", "p = ρgh = 68.67 kPa.", "Vyber možnost B (68.67 kPa)."], "subject": "engineering", "text": "Answer: 68.67 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 7 m.\n2. p = ρgh = 68.67 kPa.\n3. Vyber možnost B (68.67 kPa).\nAnswer: (B)", "topic": "fluids"}
{"answer": "Estimated strength is 980 MPa.", "choices": null, "id": "eng_0108", "kind": "worked_example", "lang": "en", "question": "Steel hardness 280 HB. Estimate tensile strength (UTS ≈ 3.5·HB).", "steps": ["Hardness = 280 HB.", "UTS ≈ 3.5×280 = 980 MPa.", "Result 980 MPa."], "subject": "engineering", "text": "Answer: 980 MPa.\nSteps:\n1. Hardness = 280 HB.\n2. UTS ≈ 3.5×280 = 980 MPa.\n3. Result 980 MPa.", "topic": "materials"}
{"answer": "Moment dvojice je 420 N·m.", "choices": {"A": "450 N·m", "B": "420 N·m", "C": "390 N·m", "D": "480 N·m"}, "id": "eng_0109", "kind": "multiple_choice", "lang": "cs", "question": "Dvojice sil 140 N má rameno 3 m. Jaký je její moment?", "steps": ["F = 140 N, d = 3 m.", "M = Fd = 420 N·m.", "Vyber možnost B (420 N·m)."], "subject": "engineering", "text": "Answer: 420 N·m.\nSteps:\n1. F = 140 N, d = 3 m.\n2. M = Fd = 420 N·m.\n3. Vyber možnost B (420 N·m).\nAnswer: (B)", "topic": "statics"}
{"answer": "The power is 500 W.", "choices": null, "id": "eng_0110", "kind": "worked_example", "lang": "en", "question": "Work 5000 J is done in 10 s. What is the power?", "steps": ["W = 5000 J, t = 10 s.", "P = W/t = 500 W.", "Result 500 W."], "subject": "engineering", "text": "Answer: 500 W.\nSteps:\n1. W = 5000 J, t = 10 s.\n2. P = W/t = 500 W.\n3. Result 500 W.", "topic": "thermodynamics"}
{"answer": "Energy used is 1100 Wh.", "choices": {"A": "1000 Wh", "B": "1100 Wh", "C": "1200 Wh", "D": "1150 Wh"}, "id": "eng_0111", "kind": "multiple_choice", "lang": "en", "question": "A 550 W bulb burns 2 h. How much energy is used?", "steps": ["P = 550 W, t = 2 h.", "E = Pt = 1100 Wh.", "Select option B (1100 Wh)."], "subject": "engineering", "text": "Answer: 1100 Wh.\nSteps:\n1. P = 550 W, t = 2 h.\n2. E = Pt = 1100 Wh.\n3. Select option B (1100 Wh).\nAnswer: (B)", "topic": "circuits"}
{"answer": "Settling time is about 32 s.", "choices": {"A": "28 s", "B": "36 s", "C": "32 s", "D": "40 s"}, "id": "eng_0112", "kind": "multiple_choice", "lang": "en", "question": "First-order system has time constant 8 s. What is 2% settling time?", "steps": ["τ = 8 s.", "ts ≈ 4τ = 32 s.", "Select option C (32 s)."], "subject": "engineering", "text": "Answer: 32 s.\nSteps:\n1. τ = 8 s.\n2. ts ≈ 4τ = 32 s.\n3. Select option C (32 s).\nAnswer: (C)", "topic": "control"}
{"answer": "Outlet velocity is 16 m/s.", "choices": {"A": "14 m/s", "B": "18 m/s", "C": "16 m/s", "D": "20 m/s"}, "id": "eng_0113", "kind": "multiple_choice", "lang": "en", "question": "Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 8 m/s. What is outlet velocity?", "steps": ["A1v1 = 0.02×8 m³/s.", "v2 = 16 m/s.", "Select option C (16 m/s)."], "subject": "engineering", "text": "Answer: 16 m/s.\nSteps:\n1. A1v1 = 0.02×8 m³/s.\n2. v2 = 16 m/s.\n3. Select option C (16 m/s).\nAnswer: (C)", "topic": "fluids"}
{"answer": "The factor of safety is 2.", "choices": {"A": "2 (dimensionless)", "B": "2.5 (dimensionless)", "C": "1.5 (dimensionless)", "D": "3 (dimensionless)"}, "id": "eng_0114", "kind": "multiple_choice", "lang": "en", "question": "Yield 300 MPa, working stress 150 MPa. What is the factor of safety?", "steps": ["σy = 300 MPa, σw = 150 MPa.", "n = 2 (dimensionless).", "Select option A (2 (dimensionless))."], "subject": "engineering", "text": "Answer: 2 (dimensionless).\nSteps:\n1. σy = 300 MPa, σw = 150 MPa.\n2. n = 2 (dimensionless).\n3. Select option A (2 (dimensionless)).\nAnswer: (A)", "topic": "materials"}
{"answer": "Newton's first law says a body keeps its velocity unless a net force acts on it.", "choices": null, "id": "eng_0115", "kind": "concept", "lang": "en", "question": "What is Newton's first law?", "steps": ["No net force.", "No acceleration.", "Inertia rules."], "subject": "engineering", "text": "Answer: Keep velocity.\nSteps:\n1. No net force.\n2. No acceleration.\n3. Inertia rules.", "topic": "statics"}
{"answer": "Carnotova účinnost je 60 %.", "choices": {"A": "65%", "B": "55%", "C": "70%", "D": "60%"}, "id": "eng_0116", "kind": "multiple_choice", "lang": "cs", "question": "Carnotův stroj mezi 300 K a 750 K. Jaká je jeho účinnost?", "steps": ["Tc = 300 K, Th = 750 K.", "η = 1 − 300/750 = 60%.", "Vyber možnost D (60%)."], "subject": "engineering", "text": "Answer: 60%.\nSteps:\n1. Tc = 300 K, Th = 750 K.\n2. η = 1 − 300/750 = 60%.\n3. Vyber možnost D (60%).\nAnswer: (D)", "topic": "thermodynamics"}
{"answer": "Kirchhoff's voltage law says voltages around any loop sum to zero.", "choices": null, "id": "eng_0117", "kind": "concept", "lang": "en", "question": "What is Kirchhoff's voltage law?", "steps": ["Add volts.", "Rises equal drops.", "Energy conserves."], "subject": "engineering", "text": "Answer: Loop sums zero.\nSteps:\n1. Add volts.\n2. Rises equal drops.\n3. Energy conserves.", "topic": "circuits"}
{"answer": "Konečná hodnota je 24 jednotek.", "choices": null, "id": "eng_0118", "kind": "worked_example", "lang": "cs", "question": "Soustava se zesílením 8 dostane skok 3. Jaká je konečná hodnota?", "steps": ["K = 8 (dimensionless), step 3 units.", "Final = 3×8 = 24 units.", "Result 24 units."], "subject": "engineering", "text": "Answer: 24 units.\nSteps:\n1. K = 8 (dimensionless), step 3 units.\n2. Final = 3×8 = 24 units.\n3. Result 24 units.", "topic": "control"}
{"answer": "The flow rate is 18 L/s.", "choices": {"A": "16 L/s", "B": "20 L/s", "C": "22 L/s", "D": "18 L/s"}, "id": "eng_0119", "kind": "multiple_choice", "lang": "en", "question": "Pipe area 20 cm², velocity 9 m/s. What is flow in litres per second?", "steps": ["A = 20 cm², v = 9 m/s.", "Q = Av = 18 L/s.", "Select option D (18 L/s)."], "subject": "engineering", "text": "Answer: 18 L/s.\nSteps:\n1. A = 20 cm², v = 9 m/s.\n2. Q = Av = 18 L/s.\n3. Select option D (18 L/s).\nAnswer: (D)", "topic": "fluids"}
{"answer": "The stress is 70 MPa.", "choices": {"A": "60 MPa", "B": "70 MPa", "C": "80 MPa", "D": "90 MPa"}, "id": "eng_0120", "kind": "multiple_choice", "lang": "en", "question": "Tensile force 7 kN on 100 mm² bar. What is the stress?", "steps": ["F = 7 kN, A = 100 mm².", "σ = F/A = 70 MPa.", "Select option B (70 MPa)."], "subject": "engineering", "text": "Answer: 70 MPa.\nSteps:\n1. F = 7 kN, A = 100 mm².\n2. σ = F/A = 70 MPa.\n3. Select option B (70 MPa).\nAnswer: (B)", "topic": "materials"}
{"answer": "Each end reaction is 700 N.", "choices": null, "id": "eng_0121", "kind": "worked_example", "lang": "en", "question": "Uniform beam weighs 1400 N over 8 m. What is each end reaction?", "steps": ["W = 1400 N, midspan 4 m.", "R = W/2 = 700 N.", "Result 700 N."], "subject": "engineering", "text": "Answer: 700 N.\nSteps:\n1. W = 1400 N, midspan 4 m.\n2. R = W/2 = 700 N.\n3. Result 700 N.", "topic": "statics"}
{"answer": "Potřebné teplo je 108.68 kJ.", "choices": {"A": "108.68 kJ", "B": "118.68 kJ", "C": "98.68 kJ", "D": "128.68 kJ"}, "id": "eng_0122", "kind": "multiple_choice", "lang": "cs", "question": "2 kg vody se ohřejí o 13 K (c = 4,18 kJ/(kg·K)). Kolik tepla?", "steps": ["m = 2 kg, ΔT = 13 K.", "Q = mcΔT = 108.68 kJ.", "Vyber možnost A (108.68 kJ)."], "subject": "engineering", "text": "Answer: 108.68 kJ.\nSteps:\n1. m = 2 kg, ΔT = 13 K.\n2. Q = mcΔT = 108.68 kJ.\n3. Vyber možnost A (108.68 kJ).\nAnswer: (A)", "topic": "thermodynamics"}
{"answer": "Series resistors add directly, so total resistance is the sum in ohms.", "choices": null, "id": "eng_0123", "kind": "concept", "lang": "en", "question": "How do series resistors combine?", "steps": ["Same current.", "Voltages split.", "R sums."], "subject": "engineering", "text": "Answer: Add in series.\nSteps:\n1. Same current.\n2. Voltages split.\n3. R sums.", "topic": "circuits"}
{"answer": "Settling time is about 27 s.", "choices": null, "id": "eng_0124", "kind": "worked_example", "lang": "en", "question": "Time constant 9 s. What is 5% settling time?", "steps": ["τ = 9 s.", "ts ≈ 3τ = 27 s.", "Result 27 s."], "subject": "engineering", "text": "Answer: 27 s.\nSteps:\n1. τ = 9 s.\n2. ts ≈ 3τ = 27 s.\n3. Result 27 s.", "topic": "control"}
{"answer": "The Reynolds number is 225000.", "choices": {"A": "225000 (dimensionless)", "B": "200000 (dimensionless)", "C": "250000 (dimensionless)", "D": "275000 (dimensionless)"}, "id": "eng_0125", "kind": "multiple_choice", "lang": "en", "question": "Water at 4.5 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number?", "steps": ["ρ = 1000 kg/m³, v = 4.5 m/s, D = 0.05 m.", "Re = ρvD/μ = 225000 (dimensionless).", "Select option A (225000 (dimensionless))."], "subject": "engineering", "text": "Answer: 225000 (dimensionless).\nSteps:\n1. ρ = 1000 kg/m³, v = 4.5 m/s, D = 0.05 m.\n2. Re = ρvD/μ = 225000 (dimensionless).\n3. Select option A (225000 (dimensionless)).\nAnswer: (A)", "topic": "fluids"}
{"answer": "Yield strength is the stress where permanent deformation begins.", "choices": null, "id": "eng_0126", "kind": "concept", "lang": "en", "question": "What is yield strength?", "steps": ["Below elastic.", "Above stays bent.", "Design limit."], "subject": "engineering", "text": "Answer: Plastic onset.\nSteps:\n1. Below elastic.\n2. Above stays bent.\n3. Design limit.", "topic": "materials"}
{"answer": "The resultant is 550 N.", "choices": {"A": "500 N", "B": "600 N", "C": "550 N", "D": "650 N"}, "id": "eng_0127", "kind": "multiple_choice", "lang": "en", "question": "Forces 330 N east and 440 N north act on a bolt. What is the resultant?", "steps": ["Fx = 330 N, Fy = 440 N.", "R = √(330²+440²) = 550 N.", "Select option C (550 N)."], "subject": "engineering", "text": "Answer: 550 N.\nSteps:\n1. Fx = 330 N, Fy = 440 N.\n2. R = √(330²+440²) = 550 N.\n3. Select option C (550 N).\nAnswer: (C)", "topic": "statics"}
{"answer": "Internal energy rises 75 kJ.", "choices": {"A": "80 kJ", "B": "75 kJ", "C": "70 kJ", "D": "85 kJ"}, "id": "eng_0128", "kind": "multiple_choice", "lang": "en", "question": "System gains 140 kJ of heat and does 65 kJ of work. What is internal energy change?", "steps": ["Q = 140 kJ, W = 65 kJ.", "ΔU = Q−W = 75 kJ.", "Select option B (75 kJ)."], "subject": "engineering", "text": "Answer: 75 kJ.\nSteps:\n1. Q = 140 kJ, W = 65 kJ.\n2. ΔU = Q−W = 75 kJ.\n3. Select option B (75 kJ).\nAnswer: (B)", "topic": "thermodynamics"}
{"answer": "The tap voltage is 13 V.", "choices": null, "id": "eng_0129", "kind": "worked_example", "lang": "en", "question": "Divider with two 1000 Ω resistors fed 26 V. What is the tap voltage?", "steps": ["Vin = 26 V, halves.", "Vout = 13 V.", "Result 13 V."], "subject": "engineering", "text": "Answer: 13 V.\nSteps:\n1. Vin = 26 V, halves.\n2. Vout = 13 V.\n3. Result 13 V.", "topic": "circuits"}
{"answer": "Steady-state error is the lasting gap between setpoint and output.", "choices": null, "id": "eng_0130", "kind": "concept", "lang": "en", "question": "What is steady-state error?", "steps": ["Wait long.", "Read offset.", "Type sets it."], "subject": "engineering", "text": "Answer: Lasting gap.\nSteps:\n1. Wait long.\n2. Read offset.\n3. Type sets it.", "topic": "control"}
{"answer": "Viscosity is a fluid's resistance to shearing flow.", "choices": null, "id": "eng_0131", "kind": "concept", "lang": "en", "question": "What is viscosity?", "steps": ["Honey high.", "Water low.", "Pa·s unit."], "subject": "engineering", "text": "Answer: Flow resistance.\nSteps:\n1. Honey high.\n2. Water low.\n3. Pa·s unit.", "topic": "fluids"}
{"answer": "The mass is 86.35 kg.", "choices": null, "id": "eng_0132", "kind": "worked_example", "lang": "en", "question": "Steel part volume 0.011 m³ (ρ = 7850 kg/m³). What is its mass?", "steps": ["V = 0.011 m³, ρ = 7850 kg/m³.", "m = ρV = 86.35 kg.", "Result 86.35 kg."], "subject": "engineering", "text": "Answer: 86.35 kg.\nSteps:\n1. V = 0.011 m³, ρ = 7850 kg/m³.\n2. m = ρV = 86.35 kg.\n3. Result 86.35 kg.", "topic": "materials"}
{"answer": "Moment je 1300 N·m.", "choices": {"A": "1200 N·m", "B": "1400 N·m", "C": "1350 N·m", "D": "1300 N·m"}, "id": "eng_0133", "kind": "multiple_choice", "lang": "cs", "question": "Síla 650 N působí 2 m od čepu. Jaký je moment?", "steps": ["F = 650 N, d = 2 m.", "M = Fd = 1300 N·m.", "Vyber možnost D (1300 N·m)."], "subject": "engineering", "text": "Answer: 1300 N·m.\nSteps:\n1. F = 650 N, d = 2 m.\n2. M = Fd = 1300 N·m.\n3. Vyber možnost D (1300 N·m).\nAnswer: (D)", "topic": "statics"}
{"answer": "The efficiency is 19%.", "choices": null, "id": "eng_0134", "kind": "worked_example", "lang": "en", "question": "Engine turns 190 J of 1000 J heat into work. What is the efficiency?", "steps": ["W = 190 J, Q = 1000 J.", "η = W/Q = 19%.", "Result 19%."], "subject": "engineering", "text": "Answer: 19%.\nSteps:\n1. W = 190 J, Q = 1000 J.\n2. η = W/Q = 19%.\n3. Result 19%.", "topic": "thermodynamics"}
{"answer": "The leaving current is 14 A.", "choices": null, "id": "eng_0135", "kind": "worked_example", "lang": "en", "question": "Currents 2 A and 12 A enter a node. What current leaves?", "steps": ["I1 = 2 A, I2 = 12 A.", "I3 = 14 A.", "Result 14 A."], "subject": "engineering", "text": "Answer: 14 A.\nSteps:\n1. I1 = 2 A, I2 = 12 A.\n2. I3 = 14 A.\n3. Result 14 A.", "topic": "circuits"}
{"answer": "Steady-state error is 20%.", "choices": {"A": "22%", "B": "18%", "C": "25%", "D": "20%"}, "id": "eng_0136", "kind": "multiple_choice", "lang": "en", "question": "Type-0 loop has position constant Kp = 4. What is step steady-state error?", "steps": ["Kp = 4 (dimensionless).", "ess = 100/5 = 20%.", "Select option D (20%)."], "subject": "engineering", "text": "Answer: 20%.\nSteps:\n1. Kp = 4 (dimensionless).\n2. ess = 100/5 = 20%.\n3. Select option D (20%).\nAnswer: (D)", "topic": "control"}
{"answer": "Tlak u dna je 107.91 kPa.", "choices": null, "id": "eng_0137", "kind": "worked_example", "lang": "cs", "question": "Sloupec klidné vody 11 m. Jaký je tlak u dna?", "steps": ["ρ = 1000 kg/m³, h = 11 m.", "p = ρgh = 107.91 kPa.", "Result 107.91 kPa."], "subject": "engineering", "text": "Answer: 107.91 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 11 m.\n2. p = ρgh = 107.91 kPa.\n3. Result 107.91 kPa.", "topic": "fluids"}
{"answer": "The modulus is 81.8 GPa.", "choices": null, "id": "eng_0138", "kind": "worked_example", "lang": "en", "question": "Composite with fibre fraction 0.4 (Ef = 200 GPa, Em = 3 GPa). What is the modulus?", "steps": ["Vf = 0.4, Ef = 200 GPa.", "E = VfEf+VmEm = 81.8 GPa.", "Result 81.8 GPa."], "subject": "engineering", "text": "Answer: 81.8 GPa.\nSteps:\n1. Vf = 0.4, Ef = 200 GPa.\n2. E = VfEf+VmEm = 81.8 GPa.\n3. Result 81.8 GPa.", "topic": "materials"}
{"answer": "Newton's third law says every action has an equal and opposite reaction.", "choices": null, "id": "eng_0139", "kind": "concept", "lang": "en", "question": "What is Newton's third law?", "steps": ["Push object.", "Object pushes back.", "Pair acts."], "subject": "engineering", "text": "Answer: Equal opposite reaction.\nSteps:\n1. Push object.\n2. Object pushes back.\n3. Pair acts.", "topic": "statics"}
{"answer": "The new volume is 8 m³.", "choices": null, "id": "eng_0140", "kind": "worked_example", "lang": "en", "question": "Gas 3 m³ at 300 K warms to 800 K at constant pressure. What is the new volume?", "steps": ["V1 = 3 m³, T1 = 300 K.", "V2 = 3×800/300 = 8 m³.", "Result 8 m³."], "subject": "engineering", "text": "Answer: 8 m³.\nSteps:\n1. V1 = 3 m³, T1 = 300 K.\n2. V2 = 3×800/300 = 8 m³.\n3. Result 8 m³.", "topic": "thermodynamics"}
{"answer": "The voltage is 144 V.", "choices": {"A": "132 V", "B": "156 V", "C": "144 V", "D": "168 V"}, "id": "eng_0141", "kind": "multiple_choice", "lang": "en", "question": "Current 12 A flows through 12 Ω. What is the voltage?", "steps": ["I = 12 A, R = 12 Ω.", "V = IR = 144 V.", "Select option C (144 V)."], "subject": "engineering", "text": "Answer: 144 V.\nSteps:\n1. I = 12 A, R = 12 Ω.\n2. V = IR = 144 V.\n3. Select option C (144 V).\nAnswer: (C)", "topic": "circuits"}
{"answer": "The controller output is 90 V.", "choices": {"A": "90 V", "B": "80 V", "C": "100 V", "D": "110 V"}, "id": "eng_0142", "kind": "multiple_choice", "lang": "en", "question": "P-controller with Kp = 2 V/V sees error 45 units. What is the output?", "steps": ["Kp = 2 V/V, e = 45 units.", "u = Kp·e = 90 V.", "Select option A (90 V)."], "subject": "engineering", "text": "Answer: 90 V.\nSteps:\n1. Kp = 2 V/V, e = 45 units.\n2. u = Kp·e = 90 V.\n3. Select option A (90 V).\nAnswer: (A)", "topic": "control"}
{"answer": "The buoyant force is 107910 N.", "choices": {"A": "98100 N", "B": "107910 N", "C": "117720 N", "D": "127530 N"}, "id": "eng_0143", "kind": "multiple_choice", "lang": "en", "question": "A hull displaces 11 m³ of water. What is the buoyant force?", "steps": ["V = 11 m³, ρ = 1000 kg/m³.", "F = ρgV = 107910 N.", "Select option B (107910 N)."], "subject": "engineering", "text": "Answer: 107910 N.\nSteps:\n1. V = 11 m³, ρ = 1000 kg/m³.\n2. F = ρgV = 107910 N.\n3. Select option B (107910 N).\nAnswer: (B)", "topic": "fluids"}
{"answer": "The shear stress is 56 MPa.", "choices": null, "id": "eng_0144", "kind": "worked_example", "lang": "en", "question": "Shear force 28 kN on 500 mm² section. What is the shear stress?", "steps": ["F = 28 kN, A = 500 mm².", "τ = F/A = 56 MPa.", "Result 56 MPa."], "subject": "engineering", "text": "Answer: 56 MPa.\nSteps:\n1. F = 28 kN, A = 500 mm².\n2. τ = F/A = 56 MPa.\n3. Result 56 MPa.", "topic": "materials"}
{"answer": "Max friction is 700 N.", "choices": {"A": "700 N", "B": "750 N", "C": "650 N", "D": "800 N"}, "id": "eng_0145", "kind": "multiple_choice", "lang": "en", "question": "Normal force 1400 N, friction coefficient 0.5. What is max friction?", "steps": ["μ = 0.5 (dimensionless), N = 1400 N.", "F = μN = 700 N.", "Select option A (700 N)."], "subject": "engineering", "text": "Answer: 700 N.\nSteps:\n1. μ = 0.5 (dimensionless), N = 1400 N.\n2. F = μN = 700 N.\n3. Select option A (700 N).\nAnswer: (A)", "topic": "statics"}
{"answer": "The pressure is 1300 kPa.", "choices": null, "id": "eng_0146", "kind": "worked_example", "lang": "en", "question": "Gas 13 m³ at 100 kPa is squeezed to 1 m³ at constant temperature. What is the pressure?", "steps": ["p1 = 100 kPa, V1 = 13 m³.", "p2 = 100×13 = 1300 kPa.", "Result 1300 kPa."], "subject": "engineering", "text": "Answer: 1300 kPa.\nSteps:\n1. p1 = 100 kPa, V1 = 13 m³.\n2. p2 = 100×13 = 1300 kPa.\n3. Result 1300 kPa.", "topic": "thermodynamics"}
{"answer": "Příkon je 2990 W.", "choices": {"A": "2760 W", "B": "3220 W", "C": "3105 W", "D": "2990 W"}, "id": "eng_0147", "kind": "multiple_choice", "lang": "cs", "question": "Spotřebič na 230 V odebírá 13 A. Jaký je jeho příkon?", "steps": ["V = 230 V, I = 13 A.", "P = VI = 2990 W.", "Vyber možnost D (2990 W)."], "subject": "engineering", "text": "Answer: 2990 W.\nSteps:\n1. V = 230 V, I = 13 A.\n2. P = VI = 2990 W.\n3. Vyber možnost D (2990 W).\nAnswer: (D)", "topic": "circuits"}
{"answer": "Integrační výstup je 45 V.", "choices": null, "id": "eng_0148", "kind": "worked_example", "lang": "cs", "question": "Chyba 2 jednotky trvá 45 s při Ki = 0,5 1/s. Jaký je integrační výstup?", "steps": ["e = 2 units, t = 45 s.", "u = 0.5×2×45 = 45 V.", "Result 45 V."], "subject": "engineering", "text": "Answer: 45 V.\nSteps:\n1. e = 2 units, t = 45 s.\n2. u = 0.5×2×45 = 45 V.\n3. Result 45 V.", "topic": "control"}
{"answer": "Laminar flow is smooth layered motion while turbulent flow is chaotic mixing.", "choices": null, "id": "eng_0149", "kind": "concept", "lang": "en", "question": "How do laminar and turbulent flow differ?", "steps": ["Low Re calm.", "High Re wild.", "Drag differs."], "subject": "engineering", "text": "Answer: Smooth versus chaotic.\nSteps:\n1. Low Re calm.\n2. High Re wild.\n3. Drag differs.", "topic": "fluids"}
{"answer": "Thermal stress is 180 MPa.", "choices": null, "id": "eng_0150", "kind": "worked_example", "lang": "en", "question": "Steel bar (E = 200 GPa, α = 12e-6/K) cools 75 K constrained. What thermal stress arises?", "steps": ["E = 200 GPa, ΔT = 75 K.", "σ = EαΔT = 180 MPa.", "Result 180 MPa."], "subject": "engineering", "text": "Answer: 180 MPa.\nSteps:\n1. E = 200 GPa, ΔT = 75 K.\n2. σ = EαΔT = 180 MPa.\n3. Result 180 MPa.", "topic": "materials"}
{"answer": "The net moment is 1100 N·m clockwise.", "choices": null, "id": "eng_0151", "kind": "worked_example", "lang": "en", "question": "500 N at 4 m clockwise, 300 N at 3 m counter-clockwise. What is the net moment?", "steps": ["M1 = 500×4 = 2000 N·m.", "M2 = 300×3 = 900 N·m.", "Net 1100 N·m."], "subject": "engineering", "text": "Answer: 1100 N·m.\nSteps:\n1. M1 = 500×4 = 2000 N·m.\n2. M2 = 300×3 = 900 N·m.\n3. Net 1100 N·m.", "topic": "statics"}
{"answer": "Entropy measures energy dispersal and disorder, rising in irreversible processes.", "choices": null, "id": "eng_0152", "kind": "concept", "lang": "en", "question": "What is entropy?", "steps": ["Joules per K.", "Always grows.", "Limits engines."], "subject": "engineering", "text": "Answer: Dispersal measure.\nSteps:\n1. Joules per K.\n2. Always grows.\n3. Limits engines.", "topic": "thermodynamics"}
{"answer": "The stored charge is 6000 μC.", "choices": null, "id": "eng_0153", "kind": "worked_example", "lang": "en", "question": "Capacitor 600 μF charged to 10 V. What charge is stored?", "steps": ["C = 600 μF, V = 10 V.", "Q = CV = 6000 μC.", "Result 6000 μC."], "subject": "engineering", "text": "Answer: 6000 μC.\nSteps:\n1. C = 600 μF, V = 10 V.\n2. Q = CV = 6000 μC.\n3. Result 6000 μC.", "topic": "circuits"}
{"answer": "A time constant is the time to reach 63 percent of a step response.", "choices": null, "id": "eng_0154", "kind": "concept", "lang": "en", "question": "What is a time constant?", "steps": ["Tau in s.", "One tau mark.", "Speed gauge."], "subject": "engineering", "text": "Answer: 63 percent time.\nSteps:\n1. Tau in s.\n2. One tau mark.\n3. Speed gauge.", "topic": "control"}
{"answer": "Hydrostatický tlak roste s hloubkou jako ró gé há.", "choices": null, "id": "eng_0155", "kind": "concept", "lang": "cs", "question": "Co je hydrostatický tlak?", "steps": ["Hloubka v m.", "Krát ró gé.", "kPa rozdíl."], "subject": "engineering", "text": "Answer: Ró gé há.\nSteps:\n1. Hloubka v m.\n2. Krát ró gé.\n3. kPa rozdíl.", "topic": "fluids"}
{"answer": "The strain is 700 microstrain.", "choices": {"A": "600 microstrain", "B": "800 microstrain", "C": "700 microstrain", "D": "900 microstrain"}, "id": "eng_0156", "kind": "multiple_choice", "lang": "en", "question": "Bar 1000 mm stretches 0.7 mm. What is the strain?", "steps": ["ΔL = 0.7 mm, L = 1000 mm.", "ε = 700 microstrain.", "Select option C (700 microstrain)."], "subject": "engineering", "text": "Answer: 700 microstrain.\nSteps:\n1. ΔL = 0.7 mm, L = 1000 mm.\n2. ε = 700 microstrain.\n3. Select option C (700 microstrain).\nAnswer: (C)", "topic": "materials"}
{"answer": "Equilibrium needs zero net force and zero net moment on a body.", "choices": null, "id": "eng_0157", "kind": "concept", "lang": "en", "question": "What are equilibrium conditions?", "steps": ["Sum Fx zero.", "Sum Fy zero.", "Sum M zero."], "subject": "engineering", "text": "Answer: Zero force and moment.\nSteps:\n1. Sum Fx zero.\n2. Sum Fy zero.\n3. Sum M zero.", "topic": "statics"}
{"answer": "The ideal gas law links pressure, volume, and temperature as pV equals nRT.", "choices": null, "id": "eng_0158", "kind": "concept", "lang": "en", "question": "What is the ideal gas law?", "steps": ["p in Pa.", "V in m³.", "T in K."], "subject": "engineering", "text": "Answer: pV equals nRT.\nSteps:\n1. p in Pa.\n2. V in m³.\n3. T in K.", "topic": "thermodynamics"}
{"answer": "The power lost is 240 W.", "choices": null, "id": "eng_0159", "kind": "worked_example", "lang": "en", "question": "Current 2 A through 60 Ω. What power is lost?", "steps": ["I = 2 A, R = 60 Ω.", "P = I²R = 240 W.", "Result 240 W."], "subject": "engineering", "text": "Answer: 240 W.\nSteps:\n1. I = 2 A, R = 60 Ω.\n2. P = I²R = 240 W.\n3. Result 240 W.", "topic": "circuits"}
{"answer": "The D output is 20 V.", "choices": null, "id": "eng_0160", "kind": "worked_example", "lang": "en", "question": "Error jumps 0 to 100 units in 2 s with Kd = 0.4 s. What is the D output?", "steps": ["Slope = 100/2 units/s.", "u = 0.4×slope = 20 V.", "Result 20 V."], "subject": "engineering", "text": "Answer: 20 V.\nSteps:\n1. Slope = 100/2 units/s.\n2. u = 0.4×slope = 20 V.\n3. Result 20 V.", "topic": "control"}
{"answer": "The exit velocity is 10 m/s.", "choices": null, "id": "eng_0161", "kind": "worked_example", "lang": "en", "question": "Tank head 5 m (take g = 10 m/s²). What is the Torricelli velocity?", "steps": ["h = 5 m, g = 10 m/s².", "v = √(2gh) = 10 m/s.", "Result 10 m/s."], "subject": "engineering", "text": "Answer: 10 m/s.\nSteps:\n1. h = 5 m, g = 10 m/s².\n2. v = √(2gh) = 10 m/s.\n3. Result 10 m/s.", "topic": "fluids"}
{"answer": "Transverse strain is -1140 microstrain.", "choices": null, "id": "eng_0162", "kind": "worked_example", "lang": "en", "question": "Bar stretches 3800 microstrain, Poisson ratio 0.3. What is transverse strain?", "steps": ["εa = 3800 microstrain, ν = 0.3.", "εt = −νεa = -1140 microstrain.", "Result -1140 microstrain."], "subject": "engineering", "text": "Answer: -1140 microstrain.\nSteps:\n1. εa = 3800 microstrain, ν = 0.3.\n2. εt = −νεa = -1140 microstrain.\n3. Result -1140 microstrain.", "topic": "materials"}
{"answer": "A moment is force times perpendicular distance, tending to rotate, in newton metres.", "choices": null, "id": "eng_0163", "kind": "concept", "lang": "en", "question": "What is a moment?", "steps": ["Force in N.", "Arm in m.", "M in N·m."], "subject": "engineering", "text": "Answer: Force times distance.\nSteps:\n1. Force in N.\n2. Arm in m.\n3. M in N·m.", "topic": "statics"}
{"answer": "The temperature is 147 °C.", "choices": null, "id": "eng_0164", "kind": "worked_example", "lang": "en", "question": "Temperature is 420 K. What is it in Celsius?", "steps": ["T = 420 K.", "C = 420 − 273 = 147 °C.", "Result 147 °C."], "subject": "engineering", "text": "Answer: 147 °C.\nSteps:\n1. T = 420 K.\n2. C = 420 − 273 = 147 °C.\n3. Result 147 °C.", "topic": "thermodynamics"}
{"answer": "Proud je 14 A.", "choices": null, "id": "eng_0165", "kind": "worked_example", "lang": "cs", "question": "Napětí 84 V na 6 Ω. Jaký je proud?", "steps": ["V = 84 V, R = 6 Ω.", "I = V/R = 14 A.", "Result 14 A."], "subject": "engineering", "text": "Answer: 14 A.\nSteps:\n1. V = 84 V, R = 6 Ω.\n2. I = V/R = 14 A.\n3. Result 14 A.", "topic": "circuits"}
{"answer": "The total gain is 24.", "choices": {"A": "22 (dimensionless)", "B": "24 (dimensionless)", "C": "26 (dimensionless)", "D": "28 (dimensionless)"}, "id": "eng_0166", "kind": "multiple_choice", "lang": "en", "question": "Two series blocks have gains 2 and 12. What is the total gain?", "steps": ["K1 = 2, K2 = 12 (dimensionless).", "K = 24 (dimensionless).", "Select option B (24 (dimensionless))."], "subject": "engineering", "text": "Answer: 24 (dimensionless).\nSteps:\n1. K1 = 2, K2 = 12 (dimensionless).\n2. K = 24 (dimensionless).\n3. Select option B (24 (dimensionless)).\nAnswer: (B)", "topic": "control"}
{"answer": "The Reynolds number is the dimensionless ratio of inertial to viscous forces.", "choices": null, "id": "eng_0167", "kind": "concept", "lang": "en", "question": "What is the Reynolds number?", "steps": ["Rho v D.", "Over mu.", "Below 2300 calm."], "subject": "engineering", "text": "Answer: Inertia over viscous.\nSteps:\n1. Rho v D.\n2. Over mu.\n3. Below 2300 calm.", "topic": "fluids"}
{"answer": "Estimated strength is 1400 MPa.", "choices": null, "id": "eng_0168", "kind": "worked_example", "lang": "en", "question": "Steel hardness 400 HB. Estimate tensile strength (UTS ≈ 3.5·HB).", "steps": ["Hardness = 400 HB.", "UTS ≈ 3.5×400 = 1400 MPa.", "Result 1400 MPa."], "subject": "engineering", "text": "Answer: 1400 MPa.\nSteps:\n1. Hardness = 400 HB.\n2. UTS ≈ 3.5×400 = 1400 MPa.\n3. Result 1400 MPa.", "topic": "materials"}
{"answer": "The moment arm is 26 m.", "choices": null, "id": "eng_0169", "kind": "worked_example", "lang": "en", "question": "Moment 3900 N·m comes from 150 N force. What is the moment arm?", "steps": ["M = 3900 N·m, F = 150 N.", "d = M/F = 26 m.", "Result 26 m."], "subject": "engineering", "text": "Answer: 26 m.\nSteps:\n1. M = 3900 N·m, F = 150 N.\n2. d = M/F = 26 m.\n3. Result 26 m.", "topic": "statics"}
{"answer": "The temperature is 343 K.", "choices": {"A": "338 K", "B": "348 K", "C": "343 K", "D": "353 K"}, "id": "eng_0170", "kind": "multiple_choice", "lang": "en", "question": "Temperature is 70 °C. What is it in kelvin?", "steps": ["T = 70 °C.", "K = 70 + 273 = 343 K.", "Select option C (343 K)."], "subject": "engineering", "text": "Answer: 343 K.\nSteps:\n1. T = 70 °C.\n2. K = 70 + 273 = 343 K.\n3. Select option C (343 K).\nAnswer: (C)", "topic": "thermodynamics"}
{"answer": "Total resistance is 1500 Ω.", "choices": {"A": "1500 Ω", "B": "1400 Ω", "C": "1600 Ω", "D": "1550 Ω"}, "id": "eng_0171", "kind": "multiple_choice", "lang": "en", "question": "Resistors 100 Ω and 1400 Ω in series. What is total resistance?", "steps": ["R1 = 100 Ω, R2 = 1400 Ω.", "R = 1500 Ω.", "Select option A (1500 Ω)."], "subject": "engineering", "text": "Answer: 1500 Ω.\nSteps:\n1. R1 = 100 Ω, R2 = 1400 Ω.\n2. R = 1500 Ω.\n3. Select option A (1500 Ω).\nAnswer: (A)", "topic": "circuits"}
{"answer": "The closed-loop gain is 0.9.", "choices": null, "id": "eng_0172", "kind": "worked_example", "lang": "en", "question": "Unity feedback loop, forward gain 9. What is the closed-loop gain?", "steps": ["K = 9 (dimensionless).", "T = K/(1+K) = 0.9 (dimensionless).", "Result 0.9 (dimensionless)."], "subject": "engineering", "text": "Answer: 0.9 (dimensionless).\nSteps:\n1. K = 9 (dimensionless).\n2. T = K/(1+K) = 0.9 (dimensionless).\n3. Result 0.9 (dimensionless).", "topic": "control"}
{"answer": "The mass flow is 10 kg/s.", "choices": null, "id": "eng_0173", "kind": "worked_example", "lang": "en", "question": "Water flows 10 L/s. What is the mass flow in kg/s?", "steps": ["Q = 10 L/s, ρ = 1000 kg/m³.", "ṁ = 10 kg/s.", "Result 10 kg/s."], "subject": "engineering", "text": "Answer: 10 kg/s.\nSteps:\n1. Q = 10 L/s, ρ = 1000 kg/m³.\n2. ṁ = 10 kg/s.\n3. Result 10 kg/s.", "topic": "fluids"}
{"answer": "The stress is 90 MPa.", "choices": {"A": "80 MPa", "B": "100 MPa", "C": "110 MPa", "D": "90 MPa"}, "id": "eng_0174", "kind": "multiple_choice", "lang": "en", "question": "Steel (E = 200 GPa) at strain 450 microstrain. What is the stress?", "steps": ["E = 200 GPa, ε = 450 microstrain.", "σ = Eε = 90 MPa.", "Select option D (90 MPa)."], "subject": "engineering", "text": "Answer: 90 MPa.\nSteps:\n1. E = 200 GPa, ε = 450 microstrain.\n2. σ = Eε = 90 MPa.\n3. Select option D (90 MPa).\nAnswer: (D)", "topic": "materials"}
{"answer": "The horizontal component is 420 N.", "choices": null, "id": "eng_0175", "kind": "worked_example", "lang": "en", "question": "Force 700 N pulls at a 3-4-5 angle. What is the horizontal component?", "steps": ["F = 700 N, cos = 3/5.", "Fx = 0.6×700 = 420 N.", "Result 420 N."], "subject": "engineering", "text": "Answer: 420 N.\nSteps:\n1. F = 700 N, cos = 3/5.\n2. Fx = 0.6×700 = 420 N.\n3. Result 420 N.", "topic": "statics"}
{"answer": "Specific heat is heat per unit mass and degree, in joules per kilogram kelvin.", "choices": null, "id": "eng_0176", "kind": "concept", "lang": "en", "question": "What is specific heat?", "steps": ["Mass in kg.", "Delta T in K.", "Q in J."], "subject": "engineering", "text": "Answer: Heat per kg K.\nSteps:\n1. Mass in kg.\n2. Delta T in K.\n3. Q in J.", "topic": "thermodynamics"}
{"answer": "Parallel resistors combine by reciprocal sum, lowering total resistance.", "choices": null, "id": "eng_0177", "kind": "concept", "lang": "en", "question": "How do parallel resistors combine?", "steps": ["Same voltage.", "Currents split.", "R drops."], "subject": "engineering", "text": "Answer: Reciprocal sum.\nSteps:\n1. Same voltage.\n2. Currents split.\n3. R drops.", "topic": "circuits"}
{"answer": "Settling time is how long output takes to stay within an error band.", "choices": null, "id": "eng_0178", "kind": "concept", "lang": "en", "question": "What is settling time?", "steps": ["2 percent band.", "About 4 tau.", "Wait done."], "subject": "engineering", "text": "Answer: Stay in band.\nSteps:\n1. 2 percent band.\n2. About 4 tau.\n3. Wait done.", "topic": "control"}
{"answer": "Gauge pressure is 117.72 kPa.", "choices": {"A": "112.72 kPa", "B": "122.72 kPa", "C": "117.72 kPa", "D": "127.72 kPa"}, "id": "eng_0179", "kind": "multiple_choice", "lang": "en", "question": "Water depth is 12 m. What is gauge pressure?", "steps": ["ρ = 1000 kg/m³, h = 12 m.", "p = ρgh = 117.72 kPa.", "Select option C (117.72 kPa)."], "subject": "engineering", "text": "Answer: 117.72 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 12 m.\n2. p = ρgh = 117.72 kPa.\n3. Select option C (117.72 kPa).\nAnswer: (C)", "topic": "fluids"}
{"answer": "Hookeův zákon říká, že napětí je úměrné deformaci v pružné oblasti.", "choices": null, "id": "eng_0180", "kind": "concept", "lang": "cs", "question": "Co je Hookeův zákon?", "steps": ["Sigma rovná E.", "Epsilon malé.", "Odtížení vrátí."], "subject": "engineering", "text": "Answer: Napětí drží deformaci.\nSteps:\n1. Sigma rovná E.\n2. Epsilon malé.\n3. Odtížení vrátí.", "topic": "materials"}
{"answer": "Rovnováha žádá nulovou sílu i nulový moment na těleso.", "choices": null, "id": "eng_0181", "kind": "concept", "lang": "cs", "question": "Co jsou podmínky rovnováhy?", "steps": ["Součet Fx nula.", "Součet Fy nula.", "Součet M nula."], "subject": "engineering", "text": "Answer: Nulová síla i moment.\nSteps:\n1. Součet Fx nula.\n2. Součet Fy nula.\n3. Součet M nula.", "topic": "statics"}
{"answer": "The work done is 320 kJ.", "choices": {"A": "300 kJ", "B": "340 kJ", "C": "360 kJ", "D": "320 kJ"}, "id": "eng_0182", "kind": "multiple_choice", "lang": "en", "question": "Gas expands at 200 kPa by 1.6 m³. What work is done?", "steps": ["p = 200 kPa, ΔV = 1.6 m³.", "W = pΔV = 320 kJ.", "Select option D (320 kJ)."], "subject": "engineering", "text": "Answer: 320 kJ.\nSteps:\n1. p = 200 kPa, ΔV = 1.6 m³.\n2. W = pΔV = 320 kJ.\n3. Select option D (320 kJ).\nAnswer: (D)", "topic": "thermodynamics"}
{"answer": "Odpor je 17 Ω.", "choices": null, "id": "eng_0183", "kind": "worked_example", "lang": "cs", "question": "Napětí 51 V žene 3 A. Jaký je odpor?", "steps": ["V = 51 V, I = 3 A.", "R = V/I = 17 Ω.", "Result 17 Ω."], "subject": "engineering", "text": "Answer: 17 Ω.\nSteps:\n1. V = 51 V, I = 3 A.\n2. R = V/I = 17 Ω.\n3. Result 17 Ω.", "topic": "circuits"}
{"answer": "The steady value is 55 units.", "choices": {"A": "50 units", "B": "60 units", "C": "55 units", "D": "65 units"}, "id": "eng_0184", "kind": "multiple_choice", "lang": "en", "question": "System K/(10s+1) with K = 55 gets a unit step. What is the steady value?", "steps": ["DC gain K = 55 (dimensionless).", "Step final = 55 units.", "Select option C (55 units)."], "subject": "engineering", "text": "Answer: 55 units.\nSteps:\n1. DC gain K = 55 (dimensionless).\n2. Step final = 55 units.\n3. Select option C (55 units).\nAnswer: (C)", "topic": "control"}
{"answer": "Dynamic pressure is 1815 Pa.", "choices": null, "id": "eng_0185", "kind": "worked_example", "lang": "en", "question": "Air (ρ = 1.2 kg/m³) moves 55 m/s. What is the dynamic pressure?", "steps": ["ρ = 1.2 kg/m³, v = 55 m/s.", "q = ½ρv² = 1815 Pa.", "Result 1815 Pa."], "subject": "engineering", "text": "Answer: 1815 Pa.\nSteps:\n1. ρ = 1.2 kg/m³, v = 55 m/s.\n2. q = ½ρv² = 1815 Pa.\n3. Result 1815 Pa.", "topic": "fluids"}
{"answer": "Ultimate tensile strength is the maximum engineering stress before necking.", "choices": null, "id": "eng_0186", "kind": "concept", "lang": "en", "question": "What is ultimate tensile strength?", "steps": ["Climb curve.", "Top breaks soon.", "MPa scale."], "subject": "engineering", "text": "Answer: Peak stress.\nSteps:\n1. Climb curve.\n2. Top breaks soon.\n3. MPa scale.", "topic": "materials"}
{"answer": "The vertical component is 600 N.", "choices": null, "id": "eng_0187", "kind": "worked_example", "lang": "en", "question": "Force 750 N pulls at a 3-4-5 angle. What is the vertical component?", "steps": ["F = 750 N, sin = 4/5.", "Fy = 0.8×750 = 600 N.", "Result 600 N."], "subject": "engineering", "text": "Answer: 600 N.\nSteps:\n1. F = 750 N, sin = 4/5.\n2. Fy = 0.8×750 = 600 N.\n3. Result 600 N.", "topic": "statics"}
{"answer": "Carnot efficiency is 70%.", "choices": {"A": "70%", "B": "75%", "C": "65%", "D": "80%"}, "id": "eng_0188", "kind": "multiple_choice", "lang": "en", "question": "Carnot engine between 300 K and 1000 K. What is its efficiency?", "steps": ["Tc = 300 K, Th = 1000 K.", "η = 1 − 300/1000 = 70%.", "Select option A (70%)."], "subject": "engineering", "text": "Answer: 70%.\nSteps:\n1. Tc = 300 K, Th = 1000 K.\n2. η = 1 − 300/1000 = 70%.\n3. Select option A (70%).\nAnswer: (A)", "topic": "thermodynamics"}
{"answer": "The tap voltage is 19 V.", "choices": null, "id": "eng_0189", "kind": "worked_example", "lang": "en", "question": "Divider with two 1000 Ω resistors fed 38 V. What is the tap voltage?", "steps": ["Vin = 38 V, halves.", "Vout = 19 V.", "Result 19 V."], "subject": "engineering", "text": "Answer: 19 V.\nSteps:\n1. Vin = 38 V, halves.\n2. Vout = 19 V.\n3. Result 19 V.", "topic": "circuits"}
{"answer": "Settling time is about 52 s.", "choices": {"A": "48 s", "B": "56 s", "C": "60 s", "D": "52 s"}, "id": "eng_0190", "kind": "multiple_choice", "lang": "en", "question": "First-order system has time constant 13 s. What is 2% settling time?", "steps": ["τ = 13 s.", "ts ≈ 4τ = 52 s.", "Select option D (52 s)."], "subject": "engineering", "text": "Answer: 52 s.\nSteps:\n1. τ = 13 s.\n2. ts ≈ 4τ = 52 s.\n3. Select option D (52 s).\nAnswer: (D)", "topic": "control"}
{"answer": "Outlet velocity is 26 m/s.", "choices": {"A": "24 m/s", "B": "28 m/s", "C": "30 m/s", "D": "26 m/s"}, "id": "eng_0191", "kind": "multiple_choice", "lang": "en", "question": "Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 13 m/s. What is outlet velocity?", "steps": ["A1v1 = 0.02×13 m³/s.", "v2 = 26 m/s.", "Select option D (26 m/s)."], "subject": "engineering", "text": "Answer: 26 m/s.\nSteps:\n1. A1v1 = 0.02×13 m³/s.\n2. v2 = 26 m/s.\n3. Select option D (26 m/s).\nAnswer: (D)", "topic": "fluids"}
{"answer": "Elongation is 5 mm.", "choices": {"A": "5 mm", "B": "6 mm", "C": "4 mm", "D": "7 mm"}, "id": "eng_0192", "kind": "multiple_choice", "lang": "en", "question": "Force 50 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation?", "steps": ["F = 50 kN, L = 2 m.", "ΔL = FL/AE = 5 mm.", "Select option A (5 mm)."], "subject": "engineering", "text": "Answer: 5 mm.\nSteps:\n1. F = 50 kN, L = 2 m.\n2. ΔL = FL/AE = 5 mm.\n3. Select option A (5 mm).\nAnswer: (A)", "topic": "materials"}
{"answer": "A couple is two equal opposite parallel forces giving pure moment without net force.", "choices": null, "id": "eng_0193", "kind": "concept", "lang": "en", "question": "What is a couple?", "steps": ["Equal forces.", "Opposite sense.", "No net force."], "subject": "engineering", "text": "Answer: Pure moment.\nSteps:\n1. Equal forces.\n2. Opposite sense.\n3. No net force.", "topic": "statics"}
{"answer": "Enthalpy is internal energy plus pressure-volume work, handy for flow processes.", "choices": null, "id": "eng_0194", "kind": "concept", "lang": "en", "question": "What is enthalpy?", "steps": ["Internal plus.", "Flow work.", "kJ per kg."], "subject": "engineering", "text": "Answer: U plus pV.\nSteps:\n1. Internal plus.\n2. Flow work.\n3. kJ per kg.", "topic": "thermodynamics"}
{"answer": "The equivalent is 75 Ω.", "choices": {"A": "80 Ω", "B": "75 Ω", "C": "70 Ω", "D": "85 Ω"}, "id": "eng_0195", "kind": "multiple_choice", "lang": "en", "question": "Two 150 Ω resistors in parallel. What is the equivalent?", "steps": ["R = 150 Ω each.", "Req = R/2 = 75 Ω.", "Select option B (75 Ω)."], "subject": "engineering", "text": "Answer: 75 Ω.\nSteps:\n1. R = 150 Ω each.\n2. Req = R/2 = 75 Ω.\n3. Select option B (75 Ω).\nAnswer: (B)", "topic": "circuits"}
{"answer": "Overshoot is the peak excursion past the final value in percent.", "choices": null, "id": "eng_0196", "kind": "concept", "lang": "en", "question": "What is overshoot?", "steps": ["Percent peak.", "Damping sets.", "Less is calm."], "subject": "engineering", "text": "Answer: Peak past final.\nSteps:\n1. Percent peak.\n2. Damping sets.\n3. Less is calm.", "topic": "control"}
{"answer": "The volume is 26 m³.", "choices": null, "id": "eng_0197", "kind": "worked_example", "lang": "en", "question": "Tank base area 2 m², depth 13 m. What is the water volume?", "steps": ["A = 2 m², h = 13 m.", "V = Ah = 26 m³.", "Result 26 m³."], "subject": "engineering", "text": "Answer: 26 m³.\nSteps:\n1. A = 2 m², h = 13 m.\n2. V = Ah = 26 m³.\n3. Result 26 m³.", "topic": "fluids"}
{"answer": "The factor of safety is 3.", "choices": {"A": "3.5 (dimensionless)", "B": "3 (dimensionless)", "C": "2.5 (dimensionless)", "D": "4 (dimensionless)"}, "id": "eng_0198", "kind": "multiple_choice", "lang": "en", "question": "Yield 300 MPa, working stress 100 MPa. What is the factor of safety?", "steps": ["σy = 300 MPa, σw = 100 MPa.", "n = 3 (dimensionless).", "Select option B (3 (dimensionless))."], "subject": "engineering", "text": "Answer: 3 (dimensionless).\nSteps:\n1. σy = 300 MPa, σw = 100 MPa.\n2. n = 3 (dimensionless).\n3. Select option B (3 (dimensionless)).\nAnswer: (B)", "topic": "materials"}
{"answer": "A resultant is the single force replacing a system with the same effect.", "choices": null, "id": "eng_0199", "kind": "concept", "lang": "en", "question": "What is a resultant force?", "steps": ["Add vectors.", "Same effect.", "One force."], "subject": "engineering", "text": "Answer: Single replacement.\nSteps:\n1. Add vectors.\n2. Same effect.\n3. One force.", "topic": "statics"}
{"answer": "The specific volume is 7 m³/kg.", "choices": null, "id": "eng_0200", "kind": "worked_example", "lang": "en", "question": "Gas fills 28 m³ with mass 4 kg. What is the specific volume?", "steps": ["V = 28 m³, m = 4 kg.", "v = V/m = 7 m³/kg.", "Result 7 m³/kg."], "subject": "engineering", "text": "Answer: 7 m³/kg.\nSteps:\n1. V = 28 m³, m = 4 kg.\n2. v = V/m = 7 m³/kg.\n3. Result 7 m³/kg.", "topic": "thermodynamics"}
{"answer": "Spotřeba je 1600 Wh.", "choices": {"A": "1500 Wh", "B": "1700 Wh", "C": "1600 Wh", "D": "1650 Wh"}, "id": "eng_0201", "kind": "multiple_choice", "lang": "cs", "question": "Žárovka 800 W svítí 2 h. Kolik energie spotřebuje?", "steps": ["P = 800 W, t = 2 h.", "E = Pt = 1600 Wh.", "Vyber možnost C (1600 Wh)."], "subject": "engineering", "text": "Answer: 1600 Wh.\nSteps:\n1. P = 800 W, t = 2 h.\n2. E = Pt = 1600 Wh.\n3. Vyber možnost C (1600 Wh).\nAnswer: (C)", "topic": "circuits"}
{"answer": "A transfer function is output over input in Laplace form for linear systems.", "choices": null, "id": "eng_0202", "kind": "concept", "lang": "en", "question": "What is a transfer function?", "steps": ["Laplace s.", "Gain plus dynamics.", "Blocks multiply."], "subject": "engineering", "text": "Answer: Output over input.\nSteps:\n1. Laplace s.\n2. Gain plus dynamics.\n3. Blocks multiply.", "topic": "control"}
{"answer": "The flow rate is 28 L/s.", "choices": {"A": "28 L/s", "B": "26 L/s", "C": "30 L/s", "D": "32 L/s"}, "id": "eng_0203", "kind": "multiple_choice", "lang": "en", "question": "Pipe area 20 cm², velocity 14 m/s. What is flow in litres per second?", "steps": ["A = 20 cm², v = 14 m/s.", "Q = Av = 28 L/s.", "Select option A (28 L/s)."], "subject": "engineering", "text": "Answer: 28 L/s.\nSteps:\n1. A = 20 cm², v = 14 m/s.\n2. Q = Av = 28 L/s.\n3. Select option A (28 L/s).\nAnswer: (A)", "topic": "fluids"}
{"answer": "The stress is 120 MPa.", "choices": {"A": "110 MPa", "B": "130 MPa", "C": "120 MPa", "D": "140 MPa"}, "id": "eng_0204", "kind": "multiple_choice", "lang": "en", "question": "Tensile force 12 kN on 100 mm² bar. What is the stress?", "steps": ["F = 12 kN, A = 100 mm².", "σ = F/A = 120 MPa.", "Select option C (120 MPa)."], "subject": "engineering", "text": "Answer: 120 MPa.\nSteps:\n1. F = 12 kN, A = 100 mm².\n2. σ = F/A = 120 MPa.\n3. Select option C (120 MPa).\nAnswer: (C)", "topic": "materials"}
{"answer": "The reaction at B is 1600 N.", "choices": null, "id": "eng_0205", "kind": "worked_example", "lang": "en", "question": "Beam 6 m, load 2400 N at 4 m from A. What is reaction at B?", "steps": ["F = 2400 N, span 6 m.", "RB = 2400×4/6 = 1600 N.", "Result 1600 N."], "subject": "engineering", "text": "Answer: 1600 N.\nSteps:\n1. F = 2400 N, span 6 m.\n2. RB = 2400×4/6 = 1600 N.\n3. Result 1600 N.", "topic": "statics"}
{"answer": "Potřebné teplo je 150.48 kJ.", "choices": {"A": "160.48 kJ", "B": "150.48 kJ", "C": "140.48 kJ", "D": "170.48 kJ"}, "id": "eng_0206", "kind": "multiple_choice", "lang": "cs", "question": "2 kg vody se ohřejí o 18 K (c = 4,18 kJ/(kg·K)). Kolik tepla?", "steps": ["m = 2 kg, ΔT = 18 K.", "Q = mcΔT = 150.48 kJ.", "Vyber možnost B (150.48 kJ)."], "subject": "engineering", "text": "Answer: 150.48 kJ.\nSteps:\n1. m = 2 kg, ΔT = 18 K.\n2. Q = mcΔT = 150.48 kJ.\n3. Vyber možnost B (150.48 kJ).\nAnswer: (B)", "topic": "thermodynamics"}
{"answer": "Electric power is voltage times current, measured in watts.", "choices": null, "id": "eng_0207", "kind": "concept", "lang": "en", "question": "What is electric power?", "steps": ["Volts times amps.", "Watts out.", "Heat or work."], "subject": "engineering", "text": "Answer: V times I.\nSteps:\n1. Volts times amps.\n2. Watts out.\n3. Heat or work.", "topic": "circuits"}
{"answer": "Steady-state error is 5%.", "choices": {"A": "5%", "B": "7%", "C": "3%", "D": "10%"}, "id": "eng_0208", "kind": "multiple_choice", "lang": "en", "question": "Type-0 loop has position constant Kp = 19. What is step steady-state error?", "steps": ["Kp = 19 (dimensionless).", "ess = 100/20 = 5%.", "Select option A (5%)."], "subject": "engineering", "text": "Answer: 5%.\nSteps:\n1. Kp = 19 (dimensionless).\n2. ess = 100/20 = 5%.\n3. Select option A (5%).\nAnswer: (A)", "topic": "control"}
{"answer": "Hydraulický výkon je 3139.2 W.", "choices": null, "id": "eng_0209", "kind": "worked_example", "lang": "cs", "question": "Čerpadlo zvedá 0,02 m³/s vody o 16 m. Jaký hydraulický výkon je třeba?", "steps": ["Q = 0.02 m³/s, H = 16 m.", "P = ρgQH = 3139.2 W.", "Result 3139.2 W."], "subject": "engineering", "text": "Answer: 3139.2 W.\nSteps:\n1. Q = 0.02 m³/s, H = 16 m.\n2. P = ρgQH = 3139.2 W.\n3. Result 3139.2 W.", "topic": "fluids"}
{"answer": "The mass is 133.45 kg.", "choices": null, "id": "eng_0210", "kind": "worked_example", "lang": "en", "question": "Steel part volume 0.017 m³ (ρ = 7850 kg/m³). What is its mass?", "steps": ["V = 0.017 m³, ρ = 7850 kg/m³.", "m = ρV = 133.45 kg.", "Result 133.45 kg."], "subject": "engineering", "text": "Answer: 133.45 kg.\nSteps:\n1. V = 0.017 m³, ρ = 7850 kg/m³.\n2. m = ρV = 133.45 kg.\n3. Result 133.45 kg.", "topic": "materials"}
{"answer": "Moment je síla krát kolmá vzdálenost, jednotka newtonmetr.", "choices": null, "id": "eng_0211", "kind": "concept", "lang": "cs", "question": "Co je moment síly?", "steps": ["Síla v N.", "Rameno v m.", "Moment v N·m."], "subject": "engineering", "text": "Answer: Síla krát rameno.\nSteps:\n1. Síla v N.\n2. Rameno v m.\n3. Moment v N·m.", "topic": "statics"}
{"answer": "The Carnot cycle is the ideal reversible engine setting maximum efficiency between temperatures.", "choices": null, "id": "eng_0212", "kind": "concept", "lang": "en", "question": "What is the Carnot cycle?", "steps": ["Two isotherms.", "Two adiabats.", "Sets limit."], "subject": "engineering", "text": "Answer: Ideal max engine.\nSteps:\n1. Two isotherms.\n2. Two adiabats.\n3. Sets limit.", "topic": "thermodynamics"}
{"answer": "The leaving current is 20 A.", "choices": null, "id": "eng_0213", "kind": "worked_example", "lang": "en", "question": "Currents 2 A and 18 A enter a node. What current leaves?", "steps": ["I1 = 2 A, I2 = 18 A.", "I3 = 20 A.", "Result 20 A."], "subject": "engineering", "text": "Answer: 20 A.\nSteps:\n1. I1 = 2 A, I2 = 18 A.\n2. I3 = 20 A.\n3. Result 20 A.", "topic": "circuits"}
{"answer": "The error is 65 units.", "choices": null, "id": "eng_0214", "kind": "worked_example", "lang": "en", "question": "Setpoint 650 units, measurement 585 units. What is the error?", "steps": ["r = 650 units, y = 585 units.", "e = r−y = 65 units.", "Result 65 units."], "subject": "engineering", "text": "Answer: 65 units.\nSteps:\n1. r = 650 units, y = 585 units.\n2. e = r−y = 65 units.\n3. Result 65 units.", "topic": "control"}
{"answer": "Archimédův zákon říká, že vztlak je tíha vytlačené kapaliny.", "choices": null, "id": "eng_0215", "kind": "concept", "lang": "cs", "question": "Co je Archimédův zákon?", "steps": ["Objem ponořen.", "Krát ró gé.", "Lehké plave."], "subject": "engineering", "text": "Answer: Tíha vytlačeného.\nSteps:\n1. Objem ponořen.\n2. Krát ró gé.\n3. Lehké plave.", "topic": "fluids"}
{"answer": "The strain is 1200 microstrain.", "choices": {"A": "1100 microstrain", "B": "1300 microstrain", "C": "1400 microstrain", "D": "1200 microstrain"}, "id": "eng_0216", "kind": "multiple_choice", "lang": "en", "question": "Bar 1000 mm stretches 1.2 mm. What is the strain?", "steps": ["ΔL = 1.2 mm, L = 1000 mm.", "ε = 1200 microstrain.", "Select option D (1200 microstrain)."], "subject": "engineering", "text": "Answer: 1200 microstrain.\nSteps:\n1. ΔL = 1.2 mm, L = 1000 mm.\n2. ε = 1200 microstrain.\n3. Select option D (1200 microstrain).\nAnswer: (D)", "topic": "materials"}
{"answer": "Tření je odpor proti skluzu, nejvýše mí krát normálová síla.", "choices": null, "id": "eng_0217", "kind": "concept", "lang": "cs", "question": "Co je tření?", "steps": ["Normála v N.", "Mí faktor.", "Brání skluzu."], "subject": "engineering", "text": "Answer: Mí krát normála.\nSteps:\n1. Normála v N.\n2. Mí faktor.\n3. Brání skluzu.", "topic": "statics"}
{"answer": "The power is 800 W.", "choices": null, "id": "eng_0218", "kind": "worked_example", "lang": "en", "question": "Work 8000 J is done in 10 s. What is the power?", "steps": ["W = 8000 J, t = 10 s.", "P = W/t = 800 W.", "Result 800 W."], "subject": "engineering", "text": "Answer: 800 W.\nSteps:\n1. W = 8000 J, t = 10 s.\n2. P = W/t = 800 W.\n3. Result 800 W.", "topic": "thermodynamics"}
{"answer": "Proudy vstupující do uzlu se rovnají proudům vystupujícím.", "choices": null, "id": "eng_0219", "kind": "concept", "lang": "cs", "question": "Co je Kirchhoffův zákon proudů?", "steps": ["Součet v A.", "Vstup rovná výstup.", "Náboj se drží."], "subject": "engineering", "text": "Answer: Proudy se rovnají.\nSteps:\n1. Součet v A.\n2. Vstup rovná výstup.\n3. Náboj se drží.", "topic": "circuits"}
{"answer": "The final value is 42 units.", "choices": null, "id": "eng_0220", "kind": "worked_example", "lang": "en", "question": "Gain 14 system gets a step of amplitude 3. What is the final value?", "steps": ["K = 14 (dimensionless), step 3 units.", "Final = 3×14 = 42 units.", "Result 42 units."], "subject": "engineering", "text": "Answer: 42 units.\nSteps:\n1. K = 14 (dimensionless), step 3 units.\n2. Final = 3×14 = 42 units.\n3. Result 42 units.", "topic": "control"}
{"answer": "The Reynolds number is 350000.", "choices": {"A": "325000 (dimensionless)", "B": "350000 (dimensionless)", "C": "375000 (dimensionless)", "D": "400000 (dimensionless)"}, "id": "eng_0221", "kind": "multiple_choice", "lang": "en", "question": "Water at 7 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number?", "steps": ["ρ = 1000 kg/m³, v = 7 m/s, D = 0.05 m.", "Re = ρvD/μ = 350000 (dimensionless).", "Select option B (350000 (dimensionless))."], "subject": "engineering", "text": "Answer: 350000 (dimensionless).\nSteps:\n1. ρ = 1000 kg/m³, v = 7 m/s, D = 0.05 m.\n2. Re = ρvD/μ = 350000 (dimensionless).\n3. Select option B (350000 (dimensionless)).\nAnswer: (B)", "topic": "fluids"}
{"answer": "Mez kluzu je napětí, kde začíná trvalá deformace.", "choices": null, "id": "eng_0222", "kind": "concept", "lang": "cs", "question": "Co je mez kluzu?", "steps": ["Pod ní pružné.", "Nad ní ohne.", "Limit návrhu."], "subject": "engineering", "text": "Answer: Začátek plastiky.\nSteps:\n1. Pod ní pružné.\n2. Nad ní ohne.\n3. Limit návrhu.", "topic": "materials"}
{"answer": "Each end reaction is 1000 N.", "choices": null, "id": "eng_0223", "kind": "worked_example", "lang": "en", "question": "Uniform beam weighs 2000 N over 8 m. What is each end reaction?", "steps": ["W = 2000 N, midspan 4 m.", "R = W/2 = 1000 N.", "Result 1000 N."], "subject": "engineering", "text": "Answer: 1000 N.\nSteps:\n1. W = 2000 N, midspan 4 m.\n2. R = W/2 = 1000 N.\n3. Result 1000 N.", "topic": "statics"}
{"answer": "A heat engine turns heat into work between hot and cold reservoirs.", "choices": null, "id": "eng_0224", "kind": "concept", "lang": "en", "question": "What is a heat engine?", "steps": ["Hot source.", "Cold sink.", "Work out."], "subject": "engineering", "text": "Answer: Heat to work.\nSteps:\n1. Hot source.\n2. Cold sink.\n3. Work out.", "topic": "thermodynamics"}
{"answer": "The stored charge is 9000 μC.", "choices": null, "id": "eng_0225", "kind": "worked_example", "lang": "en", "question": "Capacitor 900 μF charged to 10 V. What charge is stored?", "steps": ["C = 900 μF, V = 10 V.", "Q = CV = 9000 μC.", "Result 9000 μC."], "subject": "engineering", "text": "Answer: 9000 μC.\nSteps:\n1. C = 900 μF, V = 10 V.\n2. Q = CV = 9000 μC.\n3. Result 9000 μC.", "topic": "circuits"}
{"answer": "Ustálená odchylka je trvalý rozdíl cíle a výstupu.", "choices": null, "id": "eng_0226", "kind": "concept", "lang": "cs", "question": "Co je ustálená odchylka?", "steps": ["Počkej dlouho.", "Odečti offset.", "Typ určuje."], "subject": "engineering", "text": "Answer: Trvalý rozdíl.\nSteps:\n1. Počkej dlouho.\n2. Odečti offset.\n3. Typ určuje.", "topic": "control"}
{"answer": "Base pressure is 166.77 kPa.", "choices": null, "id": "eng_0227", "kind": "worked_example", "lang": "en", "question": "Still water column 17 m high. What is pressure at the base?", "steps": ["ρ = 1000 kg/m³, h = 17 m.", "p = ρgh = 166.77 kPa.", "Result 166.77 kPa."], "subject": "engineering", "text": "Answer: 166.77 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 17 m.\n2. p = ρgh = 166.77 kPa.\n3. Result 166.77 kPa.", "topic": "fluids"}
{"answer": "The stress is 140 MPa.", "choices": {"A": "140 MPa", "B": "130 MPa", "C": "150 MPa", "D": "160 MPa"}, "id": "eng_0228", "kind": "multiple_choice", "lang": "en", "question": "Steel (E = 200 GPa) at strain 700 microstrain. What is the stress?", "steps": ["E = 200 GPa, ε = 700 microstrain.", "σ = Eε = 140 MPa.", "Select option A (140 MPa)."], "subject": "engineering", "text": "Answer: 140 MPa.\nSteps:\n1. E = 200 GPa, ε = 700 microstrain.\n2. σ = Eε = 140 MPa.\n3. Select option A (140 MPa).\nAnswer: (A)", "topic": "materials"}
{"answer": "The balancing reaction is 900 N upward.", "choices": {"A": "950 N", "B": "900 N", "C": "850 N", "D": "1000 N"}, "id": "eng_0229", "kind": "multiple_choice", "lang": "en", "question": "Downward forces 360 N and 540 N act on a beam. What upward reaction balances them?", "steps": ["F1 = 360 N, F2 = 540 N.", "R = 360+540 = 900 N.", "Select option B (900 N)."], "subject": "engineering", "text": "Answer: 900 N.\nSteps:\n1. F1 = 360 N, F2 = 540 N.\n2. R = 360+540 = 900 N.\n3. Select option B (900 N).\nAnswer: (B)", "topic": "statics"}
{"answer": "Internal energy rises 100 kJ.", "choices": {"A": "105 kJ", "B": "95 kJ", "C": "100 kJ", "D": "110 kJ"}, "id": "eng_0230", "kind": "multiple_choice", "lang": "en", "question": "System gains 190 kJ of heat and does 90 kJ of work. What is internal energy change?", "steps": ["Q = 190 kJ, W = 90 kJ.", "ΔU = Q−W = 100 kJ.", "Select option C (100 kJ)."], "subject": "engineering", "text": "Answer: 100 kJ.\nSteps:\n1. Q = 190 kJ, W = 90 kJ.\n2. ΔU = Q−W = 100 kJ.\n3. Select option C (100 kJ).\nAnswer: (C)", "topic": "thermodynamics"}
{"answer": "The power lost is 360 W.", "choices": null, "id": "eng_0231", "kind": "worked_example", "lang": "en", "question": "Current 2 A through 90 Ω. What power is lost?", "steps": ["I = 2 A, R = 90 Ω.", "P = I²R = 360 W.", "Result 360 W."], "subject": "engineering", "text": "Answer: 360 W.\nSteps:\n1. I = 2 A, R = 90 Ω.\n2. P = I²R = 360 W.\n3. Result 360 W.", "topic": "circuits"}
{"answer": "Settling time is about 45 s.", "choices": null, "id": "eng_0232", "kind": "worked_example", "lang": "en", "question": "Time constant 15 s. What is 5% settling time?", "steps": ["τ = 15 s.", "ts ≈ 3τ = 45 s.", "Result 45 s."], "subject": "engineering", "text": "Answer: 45 s.\nSteps:\n1. τ = 15 s.\n2. ts ≈ 3τ = 45 s.\n3. Result 45 s.", "topic": "control"}
{"answer": "The exit velocity is 15 m/s.", "choices": null, "id": "eng_0233", "kind": "worked_example", "lang": "en", "question": "Tank head 11.25 m (take g = 10 m/s²). What is the Torricelli velocity?", "steps": ["h = 11.25 m, g = 10 m/s².", "v = √(2gh) = 15 m/s.", "Result 15 m/s."], "subject": "engineering", "text": "Answer: 15 m/s.\nSteps:\n1. h = 11.25 m, g = 10 m/s².\n2. v = √(2gh) = 15 m/s.\n3. Result 15 m/s.", "topic": "fluids"}
{"answer": "Ductile materials stretch plastically before breaking, while brittle ones snap with little strain.", "choices": null, "id": "eng_0234", "kind": "concept", "lang": "en", "question": "How do ductile and brittle differ?", "steps": ["Steel stretches.", "Glass snaps.", "Elongation tells."], "subject": "engineering", "text": "Answer: Stretch versus snap.\nSteps:\n1. Steel stretches.\n2. Glass snaps.\n3. Elongation tells.", "topic": "materials"}
{"answer": "A free-body diagram shows an isolated body with all acting forces and reactions.", "choices": null, "id": "eng_0235", "kind": "concept", "lang": "en", "question": "What is a free-body diagram?", "steps": ["Cut free.", "Draw forces.", "Solve equilibrium."], "subject": "engineering", "text": "Answer: Isolated body sketch.\nSteps:\n1. Cut free.\n2. Draw forces.\n3. Solve equilibrium.", "topic": "statics"}
{"answer": "The temperature is 368 K.", "choices": {"A": "363 K", "B": "373 K", "C": "378 K", "D": "368 K"}, "id": "eng_0236", "kind": "multiple_choice", "lang": "en", "question": "Temperature is 95 °C. What is it in kelvin?", "steps": ["T = 95 °C.", "K = 95 + 273 = 368 K.", "Select option D (368 K)."], "subject": "engineering", "text": "Answer: 368 K.\nSteps:\n1. T = 95 °C.\n2. K = 95 + 273 = 368 K.\n3. Select option D (368 K).\nAnswer: (D)", "topic": "thermodynamics"}
{"answer": "A capacitor stores charge and blocks steady direct current.", "choices": null, "id": "eng_0237", "kind": "concept", "lang": "en", "question": "What does a capacitor do?", "steps": ["Plates hold Q.", "DC blocked.", "AC passes."], "subject": "engineering", "text": "Answer: Stores charge.\nSteps:\n1. Plates hold Q.\n2. DC blocked.\n3. AC passes.", "topic": "circuits"}
{"answer": "Poles are transfer function roots setting speed and stability of modes.", "choices": null, "id": "eng_0238", "kind": "concept", "lang": "en", "question": "What are poles?", "steps": ["Denominator zero.", "Left is stable.", "Right blows."], "subject": "engineering", "text": "Answer: Stability roots.\nSteps:\n1. Denominator zero.\n2. Left is stable.\n3. Right blows.", "topic": "control"}
{"answer": "Vztlak je 156960 N.", "choices": {"A": "147150 N", "B": "166770 N", "C": "156960 N", "D": "176580 N"}, "id": "eng_0239", "kind": "multiple_choice", "lang": "cs", "question": "Trup vytlačí 16 m³ vody. Jaký je vztlak?", "steps": ["V = 16 m³, ρ = 1000 kg/m³.", "F = ρgV = 156960 N.", "Vyber možnost C (156960 N)."], "subject": "engineering", "text": "Answer: 156960 N.\nSteps:\n1. V = 16 m³, ρ = 1000 kg/m³.\n2. F = ρgV = 156960 N.\n3. Vyber možnost C (156960 N).\nAnswer: (C)", "topic": "fluids"}
{"answer": "Elongation is 7.5 mm.", "choices": {"A": "8.5 mm", "B": "7.5 mm", "C": "6.5 mm", "D": "9.5 mm"}, "id": "eng_0240", "kind": "multiple_choice", "lang": "en", "question": "Force 75 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation?", "steps": ["F = 75 kN, L = 2 m.", "ΔL = FL/AE = 7.5 mm.", "Select option B (7.5 mm)."], "subject": "engineering", "text": "Answer: 7.5 mm.\nSteps:\n1. F = 75 kN, L = 2 m.\n2. ΔL = FL/AE = 7.5 mm.\n3. Select option B (7.5 mm).\nAnswer: (B)", "topic": "materials"}
{"answer": "Coulomb friction caps at mu times normal force and opposes slipping.", "choices": null, "id": "eng_0241", "kind": "concept", "lang": "en", "question": "What is Coulomb friction?", "steps": ["Normal in N.", "Mu factor.", "Opposes motion."], "subject": "engineering", "text": "Answer: Mu times normal.\nSteps:\n1. Normal in N.\n2. Mu factor.\n3. Opposes motion.", "topic": "statics"}
{"answer": "The efficiency is 25%.", "choices": null, "id": "eng_0242", "kind": "worked_example", "lang": "en", "question": "Engine turns 250 J of 1000 J heat into work. What is the efficiency?", "steps": ["W = 250 J, Q = 1000 J.", "η = W/Q = 25%.", "Result 25%."], "subject": "engineering", "text": "Answer: 25%.\nSteps:\n1. W = 250 J, Q = 1000 J.\n2. η = W/Q = 25%.\n3. Result 25%.", "topic": "thermodynamics"}
{"answer": "The voltage is 204 V.", "choices": {"A": "192 V", "B": "216 V", "C": "228 V", "D": "204 V"}, "id": "eng_0243", "kind": "multiple_choice", "lang": "en", "question": "Current 17 A flows through 12 Ω. What is the voltage?", "steps": ["I = 17 A, R = 12 Ω.", "V = IR = 204 V.", "Select option D (204 V)."], "subject": "engineering", "text": "Answer: 204 V.\nSteps:\n1. I = 17 A, R = 12 Ω.\n2. V = IR = 204 V.\n3. Select option D (204 V).\nAnswer: (D)", "topic": "circuits"}
{"answer": "The Routh criterion tests stability from characteristic coefficients without solving.", "choices": null, "id": "eng_0244", "kind": "concept", "lang": "en", "question": "What is the Routh criterion?", "steps": ["Build array.", "First column.", "Sign flips bad."], "subject": "engineering", "text": "Answer: Table test.\nSteps:\n1. Build array.\n2. First column.\n3. Sign flips bad.", "topic": "control"}
{"answer": "Torricelli's law gives exit velocity as root of two g h under gravity.", "choices": null, "id": "eng_0245", "kind": "concept", "lang": "en", "question": "What is Torricelli's law?", "steps": ["Head in m.", "g pulls.", "v in m/s."], "subject": "engineering", "text": "Answer: Root two g h.\nSteps:\n1. Head in m.\n2. g pulls.\n3. v in m/s.", "topic": "fluids"}
{"answer": "Hardness is resistance to surface indentation, ranked by Brinell or Rockwell scales.", "choices": null, "id": "eng_0246", "kind": "concept", "lang": "en", "question": "What is hardness?", "steps": ["Press indenter.", "Small dent hard.", "Wear link."], "subject": "engineering", "text": "Answer: Dent resistance.\nSteps:\n1. Press indenter.\n2. Small dent hard.\n3. Wear link.", "topic": "materials"}
{"answer": "Výsledný moment je 740 N·m po směru.", "choices": null, "id": "eng_0247", "kind": "worked_example", "lang": "cs", "question": "500 N ve 4 m po směru, 420 N ve 3 m proti směru. Jaký je výsledný moment?", "steps": ["M1 = 500×4 = 2000 N·m.", "M2 = 420×3 = 1260 N·m.", "Net 740 N·m."], "subject": "engineering", "text": "Answer: 740 N·m.\nSteps:\n1. M1 = 500×4 = 2000 N·m.\n2. M2 = 420×3 = 1260 N·m.\n3. Net 740 N·m.", "topic": "statics"}
{"answer": "Refrigerator COP is cooling delivered per unit of work input.", "choices": null, "id": "eng_0248", "kind": "concept", "lang": "en", "question": "What is a refrigerator COP?", "steps": ["Q cold.", "W in.", "Ratio counts."], "subject": "engineering", "text": "Answer: Cooling per work.\nSteps:\n1. Q cold.\n2. W in.\n3. Ratio counts.", "topic": "thermodynamics"}
{"answer": "The current is 20 A.", "choices": null, "id": "eng_0249", "kind": "worked_example", "lang": "en", "question": "Voltage 120 V across 6 Ω. What is the current?", "steps": ["V = 120 V, R = 6 Ω.", "I = V/R = 20 A.", "Result 20 A."], "subject": "engineering", "text": "Answer: 20 A.\nSteps:\n1. V = 120 V, R = 6 Ω.\n2. I = V/R = 20 A.\n3. Result 20 A.", "topic": "circuits"}
{"answer": "A Bode plot shows gain and phase versus frequency on log scales.", "choices": null, "id": "eng_0250", "kind": "concept", "lang": "en", "question": "What is a Bode plot?", "steps": ["dB magnitude.", "Degrees phase.", "Margins read."], "subject": "engineering", "text": "Answer: Gain phase curves.\nSteps:\n1. dB magnitude.\n2. Degrees phase.\n3. Margins read.", "topic": "control"}
{"answer": "Bernoulliova rovnice směňuje tlak, rychlost a výšku podél proudnice.", "choices": null, "id": "eng_0251", "kind": "concept", "lang": "cs", "question": "Co je Bernoulliova rovnice?", "steps": ["Rychle znamená tlak dolů.", "Vysoko pomalu.", "Stálé ideální."], "subject": "engineering", "text": "Answer: Směna energií.\nSteps:\n1. Rychle znamená tlak dolů.\n2. Vysoko pomalu.\n3. Stálé ideální.", "topic": "fluids"}
{"answer": "The modulus is 101.5 GPa.", "choices": null, "id": "eng_0252", "kind": "worked_example", "lang": "en", "question": "Composite with fibre fraction 0.5 (Ef = 200 GPa, Em = 3 GPa). What is the modulus?", "steps": ["Vf = 0.5, Ef = 200 GPa.", "E = VfEf+VmEm = 101.5 GPa.", "Result 101.5 GPa."], "subject": "engineering", "text": "Answer: 101.5 GPa.\nSteps:\n1. Vf = 0.5, Ef = 200 GPa.\n2. E = VfEf+VmEm = 101.5 GPa.\n3. Result 101.5 GPa.", "topic": "materials"}
{"answer": "The moment arm is 38 m.", "choices": null, "id": "eng_0253", "kind": "worked_example", "lang": "en", "question": "Moment 5700 N·m comes from 150 N force. What is the moment arm?", "steps": ["M = 5700 N·m, F = 150 N.", "d = M/F = 38 m.", "Result 38 m."], "subject": "engineering", "text": "Answer: 38 m.\nSteps:\n1. M = 5700 N·m, F = 150 N.\n2. d = M/F = 38 m.\n3. Result 38 m.", "topic": "statics"}
{"answer": "The new volume is 11 m³.", "choices": null, "id": "eng_0254", "kind": "worked_example", "lang": "en", "question": "Gas 3 m³ at 300 K warms to 1100 K at constant pressure. What is the new volume?", "steps": ["V1 = 3 m³, T1 = 300 K.", "V2 = 3×1100/300 = 11 m³.", "Result 11 m³."], "subject": "engineering", "text": "Answer: 11 m³.\nSteps:\n1. V1 = 3 m³, T1 = 300 K.\n2. V2 = 3×1100/300 = 11 m³.\n3. Result 11 m³.", "topic": "thermodynamics"}
{"answer": "The power is 4140 W.", "choices": {"A": "4140 W", "B": "3910 W", "C": "4370 W", "D": "4255 W"}, "id": "eng_0255", "kind": "multiple_choice", "lang": "en", "question": "A 230 V appliance draws 18 A. What is its power?", "steps": ["V = 230 V, I = 18 A.", "P = VI = 4140 W.", "Select option A (4140 W)."], "subject": "engineering", "text": "Answer: 4140 W.\nSteps:\n1. V = 230 V, I = 18 A.\n2. P = VI = 4140 W.\n3. Select option A (4140 W).\nAnswer: (A)", "topic": "circuits"}
{"answer": "The integral output is 75 V.", "choices": null, "id": "eng_0256", "kind": "worked_example", "lang": "en", "question": "Error 2 units lasts 75 s with Ki = 0.5 1/s. What is the integral output?", "steps": ["e = 2 units, t = 75 s.", "u = 0.5×2×75 = 75 V.", "Result 75 V."], "subject": "engineering", "text": "Answer: 75 V.\nSteps:\n1. e = 2 units, t = 75 s.\n2. u = 0.5×2×75 = 75 V.\n3. Result 75 V.", "topic": "control"}
{"answer": "The mass flow is 16 kg/s.", "choices": null, "id": "eng_0257", "kind": "worked_example", "lang": "en", "question": "Water flows 16 L/s. What is the mass flow in kg/s?", "steps": ["Q = 16 L/s, ρ = 1000 kg/m³.", "ṁ = 16 kg/s.", "Result 16 kg/s."], "subject": "engineering", "text": "Answer: 16 kg/s.\nSteps:\n1. Q = 16 L/s, ρ = 1000 kg/m³.\n2. ṁ = 16 kg/s.\n3. Result 16 kg/s.", "topic": "fluids"}
{"answer": "Fatigue failure is cracking under repeated cyclic loads below static strength.", "choices": null, "id": "eng_0258", "kind": "concept", "lang": "en", "question": "What is fatigue failure?", "steps": ["Load cycles.", "Crack grows.", "Sudden break."], "subject": "engineering", "text": "Answer: Cyclic cracking.\nSteps:\n1. Load cycles.\n2. Crack grows.\n3. Sudden break.", "topic": "materials"}
{"answer": "The horizontal component is 600 N.", "choices": null, "id": "eng_0259", "kind": "worked_example", "lang": "en", "question": "Force 1000 N pulls at a 3-4-5 angle. What is the horizontal component?", "steps": ["F = 1000 N, cos = 3/5.", "Fx = 0.6×1000 = 600 N.", "Result 600 N."], "subject": "engineering", "text": "Answer: 600 N.\nSteps:\n1. F = 1000 N, cos = 3/5.\n2. Fx = 0.6×1000 = 600 N.\n3. Result 600 N.", "topic": "statics"}
{"answer": "An isothermal process holds temperature constant while heat and work exchange.", "choices": null, "id": "eng_0260", "kind": "concept", "lang": "en", "question": "What is an isothermal process?", "steps": ["T fixed.", "Heat flows.", "Work matches."], "subject": "engineering", "text": "Answer: Constant temperature.\nSteps:\n1. T fixed.\n2. Heat flows.\n3. Work matches.", "topic": "thermodynamics"}
{"answer": "An inductor stores magnetic energy and resists current change.", "choices": null, "id": "eng_0261", "kind": "concept", "lang": "en", "question": "What does an inductor do?", "steps": ["Coil field.", "Current lags.", "DC passes."], "subject": "engineering", "text": "Answer: Resists change.\nSteps:\n1. Coil field.\n2. Current lags.\n3. DC passes.", "topic": "circuits"}
{"answer": "The D output is 32 V.", "choices": null, "id": "eng_0262", "kind": "worked_example", "lang": "en", "question": "Error jumps 0 to 160 units in 2 s with Kd = 0.4 s. What is the D output?", "steps": ["Slope = 160/2 units/s.", "u = 0.4×slope = 32 V.", "Result 32 V."], "subject": "engineering", "text": "Answer: 32 V.\nSteps:\n1. Slope = 160/2 units/s.\n2. u = 0.4×slope = 32 V.\n3. Result 32 V.", "topic": "control"}
{"answer": "Gauge pressure is 166.77 kPa.", "choices": {"A": "161.77 kPa", "B": "171.77 kPa", "C": "176.77 kPa", "D": "166.77 kPa"}, "id": "eng_0263", "kind": "multiple_choice", "lang": "en", "question": "Water depth is 17 m. What is gauge pressure?", "steps": ["ρ = 1000 kg/m³, h = 17 m.", "p = ρgh = 166.77 kPa.", "Select option D (166.77 kPa)."], "subject": "engineering", "text": "Answer: 166.77 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 17 m.\n2. p = ρgh = 166.77 kPa.\n3. Select option D (166.77 kPa).\nAnswer: (D)", "topic": "fluids"}
{"answer": "Bezpečnost je 2.5.", "choices": {"A": "3.0 (dimensionless)", "B": "2.0 (dimensionless)", "C": "2.5 (dimensionless)", "D": "3.5 (dimensionless)"}, "id": "eng_0264", "kind": "multiple_choice", "lang": "cs", "question": "Mez kluzu 300 MPa, provozní napětí 120 MPa. Jaká je bezpečnost?", "steps": ["σy = 300 MPa, σw = 120 MPa.", "n = 2.5 (dimensionless).", "Vyber možnost C (2.5 (dimensionless))."], "subject": "engineering", "text": "Answer: 2.5 (dimensionless).\nSteps:\n1. σy = 300 MPa, σw = 120 MPa.\n2. n = 2.5 (dimensionless).\n3. Vyber možnost C (2.5 (dimensionless)).\nAnswer: (C)", "topic": "materials"}
{"answer": "Těžiště je bod, kde je plocha či těleso v rovnováze.", "choices": null, "id": "eng_0265", "kind": "concept", "lang": "cs", "question": "Co je těžiště?", "steps": ["Symetrie střed.", "Složené váží.", "Váha zde."], "subject": "engineering", "text": "Answer: Střed rovnováhy.\nSteps:\n1. Symetrie střed.\n2. Složené váží.\n3. Váha zde.", "topic": "statics"}
{"answer": "The pressure is 1900 kPa.", "choices": null, "id": "eng_0266", "kind": "worked_example", "lang": "en", "question": "Gas 19 m³ at 100 kPa is squeezed to 1 m³ at constant temperature. What is the pressure?", "steps": ["p1 = 100 kPa, V1 = 19 m³.", "p2 = 100×19 = 1900 kPa.", "Result 1900 kPa."], "subject": "engineering", "text": "Answer: 1900 kPa.\nSteps:\n1. p1 = 100 kPa, V1 = 19 m³.\n2. p2 = 100×19 = 1900 kPa.\n3. Result 1900 kPa.", "topic": "thermodynamics"}
{"answer": "A short has near-zero resistance with large current, while an open has no path and zero current.", "choices": null, "id": "eng_0267", "kind": "concept", "lang": "en", "question": "How do short and open circuits differ?", "steps": ["Short: big amps.", "Open: zero amps.", "Opposite faults."], "subject": "engineering", "text": "Answer: Zero versus none.\nSteps:\n1. Short: big amps.\n2. Open: zero amps.\n3. Opposite faults.", "topic": "circuits"}
{"answer": "Výstup regulátoru je 140 V.", "choices": {"A": "130 V", "B": "140 V", "C": "150 V", "D": "160 V"}, "id": "eng_0268", "kind": "multiple_choice", "lang": "cs", "question": "P-regulátor s Kp = 2 V/V vidí chybu 70 jednotek. Jaký je výstup?", "steps": ["Kp = 2 V/V, e = 70 units.", "u = Kp·e = 140 V.", "Vyber možnost B (140 V)."], "subject": "engineering", "text": "Answer: 140 V.\nSteps:\n1. Kp = 2 V/V, e = 70 units.\n2. u = Kp·e = 140 V.\n3. Vyber možnost B (140 V).\nAnswer: (B)", "topic": "control"}
{"answer": "Dynamic pressure is 4335 Pa.", "choices": null, "id": "eng_0269", "kind": "worked_example", "lang": "en", "question": "Air (ρ = 1.2 kg/m³) moves 85 m/s. What is the dynamic pressure?", "steps": ["ρ = 1.2 kg/m³, v = 85 m/s.", "q = ½ρv² = 4335 Pa.", "Result 4335 Pa."], "subject": "engineering", "text": "Answer: 4335 Pa.\nSteps:\n1. ρ = 1.2 kg/m³, v = 85 m/s.\n2. q = ½ρv² = 4335 Pa.\n3. Result 4335 Pa.", "topic": "fluids"}
{"answer": "Creep is slow deformation under steady load at high temperature over time.", "choices": null, "id": "eng_0270", "kind": "concept", "lang": "en", "question": "What is creep?", "steps": ["Heat softens.", "Load holds.", "Strain creeps."], "subject": "engineering", "text": "Answer: Slow hot sag.\nSteps:\n1. Heat softens.\n2. Load holds.\n3. Strain creeps.", "topic": "materials"}
{"answer": "Static friction holds up to a limit before motion, while kinetic acts during sliding, usually lower.", "choices": null, "id": "eng_0271", "kind": "concept", "lang": "en", "question": "How do static and kinetic friction differ?", "steps": ["Static holds.", "Kinetic slides.", "Static higher."], "subject": "engineering", "text": "Answer: Before versus during.\nSteps:\n1. Static holds.\n2. Kinetic slides.\n3. Static higher.", "topic": "statics"}
{"answer": "Vykonaná práce je 420 kJ.", "choices": {"A": "420 kJ", "B": "400 kJ", "C": "440 kJ", "D": "460 kJ"}, "id": "eng_0272", "kind": "multiple_choice", "lang": "cs", "question": "Plyn expanduje při 200 kPa o 2.1 m³. Jaká je práce?", "steps": ["p = 200 kPa, ΔV = 2.1 m³.", "W = pΔV = 420 kJ.", "Vyber možnost A (420 kJ)."], "subject": "engineering", "text": "Answer: 420 kJ.\nSteps:\n1. p = 200 kPa, ΔV = 2.1 m³.\n2. W = pΔV = 420 kJ.\n3. Vyber možnost A (420 kJ).\nAnswer: (A)", "topic": "thermodynamics"}
{"answer": "The resistance is 23 Ω.", "choices": null, "id": "eng_0273", "kind": "worked_example", "lang": "en", "question": "Voltage 69 V drives 3 A. What is the resistance?", "steps": ["V = 69 V, I = 3 A.", "R = V/I = 23 Ω.", "Result 23 Ω."], "subject": "engineering", "text": "Answer: 23 Ω.\nSteps:\n1. V = 69 V, I = 3 A.\n2. R = V/I = 23 Ω.\n3. Result 23 Ω.", "topic": "circuits"}
{"answer": "The closed-loop gain is 0.95.", "choices": null, "id": "eng_0274", "kind": "worked_example", "lang": "en", "question": "Unity feedback loop, forward gain 19. What is the closed-loop gain?", "steps": ["K = 19 (dimensionless).", "T = K/(1+K) = 0.95 (dimensionless).", "Result 0.95 (dimensionless)."], "subject": "engineering", "text": "Answer: 0.95 (dimensionless).\nSteps:\n1. K = 19 (dimensionless).\n2. T = K/(1+K) = 0.95 (dimensionless).\n3. Result 0.95 (dimensionless).", "topic": "control"}
{"answer": "The volume is 38 m³.", "choices": null, "id": "eng_0275", "kind": "worked_example", "lang": "en", "question": "Tank base area 2 m², depth 19 m. What is the water volume?", "steps": ["A = 2 m², h = 19 m.", "V = Ah = 38 m³.", "Result 38 m³."], "subject": "engineering", "text": "Answer: 38 m³.\nSteps:\n1. A = 2 m², h = 19 m.\n2. V = Ah = 38 m³.\n3. Result 38 m³.", "topic": "fluids"}
{"answer": "The shear stress is 80 MPa.", "choices": null, "id": "eng_0276", "kind": "worked_example", "lang": "en", "question": "Shear force 40 kN on 500 mm² section. What is the shear stress?", "steps": ["F = 40 kN, A = 500 mm².", "τ = F/A = 80 MPa.", "Result 80 MPa."], "subject": "engineering", "text": "Answer: 80 MPa.\nSteps:\n1. F = 40 kN, A = 500 mm².\n2. τ = F/A = 80 MPa.\n3. Result 80 MPa.", "topic": "materials"}
{"answer": "Svislá složka je 840 N.", "choices": null, "id": "eng_0277", "kind": "worked_example", "lang": "cs", "question": "Síla 1050 N táhne pod úhlem 3-4-5. Jaká je svislá složka?", "steps": ["F = 1050 N, sin = 4/5.", "Fy = 0.8×1050 = 840 N.", "Result 840 N."], "subject": "engineering", "text": "Answer: 840 N.\nSteps:\n1. F = 1050 N, sin = 4/5.\n2. Fy = 0.8×1050 = 840 N.\n3. Result 840 N.", "topic": "statics"}
{"answer": "Teplota je 207 °C.", "choices": null, "id": "eng_0278", "kind": "worked_example", "lang": "cs", "question": "Teplota je 480 K. Kolik je to stupňů Celsia?", "steps": ["T = 480 K.", "C = 480 − 273 = 207 °C.", "Result 207 °C."], "subject": "engineering", "text": "Answer: 207 °C.\nSteps:\n1. T = 480 K.\n2. C = 480 − 273 = 207 °C.\n3. Result 207 °C.", "topic": "thermodynamics"}
{"answer": "A voltage divider splits input voltage across series resistors by ratio.", "choices": null, "id": "eng_0279", "kind": "concept", "lang": "en", "question": "What is a voltage divider?", "steps": ["Two resistors.", "Tap middle.", "Vout fraction."], "subject": "engineering", "text": "Answer: Split by ratio.\nSteps:\n1. Two resistors.\n2. Tap middle.\n3. Vout fraction.", "topic": "circuits"}
{"answer": "The total gain is 34.", "choices": {"A": "32 (dimensionless)", "B": "36 (dimensionless)", "C": "34 (dimensionless)", "D": "38 (dimensionless)"}, "id": "eng_0280", "kind": "multiple_choice", "lang": "en", "question": "Two series blocks have gains 2 and 17. What is the total gain?", "steps": ["K1 = 2, K2 = 17 (dimensionless).", "K = 34 (dimensionless).", "Select option C (34 (dimensionless))."], "subject": "engineering", "text": "Answer: 34 (dimensionless).\nSteps:\n1. K1 = 2, K2 = 17 (dimensionless).\n2. K = 34 (dimensionless).\n3. Select option C (34 (dimensionless)).\nAnswer: (C)", "topic": "control"}
{"answer": "A manometer measures pressure from a liquid column height difference.", "choices": null, "id": "eng_0281", "kind": "concept", "lang": "en", "question": "What does a manometer measure?", "steps": ["Height in mm.", "Times rho g.", "Pa result."], "subject": "engineering", "text": "Answer: Column pressure.\nSteps:\n1. Height in mm.\n2. Times rho g.\n3. Pa result.", "topic": "fluids"}
{"answer": "Teplotní napětí je 252 MPa.", "choices": null, "id": "eng_0282", "kind": "worked_example", "lang": "cs", "question": "Ocelová tyč (E = 200 GPa, α = 12e-6/K) chladne o 105 K vetknutá. Jaké vznikne napětí?", "steps": ["E = 200 GPa, ΔT = 105 K.", "σ = EαΔT = 252 MPa.", "Result 252 MPa."], "subject": "engineering", "text": "Answer: 252 MPa.\nSteps:\n1. E = 200 GPa, ΔT = 105 K.\n2. σ = EαΔT = 252 MPa.\n3. Result 252 MPa.", "topic": "materials"}
{"answer": "The reaction at B is 2200 N.", "choices": null, "id": "eng_0283", "kind": "worked_example", "lang": "en", "question": "Beam 6 m, load 3300 N at 4 m from A. What is reaction at B?", "steps": ["F = 3300 N, span 6 m.", "RB = 3300×4/6 = 2200 N.", "Result 2200 N."], "subject": "engineering", "text": "Answer: 2200 N.\nSteps:\n1. F = 3300 N, span 6 m.\n2. RB = 3300×4/6 = 2200 N.\n3. Result 2200 N.", "topic": "statics"}
{"answer": "The specific volume is 10 m³/kg.", "choices": null, "id": "eng_0284", "kind": "worked_example", "lang": "en", "question": "Gas fills 40 m³ with mass 4 kg. What is the specific volume?", "steps": ["V = 40 m³, m = 4 kg.", "v = V/m = 10 m³/kg.", "Result 10 m³/kg."], "subject": "engineering", "text": "Answer: 10 m³/kg.\nSteps:\n1. V = 40 m³, m = 4 kg.\n2. v = V/m = 10 m³/kg.\n3. Result 10 m³/kg.", "topic": "thermodynamics"}
{"answer": "The tap voltage is 25 V.", "choices": null, "id": "eng_0285", "kind": "worked_example", "lang": "en", "question": "Divider with two 1000 Ω resistors fed 50 V. What is the tap voltage?", "steps": ["Vin = 50 V, halves.", "Vout = 25 V.", "Result 25 V."], "subject": "engineering", "text": "Answer: 25 V.\nSteps:\n1. Vin = 50 V, halves.\n2. Vout = 25 V.\n3. Result 25 V.", "topic": "circuits"}
{"answer": "The error is 95 units.", "choices": null, "id": "eng_0286", "kind": "worked_example", "lang": "en", "question": "Setpoint 950 units, measurement 855 units. What is the error?", "steps": ["r = 950 units, y = 855 units.", "e = r−y = 95 units.", "Result 95 units."], "subject": "engineering", "text": "Answer: 95 units.\nSteps:\n1. r = 950 units, y = 855 units.\n2. e = r−y = 95 units.\n3. Result 95 units.", "topic": "control"}
{"answer": "Cavitation is vapor bubble collapse from low pressure, eroding pumps and propellers.", "choices": null, "id": "eng_0287", "kind": "concept", "lang": "en", "question": "What is cavitation?", "steps": ["Pressure dips.", "Bubbles burst.", "Metal pits."], "subject": "engineering", "text": "Answer: Bubble collapse.\nSteps:\n1. Pressure dips.\n2. Bubbles burst.\n3. Metal pits.", "topic": "fluids"}
{"answer": "Poisson's ratio is transverse shrink over axial stretch, about 0.3 for steel.", "choices": null, "id": "eng_0288", "kind": "concept", "lang": "en", "question": "What is Poisson's ratio?", "steps": ["Pull bar.", "Sides pinch.", "Ratio 0.3."], "subject": "engineering", "text": "Answer: Side over length.\nSteps:\n1. Pull bar.\n2. Sides pinch.\n3. Ratio 0.3.", "topic": "materials"}
{"answer": "Each end reaction is 1300 N.", "choices": null, "id": "eng_0289", "kind": "worked_example", "lang": "en", "question": "Uniform beam weighs 2600 N over 8 m. What is each end reaction?", "steps": ["W = 2600 N, midspan 4 m.", "R = W/2 = 1300 N.", "Result 1300 N."], "subject": "engineering", "text": "Answer: 1300 N.\nSteps:\n1. W = 2600 N, midspan 4 m.\n2. R = W/2 = 1300 N.\n3. Result 1300 N.", "topic": "statics"}
{"answer": "Carnot efficiency is 80%.", "choices": {"A": "85%", "B": "80%", "C": "75%", "D": "90%"}, "id": "eng_0290", "kind": "multiple_choice", "lang": "en", "question": "Carnot engine between 300 K and 1500 K. What is its efficiency?", "steps": ["Tc = 300 K, Th = 1500 K.", "η = 1 − 300/1500 = 80%.", "Select option B (80%)."], "subject": "engineering", "text": "Answer: 80%.\nSteps:\n1. Tc = 300 K, Th = 1500 K.\n2. η = 1 − 300/1500 = 80%.\n3. Select option B (80%).\nAnswer: (B)", "topic": "thermodynamics"}
{"answer": "Ground is the zero-volt reference node for all measurements.", "choices": null, "id": "eng_0291", "kind": "concept", "lang": "en", "question": "What is ground in a circuit?", "steps": ["0 V defined.", "Currents return.", "Safety sink."], "subject": "engineering", "text": "Answer: Zero reference.\nSteps:\n1. 0 V defined.\n2. Currents return.\n3. Safety sink.", "topic": "circuits"}
{"answer": "The steady value is 80 units.", "choices": {"A": "75 units", "B": "85 units", "C": "90 units", "D": "80 units"}, "id": "eng_0292", "kind": "multiple_choice", "lang": "en", "question": "System K/(10s+1) with K = 80 gets a unit step. What is the steady value?", "steps": ["DC gain K = 80 (dimensionless).", "Step final = 80 units.", "Select option D (80 units)."], "subject": "engineering", "text": "Answer: 80 units.\nSteps:\n1. DC gain K = 80 (dimensionless).\n2. Step final = 80 units.\n3. Select option D (80 units).\nAnswer: (D)", "topic": "control"}
{"answer": "Outlet velocity is 36 m/s.", "choices": {"A": "36 m/s", "B": "34 m/s", "C": "38 m/s", "D": "40 m/s"}, "id": "eng_0293", "kind": "multiple_choice", "lang": "en", "question": "Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 18 m/s. What is outlet velocity?", "steps": ["A1v1 = 0.02×18 m³/s.", "v2 = 36 m/s.", "Select option A (36 m/s)."], "subject": "engineering", "text": "Answer: 36 m/s.\nSteps:\n1. A1v1 = 0.02×18 m³/s.\n2. v2 = 36 m/s.\n3. Select option A (36 m/s).\nAnswer: (A)", "topic": "fluids"}
{"answer": "The stress is 170 MPa.", "choices": {"A": "160 MPa", "B": "180 MPa", "C": "190 MPa", "D": "170 MPa"}, "id": "eng_0294", "kind": "multiple_choice", "lang": "en", "question": "Tensile force 17 kN on 100 mm² bar. What is the stress?", "steps": ["F = 17 kN, A = 100 mm².", "σ = F/A = 170 MPa.", "Select option D (170 MPa)."], "subject": "engineering", "text": "Answer: 170 MPa.\nSteps:\n1. F = 17 kN, A = 100 mm².\n2. σ = F/A = 170 MPa.\n3. Select option D (170 MPa).\nAnswer: (D)", "topic": "materials"}
{"answer": "The couple moment is 570 N·m.", "choices": {"A": "600 N·m", "B": "540 N·m", "C": "570 N·m", "D": "630 N·m"}, "id": "eng_0295", "kind": "multiple_choice", "lang": "en", "question": "A couple has forces 190 N spaced 3 m apart. What is its moment?", "steps": ["F = 190 N, d = 3 m.", "M = Fd = 570 N·m.", "Select option C (570 N·m)."], "subject": "engineering", "text": "Answer: 570 N·m.\nSteps:\n1. F = 190 N, d = 3 m.\n2. M = Fd = 570 N·m.\n3. Select option C (570 N·m).\nAnswer: (C)", "topic": "statics"}
{"answer": "The heat required is 192.28 kJ.", "choices": {"A": "202.28 kJ", "B": "182.28 kJ", "C": "192.28 kJ", "D": "212.28 kJ"}, "id": "eng_0296", "kind": "multiple_choice", "lang": "en", "question": "2 kg of water warms by 23 K (c = 4.18 kJ/(kg·K)). How much heat?", "steps": ["m = 2 kg, ΔT = 23 K.", "Q = mcΔT = 192.28 kJ.", "Select option C (192.28 kJ)."], "subject": "engineering", "text": "Answer: 192.28 kJ.\nSteps:\n1. m = 2 kg, ΔT = 23 K.\n2. Q = mcΔT = 192.28 kJ.\n3. Select option C (192.28 kJ).\nAnswer: (C)", "topic": "thermodynamics"}
{"answer": "Sériové odpory se sčítají, celkový odpor je součet v ohmech.", "choices": null, "id": "eng_0297", "kind": "concept", "lang": "cs", "question": "Co je sériové řazení odporů?", "steps": ["Stejný proud.", "Napětí dělí.", "R součet."], "subject": "engineering", "text": "Answer: Sčítání v sérii.\nSteps:\n1. Stejný proud.\n2. Napětí dělí.\n3. R součet.", "topic": "circuits"}
{"answer": "Doba ustálení je asi 72 s.", "choices": {"A": "72 s", "B": "68 s", "C": "76 s", "D": "80 s"}, "id": "eng_0298", "kind": "multiple_choice", "lang": "cs", "question": "Soustava má časovou konstantu 18 s. Jaká je doba ustálení 2 %?", "steps": ["τ = 18 s.", "ts ≈ 4τ = 72 s.", "Vyber možnost A (72 s)."], "subject": "engineering", "text": "Answer: 72 s.\nSteps:\n1. τ = 18 s.\n2. ts ≈ 4τ = 72 s.\n3. Vyber možnost A (72 s).\nAnswer: (A)", "topic": "control"}
{"answer": "Hydraulic power is 4316.4 W.", "choices": null, "id": "eng_0299", "kind": "worked_example", "lang": "en", "question": "Pump lifts 0.02 m³/s of water 22 m. What hydraulic power is needed?", "steps": ["Q = 0.02 m³/s, H = 22 m.", "P = ρgQH = 4316.4 W.", "Result 4316.4 W."], "subject": "engineering", "text": "Answer: 4316.4 W.\nSteps:\n1. Q = 0.02 m³/s, H = 22 m.\n2. P = ρgQH = 4316.4 W.\n3. Result 4316.4 W.", "topic": "fluids"}
{"answer": "Shear stress is parallel force per area sliding layers past each other.", "choices": null, "id": "eng_0300", "kind": "concept", "lang": "en", "question": "What is shear stress?", "steps": ["Cut action.", "Tau symbol.", "Pa unit."], "subject": "engineering", "text": "Answer: Sliding force.\nSteps:\n1. Cut action.\n2. Tau symbol.\n3. Pa unit.", "topic": "materials"}
{"answer": "The net moment is 380 N·m clockwise.", "choices": null, "id": "eng_0301", "kind": "worked_example", "lang": "en", "question": "500 N at 4 m clockwise, 540 N at 3 m counter-clockwise. What is the net moment?", "steps": ["M1 = 500×4 = 2000 N·m.", "M2 = 540×3 = 1620 N·m.", "Net 380 N·m."], "subject": "engineering", "text": "Answer: 380 N·m.\nSteps:\n1. M1 = 500×4 = 2000 N·m.\n2. M2 = 540×3 = 1620 N·m.\n3. Net 380 N·m.", "topic": "statics"}
{"answer": "Entropie měří rozptyl energie a vratně nikdy neklesá.", "choices": null, "id": "eng_0302", "kind": "concept", "lang": "cs", "question": "Co je entropie?", "steps": ["Jouly na K.", "Stále roste.", "Limituje stroje."], "subject": "engineering", "text": "Answer: Míra rozptylu.\nSteps:\n1. Jouly na K.\n2. Stále roste.\n3. Limituje stroje.", "topic": "thermodynamics"}
{"answer": "DC holds steady polarity while AC alternates direction periodically.", "choices": null, "id": "eng_0303", "kind": "concept", "lang": "en", "question": "How do AC and DC differ?", "steps": ["Battery DC.", "Mains AC.", "Hz counts."], "subject": "engineering", "text": "Answer: Steady versus alternating.\nSteps:\n1. Battery DC.\n2. Mains AC.\n3. Hz counts.", "topic": "circuits"}
{"answer": "Steady-state error is 4%.", "choices": {"A": "6%", "B": "4%", "C": "2%", "D": "9%"}, "id": "eng_0304", "kind": "multiple_choice", "lang": "en", "question": "Type-0 loop has position constant Kp = 24. What is step steady-state error?", "steps": ["Kp = 24 (dimensionless).", "ess = 100/25 = 4%.", "Select option B (4%)."], "subject": "engineering", "text": "Answer: 4%.\nSteps:\n1. Kp = 24 (dimensionless).\n2. ess = 100/25 = 4%.\n3. Select option B (4%).\nAnswer: (B)", "topic": "control"}
{"answer": "Base pressure is 225.63 kPa.", "choices": null, "id": "eng_0305", "kind": "worked_example", "lang": "en", "question": "Still water column 23 m high. What is pressure at the base?", "steps": ["ρ = 1000 kg/m³, h = 23 m.", "p = ρgh = 225.63 kPa.", "Result 225.63 kPa."], "subject": "engineering", "text": "Answer: 225.63 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 23 m.\n2. p = ρgh = 225.63 kPa.\n3. Result 225.63 kPa.", "topic": "fluids"}
{"answer": "Transverse strain is -1500 microstrain.", "choices": null, "id": "eng_0306", "kind": "worked_example", "lang": "en", "question": "Bar stretches 5000 microstrain, Poisson ratio 0.3. What is transverse strain?", "steps": ["εa = 5000 microstrain, ν = 0.3.", "εt = −νεa = -1500 microstrain.", "Result -1500 microstrain."], "subject": "engineering", "text": "Answer: -1500 microstrain.\nSteps:\n1. εa = 5000 microstrain, ν = 0.3.\n2. εt = −νεa = -1500 microstrain.\n3. Result -1500 microstrain.", "topic": "materials"}
{"answer": "A centroid is the geometric center where area or volume balances.", "choices": null, "id": "eng_0307", "kind": "concept", "lang": "en", "question": "What is a centroid?", "steps": ["Symmetric middle.", "Composite weighs.", "Used for weight."], "subject": "engineering", "text": "Answer: Area balance point.\nSteps:\n1. Symmetric middle.\n2. Composite weighs.\n3. Used for weight.", "topic": "statics"}
{"answer": "Výkon je 1100 W.", "choices": null, "id": "eng_0308", "kind": "worked_example", "lang": "cs", "question": "Práce 11000 J za 10 s. Jaký je výkon?", "steps": ["W = 11000 J, t = 10 s.", "P = W/t = 1100 W.", "Result 1100 W."], "subject": "engineering", "text": "Answer: 1100 W.\nSteps:\n1. W = 11000 J, t = 10 s.\n2. P = W/t = 1100 W.\n3. Result 1100 W.", "topic": "thermodynamics"}
{"answer": "The leaving current is 26 A.", "choices": null, "id": "eng_0309", "kind": "worked_example", "lang": "en", "question": "Currents 2 A and 24 A enter a node. What current leaves?", "steps": ["I1 = 2 A, I2 = 24 A.", "I3 = 26 A.", "Result 26 A."], "subject": "engineering", "text": "Answer: 26 A.\nSteps:\n1. I1 = 2 A, I2 = 24 A.\n2. I3 = 26 A.\n3. Result 26 A.", "topic": "circuits"}
{"answer": "The final value is 60 units.", "choices": null, "id": "eng_0310", "kind": "worked_example", "lang": "en", "question": "Gain 20 system gets a step of amplitude 3. What is the final value?", "steps": ["K = 20 (dimensionless), step 3 units.", "Final = 3×20 = 60 units.", "Result 60 units."], "subject": "engineering", "text": "Answer: 60 units.\nSteps:\n1. K = 20 (dimensionless), step 3 units.\n2. Final = 3×20 = 60 units.\n3. Result 60 units.", "topic": "control"}
{"answer": "Reynoldsovo číslo je bezrozměrný poměr setrvačných a vazkých sil.", "choices": null, "id": "eng_0311", "kind": "concept", "lang": "cs", "question": "Co je Reynoldsovo číslo?", "steps": ["Ró vé dé.", "Lomeno mí.", "Pod 2300 klid."], "subject": "engineering", "text": "Answer: Setrvačnost lomeno vazkost.\nSteps:\n1. Ró vé dé.\n2. Lomeno mí.\n3. Pod 2300 klid.", "topic": "fluids"}
{"answer": "Deformace je 1700 mikrostrainu.", "choices": {"A": "1700 microstrain", "B": "1600 microstrain", "C": "1800 microstrain", "D": "1900 microstrain"}, "id": "eng_0312", "kind": "multiple_choice", "lang": "cs", "question": "Tyč 1000 mm se protáhne o 1.7 mm. Jaká je deformace?", "steps": ["ΔL = 1.7 mm, L = 1000 mm.", "ε = 1700 microstrain.", "Vyber možnost A (1700 microstrain)."], "subject": "engineering", "text": "Answer: 1700 microstrain.\nSteps:\n1. ΔL = 1.7 mm, L = 1000 mm.\n2. ε = 1700 microstrain.\n3. Vyber možnost A (1700 microstrain).\nAnswer: (A)", "topic": "materials"}
{"answer": "The resultant is 800 N.", "choices": {"A": "750 N", "B": "850 N", "C": "900 N", "D": "800 N"}, "id": "eng_0313", "kind": "multiple_choice", "lang": "en", "question": "Forces 480 N east and 640 N north act on a bolt. What is the resultant?", "steps": ["Fx = 480 N, Fy = 640 N.", "R = √(480²+640²) = 800 N.", "Select option D (800 N)."], "subject": "engineering", "text": "Answer: 800 N.\nSteps:\n1. Fx = 480 N, Fy = 640 N.\n2. R = √(480²+640²) = 800 N.\n3. Select option D (800 N).\nAnswer: (D)", "topic": "statics"}
{"answer": "An adiabatic process exchanges no heat, so work changes internal energy only.", "choices": null, "id": "eng_0314", "kind": "concept", "lang": "en", "question": "What is an adiabatic process?", "steps": ["Insulated walls.", "Work only.", "T shifts."], "subject": "engineering", "text": "Answer: No heat exchange.\nSteps:\n1. Insulated walls.\n2. Work only.\n3. T shifts.", "topic": "thermodynamics"}
{"answer": "Kondenzátor ukládá náboj a stejnosměrný proud nepropustí.", "choices": null, "id": "eng_0315", "kind": "concept", "lang": "cs", "question": "Co dělá kondenzátor?", "steps": ["Desky drží Q.", "DC stojí.", "AC projde."], "subject": "engineering", "text": "Answer: Ukládá náboj.\nSteps:\n1. Desky drží Q.\n2. DC stojí.\n3. AC projde.", "topic": "circuits"}
{"answer": "Doba ustálení je asi 63 s.", "choices": null, "id": "eng_0316", "kind": "worked_example", "lang": "cs", "question": "Časová konstanta 21 s. Jaká je doba ustálení 5 %?", "steps": ["τ = 21 s.", "ts ≈ 3τ = 63 s.", "Result 63 s."], "subject": "engineering", "text": "Answer: 63 s.\nSteps:\n1. τ = 21 s.\n2. ts ≈ 3τ = 63 s.\n3. Result 63 s.", "topic": "control"}
{"answer": "A boundary layer is the thin slowed fluid film along a solid wall.", "choices": null, "id": "eng_0317", "kind": "concept", "lang": "en", "question": "What is a boundary layer?", "steps": ["Wall friction.", "Thin grows.", "Drag source."], "subject": "engineering", "text": "Answer: Slowed wall film.\nSteps:\n1. Wall friction.\n2. Thin grows.\n3. Drag source.", "topic": "fluids"}
{"answer": "Toughness is energy absorbed before fracture, the area under the curve.", "choices": null, "id": "eng_0318", "kind": "concept", "lang": "en", "question": "What is toughness?", "steps": ["Strong plus ductile.", "Area counts.", "Impact resists."], "subject": "engineering", "text": "Answer: Energy to break.\nSteps:\n1. Strong plus ductile.\n2. Area counts.\n3. Impact resists.", "topic": "materials"}
{"answer": "The moment is 1800 N·m.", "choices": {"A": "1800 N·m", "B": "1700 N·m", "C": "1900 N·m", "D": "1850 N·m"}, "id": "eng_0319", "kind": "multiple_choice", "lang": "en", "question": "Force 900 N acts at 2 m from a pivot. What is the moment?", "steps": ["F = 900 N, d = 2 m.", "M = Fd = 1800 N·m.", "Select option A (1800 N·m)."], "subject": "engineering", "text": "Answer: 1800 N·m.\nSteps:\n1. F = 900 N, d = 2 m.\n2. M = Fd = 1800 N·m.\n3. Select option A (1800 N·m).\nAnswer: (A)", "topic": "statics"}
{"answer": "The efficiency is 31%.", "choices": null, "id": "eng_0320", "kind": "worked_example", "lang": "en", "question": "Engine turns 310 J of 1000 J heat into work. What is the efficiency?", "steps": ["W = 310 J, Q = 1000 J.", "η = W/Q = 31%.", "Result 31%."], "subject": "engineering", "text": "Answer: 31%.\nSteps:\n1. W = 310 J, Q = 1000 J.\n2. η = W/Q = 31%.\n3. Result 31%.", "topic": "thermodynamics"}
{"answer": "Total resistance is 2000 Ω.", "choices": {"A": "1900 Ω", "B": "2000 Ω", "C": "2100 Ω", "D": "2050 Ω"}, "id": "eng_0321", "kind": "multiple_choice", "lang": "en", "question": "Resistors 100 Ω and 1900 Ω in series. What is total resistance?", "steps": ["R1 = 100 Ω, R2 = 1900 Ω.", "R = 2000 Ω.", "Select option B (2000 Ω)."], "subject": "engineering", "text": "Answer: 2000 Ω.\nSteps:\n1. R1 = 100 Ω, R2 = 1900 Ω.\n2. R = 2000 Ω.\n3. Select option B (2000 Ω).\nAnswer: (B)", "topic": "circuits"}
{"answer": "The controller output is 190 V.", "choices": {"A": "180 V", "B": "200 V", "C": "190 V", "D": "210 V"}, "id": "eng_0322", "kind": "multiple_choice", "lang": "en", "question": "P-controller with Kp = 2 V/V sees error 95 units. What is the output?", "steps": ["Kp = 2 V/V, e = 95 units.", "u = Kp·e = 190 V.", "Select option C (190 V)."], "subject": "engineering", "text": "Answer: 190 V.\nSteps:\n1. Kp = 2 V/V, e = 95 units.\n2. u = Kp·e = 190 V.\n3. Select option C (190 V).\nAnswer: (C)", "topic": "control"}
{"answer": "Průtok je 38 L/s.", "choices": {"A": "36 L/s", "B": "38 L/s", "C": "40 L/s", "D": "42 L/s"}, "id": "eng_0323", "kind": "multiple_choice", "lang": "cs", "question": "Průřez 20 cm², rychlost 19 m/s. Jaký je průtok v litrech za sekundu?", "steps": ["A = 20 cm², v = 19 m/s.", "Q = Av = 38 L/s.", "Vyber možnost B (38 L/s)."], "subject": "engineering", "text": "Answer: 38 L/s.\nSteps:\n1. A = 20 cm², v = 19 m/s.\n2. Q = Av = 38 L/s.\n3. Vyber možnost B (38 L/s).\nAnswer: (B)", "topic": "fluids"}
{"answer": "Tvrdost je odpor povrchu proti vtlačení, stupnice Brinell či Rockwell.", "choices": null, "id": "eng_0324", "kind": "concept", "lang": "cs", "question": "Co je tvrdost?", "steps": ["Vtlač tělísko.", "Malý důlek tvrdé.", "Vazba na otěr."], "subject": "engineering", "text": "Answer: Odpor důlku.\nSteps:\n1. Vtlač tělísko.\n2. Malý důlek tvrdé.\n3. Vazba na otěr.", "topic": "materials"}
{"answer": "The moment arm is 50 m.", "choices": null, "id": "eng_0325", "kind": "worked_example", "lang": "en", "question": "Moment 7500 N·m comes from 150 N force. What is the moment arm?", "steps": ["M = 7500 N·m, F = 150 N.", "d = M/F = 50 m.", "Result 50 m."], "subject": "engineering", "text": "Answer: 50 m.\nSteps:\n1. M = 7500 N·m, F = 150 N.\n2. d = M/F = 50 m.\n3. Result 50 m.", "topic": "statics"}
{"answer": "Ideální plyn splňuje stavovou rovnici pV rovná nRT.", "choices": null, "id": "eng_0326", "kind": "concept", "lang": "cs", "question": "Co je ideální plyn?", "steps": ["p v Pa.", "V v m³.", "T v K."], "subject": "engineering", "text": "Answer: pV rovná nRT.\nSteps:\n1. p v Pa.\n2. V v m³.\n3. T v K.", "topic": "thermodynamics"}
{"answer": "The stored charge is 12000 μC.", "choices": null, "id": "eng_0327", "kind": "worked_example", "lang": "en", "question": "Capacitor 1200 μF charged to 10 V. What charge is stored?", "steps": ["C = 1200 μF, V = 10 V.", "Q = CV = 12000 μC.", "Result 12000 μC."], "subject": "engineering", "text": "Answer: 12000 μC.\nSteps:\n1. C = 1200 μF, V = 10 V.\n2. Q = CV = 12000 μC.\n3. Result 12000 μC.", "topic": "circuits"}
{"answer": "The integral output is 105 V.", "choices": null, "id": "eng_0328", "kind": "worked_example", "lang": "en", "question": "Error 2 units lasts 105 s with Ki = 0.5 1/s. What is the integral output?", "steps": ["e = 2 units, t = 105 s.", "u = 0.5×2×105 = 105 V.", "Result 105 V."], "subject": "engineering", "text": "Answer: 105 V.\nSteps:\n1. e = 2 units, t = 105 s.\n2. u = 0.5×2×105 = 105 V.\n3. Result 105 V.", "topic": "control"}
{"answer": "The Reynolds number is 475000.", "choices": {"A": "450000 (dimensionless)", "B": "500000 (dimensionless)", "C": "475000 (dimensionless)", "D": "525000 (dimensionless)"}, "id": "eng_0329", "kind": "multiple_choice", "lang": "en", "question": "Water at 9.5 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number?", "steps": ["ρ = 1000 kg/m³, v = 9.5 m/s, D = 0.05 m.", "Re = ρvD/μ = 475000 (dimensionless).", "Select option C (475000 (dimensionless))."], "subject": "engineering", "text": "Answer: 475000 (dimensionless).\nSteps:\n1. ρ = 1000 kg/m³, v = 9.5 m/s, D = 0.05 m.\n2. Re = ρvD/μ = 475000 (dimensionless).\n3. Select option C (475000 (dimensionless)).\nAnswer: (C)", "topic": "fluids"}
{"answer": "Annealing heats and slowly cools metal to soften it and relieve stress.", "choices": null, "id": "eng_0330", "kind": "concept", "lang": "en", "question": "What is annealing?", "steps": ["Heat up.", "Cool slow.", "Ductile again."], "subject": "engineering", "text": "Answer: Soften by heat.\nSteps:\n1. Heat up.\n2. Cool slow.\n3. Ductile again.", "topic": "materials"}
{"answer": "A pin gives two reaction components while a roller gives one normal to the surface.", "choices": null, "id": "eng_0331", "kind": "concept", "lang": "en", "question": "How do pin and roller supports differ?", "steps": ["Pin fixes x,y.", "Roller normal.", "Moments free."], "subject": "engineering", "text": "Answer: Two versus one.\nSteps:\n1. Pin fixes x,y.\n2. Roller normal.\n3. Moments free.", "topic": "statics"}
{"answer": "The new volume is 14 m³.", "choices": null, "id": "eng_0332", "kind": "worked_example", "lang": "en", "question": "Gas 3 m³ at 300 K warms to 1400 K at constant pressure. What is the new volume?", "steps": ["V1 = 3 m³, T1 = 300 K.", "V2 = 3×1400/300 = 14 m³.", "Result 14 m³."], "subject": "engineering", "text": "Answer: 14 m³.\nSteps:\n1. V1 = 3 m³, T1 = 300 K.\n2. V2 = 3×1400/300 = 14 m³.\n3. Result 14 m³.", "topic": "thermodynamics"}
{"answer": "The power lost is 480 W.", "choices": null, "id": "eng_0333", "kind": "worked_example", "lang": "en", "question": "Current 2 A through 120 Ω. What power is lost?", "steps": ["I = 2 A, R = 120 Ω.", "P = I²R = 480 W.", "Result 480 W."], "subject": "engineering", "text": "Answer: 480 W.\nSteps:\n1. I = 2 A, R = 120 Ω.\n2. P = I²R = 480 W.\n3. Result 480 W.", "topic": "circuits"}
{"answer": "The D output is 44 V.", "choices": null, "id": "eng_0334", "kind": "worked_example", "lang": "en", "question": "Error jumps 0 to 220 units in 2 s with Kd = 0.4 s. What is the D output?", "steps": ["Slope = 220/2 units/s.", "u = 0.4×slope = 44 V.", "Result 44 V."], "subject": "engineering", "text": "Answer: 44 V.\nSteps:\n1. Slope = 220/2 units/s.\n2. u = 0.4×slope = 44 V.\n3. Result 44 V.", "topic": "control"}
{"answer": "The exit velocity is 20 m/s.", "choices": null, "id": "eng_0335", "kind": "worked_example", "lang": "en", "question": "Tank head 20 m (take g = 10 m/s²). What is the Torricelli velocity?", "steps": ["h = 20 m, g = 10 m/s².", "v = √(2gh) = 20 m/s.", "Result 20 m/s."], "subject": "engineering", "text": "Answer: 20 m/s.\nSteps:\n1. h = 20 m, g = 10 m/s².\n2. v = √(2gh) = 20 m/s.\n3. Result 20 m/s.", "topic": "fluids"}
{"answer": "Estimated strength is 1820 MPa.", "choices": null, "id": "eng_0336", "kind": "worked_example", "lang": "en", "question": "Steel hardness 520 HB. Estimate tensile strength (UTS ≈ 3.5·HB).", "steps": ["Hardness = 520 HB.", "UTS ≈ 3.5×520 = 1820 MPa.", "Result 1820 MPa."], "subject": "engineering", "text": "Answer: 1820 MPa.\nSteps:\n1. Hardness = 520 HB.\n2. UTS ≈ 3.5×520 = 1820 MPa.\n3. Result 1820 MPa.", "topic": "materials"}
{"answer": "The horizontal component is 780 N.", "choices": null, "id": "eng_0337", "kind": "worked_example", "lang": "en", "question": "Force 1300 N pulls at a 3-4-5 angle. What is the horizontal component?", "steps": ["F = 1300 N, cos = 3/5.", "Fx = 0.6×1300 = 780 N.", "Result 780 N."], "subject": "engineering", "text": "Answer: 780 N.\nSteps:\n1. F = 1300 N, cos = 3/5.\n2. Fx = 0.6×1300 = 780 N.\n3. Result 780 N.", "topic": "statics"}
{"answer": "Absolute zero is 0 K, the coldest limit where molecular motion is minimal.", "choices": null, "id": "eng_0338", "kind": "concept", "lang": "en", "question": "What is absolute zero?", "steps": ["Minus 273 C.", "Unreachable limit.", "Entropy base."], "subject": "engineering", "text": "Answer: Zero kelvin.\nSteps:\n1. Minus 273 C.\n2. Unreachable limit.\n3. Entropy base.", "topic": "thermodynamics"}
{"answer": "Ekvivalent je 100 Ω.", "choices": {"A": "105 Ω", "B": "95 Ω", "C": "100 Ω", "D": "110 Ω"}, "id": "eng_0339", "kind": "multiple_choice", "lang": "cs", "question": "Dva odpory 200 Ω paralelně. Jaký je ekvivalent?", "steps": ["R = 200 Ω each.", "Req = R/2 = 100 Ω.", "Vyber možnost C (100 Ω)."], "subject": "engineering", "text": "Answer: 100 Ω.\nSteps:\n1. R = 200 Ω each.\n2. Req = R/2 = 100 Ω.\n3. Vyber možnost C (100 Ω).\nAnswer: (C)", "topic": "circuits"}
{"answer": "The closed-loop gain is 0.96.", "choices": null, "id": "eng_0340", "kind": "worked_example", "lang": "en", "question": "Unity feedback loop, forward gain 24. What is the closed-loop gain?", "steps": ["K = 24 (dimensionless).", "T = K/(1+K) = 0.96 (dimensionless).", "Result 0.96 (dimensionless)."], "subject": "engineering", "text": "Answer: 0.96 (dimensionless).\nSteps:\n1. K = 24 (dimensionless).\n2. T = K/(1+K) = 0.96 (dimensionless).\n3. Result 0.96 (dimensionless).", "topic": "control"}
{"answer": "The mass flow is 22 kg/s.", "choices": null, "id": "eng_0341", "kind": "worked_example", "lang": "en", "question": "Water flows 22 L/s. What is the mass flow in kg/s?", "steps": ["Q = 22 L/s, ρ = 1000 kg/m³.", "ṁ = 22 kg/s.", "Result 22 kg/s."], "subject": "engineering", "text": "Answer: 22 kg/s.\nSteps:\n1. Q = 22 L/s, ρ = 1000 kg/m³.\n2. ṁ = 22 kg/s.\n3. Result 22 kg/s.", "topic": "fluids"}
{"answer": "Napětí je 190 MPa.", "choices": {"A": "180 MPa", "B": "190 MPa", "C": "200 MPa", "D": "210 MPa"}, "id": "eng_0342", "kind": "multiple_choice", "lang": "cs", "question": "Ocel (E = 200 GPa) při deformaci 950 mikrostrainu. Jaké je napětí?", "steps": ["E = 200 GPa, ε = 950 microstrain.", "σ = Eε = 190 MPa.", "Vyber možnost B (190 MPa)."], "subject": "engineering", "text": "Answer: 190 MPa.\nSteps:\n1. E = 200 GPa, ε = 950 microstrain.\n2. σ = Eε = 190 MPa.\n3. Vyber možnost B (190 MPa).\nAnswer: (B)", "topic": "materials"}
{"answer": "Svislá složka je 1080 N.", "choices": null, "id": "eng_0343", "kind": "worked_example", "lang": "cs", "question": "Síla 1350 N táhne pod úhlem 3-4-5. Jaká je svislá složka?", "steps": ["F = 1350 N, sin = 4/5.", "Fy = 0.8×1350 = 1080 N.", "Result 1080 N."], "subject": "engineering", "text": "Answer: 1080 N.\nSteps:\n1. F = 1350 N, sin = 4/5.\n2. Fy = 0.8×1350 = 1080 N.\n3. Result 1080 N.", "topic": "statics"}
{"answer": "Carnotův cyklus je ideální vratný oběh s největší účinností.", "choices": null, "id": "eng_0344", "kind": "concept", "lang": "cs", "question": "Co je Carnotův cyklus?", "steps": ["Dvě izotermy.", "Dvě adiabaty.", "Určuje limit."], "subject": "engineering", "text": "Answer: Ideální maximum.\nSteps:\n1. Dvě izotermy.\n2. Dvě adiabaty.\n3. Určuje limit.", "topic": "thermodynamics"}
{"answer": "The current is 26 A.", "choices": null, "id": "eng_0345", "kind": "worked_example", "lang": "en", "question": "Voltage 156 V across 6 Ω. What is the current?", "steps": ["V = 156 V, R = 6 Ω.", "I = V/R = 26 A.", "Result 26 A."], "subject": "engineering", "text": "Answer: 26 A.\nSteps:\n1. V = 156 V, R = 6 Ω.\n2. I = V/R = 26 A.\n3. Result 26 A.", "topic": "circuits"}
{"answer": "Časová konstanta je čas k 63 procentům skokové odezvy.", "choices": null, "id": "eng_0346", "kind": "concept", "lang": "cs", "question": "Co je časová konstanta?", "steps": ["Tau v s.", "Značka tau.", "Měřítko rychlosti."], "subject": "engineering", "text": "Answer: Čas 63 procent.\nSteps:\n1. Tau v s.\n2. Značka tau.\n3. Měřítko rychlosti.", "topic": "control"}
{"answer": "Vztlak je 206010 N.", "choices": {"A": "196200 N", "B": "215820 N", "C": "225630 N", "D": "206010 N"}, "id": "eng_0347", "kind": "multiple_choice", "lang": "cs", "question": "Trup vytlačí 21 m³ vody. Jaký je vztlak?", "steps": ["V = 21 m³, ρ = 1000 kg/m³.", "F = ρgV = 206010 N.", "Vyber možnost D (206010 N)."], "subject": "engineering", "text": "Answer: 206010 N.\nSteps:\n1. V = 21 m³, ρ = 1000 kg/m³.\n2. F = ρgV = 206010 N.\n3. Vyber možnost D (206010 N).\nAnswer: (D)", "topic": "fluids"}
{"answer": "The mass is 180.55 kg.", "choices": null, "id": "eng_0348", "kind": "worked_example", "lang": "en", "question": "Steel part volume 0.023 m³ (ρ = 7850 kg/m³). What is its mass?", "steps": ["V = 0.023 m³, ρ = 7850 kg/m³.", "m = ρV = 180.55 kg.", "Result 180.55 kg."], "subject": "engineering", "text": "Answer: 180.55 kg.\nSteps:\n1. V = 0.023 m³, ρ = 7850 kg/m³.\n2. m = ρV = 180.55 kg.\n3. Result 180.55 kg.", "topic": "materials"}
{"answer": "The method of joints solves truss member forces joint by joint with equilibrium.", "choices": null, "id": "eng_0349", "kind": "concept", "lang": "en", "question": "What is the method of joints?", "steps": ["Isolate joint.", "Sum Fx,Fy zero.", "Find members."], "subject": "engineering", "text": "Answer: Joint by joint.\nSteps:\n1. Isolate joint.\n2. Sum Fx,Fy zero.\n3. Find members.", "topic": "statics"}
{"answer": "Tlak je 2500 kPa.", "choices": null, "id": "eng_0350", "kind": "worked_example", "lang": "cs", "question": "Plyn 25 m³ při 100 kPa se stlačí na 1 m³ za stálé teploty. Jaký je tlak?", "steps": ["p1 = 100 kPa, V1 = 25 m³.", "p2 = 100×25 = 2500 kPa.", "Result 2500 kPa."], "subject": "engineering", "text": "Answer: 2500 kPa.\nSteps:\n1. p1 = 100 kPa, V1 = 25 m³.\n2. p2 = 100×25 = 2500 kPa.\n3. Result 2500 kPa.", "topic": "thermodynamics"}
{"answer": "Impedance is AC resistance with magnitude and phase, in ohms.", "choices": null, "id": "eng_0351", "kind": "concept", "lang": "en", "question": "What is impedance?", "steps": ["Resistor part.", "Reactance part.", "Phase shifts."], "subject": "engineering", "text": "Answer: AC ohms.\nSteps:\n1. Resistor part.\n2. Reactance part.\n3. Phase shifts.", "topic": "circuits"}
{"answer": "Celkové zesílení je 44.", "choices": {"A": "42 (dimensionless)", "B": "46 (dimensionless)", "C": "48 (dimensionless)", "D": "44 (dimensionless)"}, "id": "eng_0352", "kind": "multiple_choice", "lang": "cs", "question": "Dva sériové bloky mají zesílení 2 a 22. Jaké je celkové zesílení?", "steps": ["K1 = 2, K2 = 22 (dimensionless).", "K = 44 (dimensionless).", "Vyber možnost D (44 (dimensionless))."], "subject": "engineering", "text": "Answer: 44 (dimensionless).\nSteps:\n1. K1 = 2, K2 = 22 (dimensionless).\n2. K = 44 (dimensionless).\n3. Vyber možnost D (44 (dimensionless)).\nAnswer: (D)", "topic": "control"}
{"answer": "Dynamický tlak je 7935 Pa.", "choices": null, "id": "eng_0353", "kind": "worked_example", "lang": "cs", "question": "Vzduch (ρ = 1,2 kg/m³) letí 115 m/s. Jaký je dynamický tlak?", "steps": ["ρ = 1.2 kg/m³, v = 115 m/s.", "q = ½ρv² = 7935 Pa.", "Result 7935 Pa."], "subject": "engineering", "text": "Answer: 7935 Pa.\nSteps:\n1. ρ = 1.2 kg/m³, v = 115 m/s.\n2. q = ½ρv² = 7935 Pa.\n3. Result 7935 Pa.", "topic": "fluids"}
{"answer": "The modulus is 121.2 GPa.", "choices": null, "id": "eng_0354", "kind": "worked_example", "lang": "en", "question": "Composite with fibre fraction 0.6 (Ef = 200 GPa, Em = 3 GPa). What is the modulus?", "steps": ["Vf = 0.6, Ef = 200 GPa.", "E = VfEf+VmEm = 121.2 GPa.", "Result 121.2 GPa."], "subject": "engineering", "text": "Answer: 121.2 GPa.\nSteps:\n1. Vf = 0.6, Ef = 200 GPa.\n2. E = VfEf+VmEm = 121.2 GPa.\n3. Result 121.2 GPa.", "topic": "materials"}
{"answer": "Max friction is 950 N.", "choices": {"A": "1000 N", "B": "950 N", "C": "900 N", "D": "1050 N"}, "id": "eng_0355", "kind": "multiple_choice", "lang": "en", "question": "Normal force 1900 N, friction coefficient 0.5. What is max friction?", "steps": ["μ = 0.5 (dimensionless), N = 1900 N.", "F = μN = 950 N.", "Select option B (950 N)."], "subject": "engineering", "text": "Answer: 950 N.\nSteps:\n1. μ = 0.5 (dimensionless), N = 1900 N.\n2. F = μN = 950 N.\n3. Select option B (950 N).\nAnswer: (B)", "topic": "statics"}
{"answer": "Měrná kapacita je teplo na kilogram a kelvin, v joulech.", "choices": null, "id": "eng_0356", "kind": "concept", "lang": "cs", "question": "Co je měrná tepelná kapacita?", "steps": ["Hmotnost v kg.", "Delta T v K.", "Q v J."], "subject": "engineering", "text": "Answer: Teplo na kg K.\nSteps:\n1. Hmotnost v kg.\n2. Delta T v K.\n3. Q v J.", "topic": "thermodynamics"}
{"answer": "Resonance is the frequency where inductive and capacitive reactances cancel.", "choices": null, "id": "eng_0357", "kind": "concept", "lang": "en", "question": "What is resonance?", "steps": ["Peak current.", "Tuned Hz.", "Radio uses."], "subject": "engineering", "text": "Answer: Reactances cancel.\nSteps:\n1. Peak current.\n2. Tuned Hz.\n3. Radio uses.", "topic": "circuits"}
{"answer": "The error is 125 units.", "choices": null, "id": "eng_0358", "kind": "worked_example", "lang": "en", "question": "Setpoint 1250 units, measurement 1125 units. What is the error?", "steps": ["r = 1250 units, y = 1125 units.", "e = r−y = 125 units.", "Result 125 units."], "subject": "engineering", "text": "Answer: 125 units.\nSteps:\n1. r = 1250 units, y = 1125 units.\n2. e = r−y = 125 units.\n3. Result 125 units.", "topic": "control"}
{"answer": "The volume is 50 m³.", "choices": null, "id": "eng_0359", "kind": "worked_example", "lang": "en", "question": "Tank base area 2 m², depth 25 m. What is the water volume?", "steps": ["A = 2 m², h = 25 m.", "V = Ah = 50 m³.", "Result 50 m³."], "subject": "engineering", "text": "Answer: 50 m³.\nSteps:\n1. A = 2 m², h = 25 m.\n2. V = Ah = 50 m³.\n3. Result 50 m³.", "topic": "fluids"}
{"answer": "The shear stress is 104 MPa.", "choices": null, "id": "eng_0360", "kind": "worked_example", "lang": "en", "question": "Shear force 52 kN on 500 mm² section. What is the shear stress?", "steps": ["F = 52 kN, A = 500 mm².", "τ = F/A = 104 MPa.", "Result 104 MPa."], "subject": "engineering", "text": "Answer: 104 MPa.\nSteps:\n1. F = 52 kN, A = 500 mm².\n2. τ = F/A = 104 MPa.\n3. Result 104 MPa.", "topic": "materials"}
{"answer": "The balancing reaction is 1150 N upward.", "choices": {"A": "1200 N", "B": "1100 N", "C": "1150 N", "D": "1250 N"}, "id": "eng_0361", "kind": "multiple_choice", "lang": "en", "question": "Downward forces 460 N and 690 N act on a beam. What upward reaction balances them?", "steps": ["F1 = 460 N, F2 = 690 N.", "R = 460+690 = 1150 N.", "Select option C (1150 N)."], "subject": "engineering", "text": "Answer: 1150 N.\nSteps:\n1. F1 = 460 N, F2 = 690 N.\n2. R = 460+690 = 1150 N.\n3. Select option C (1150 N).\nAnswer: (C)", "topic": "statics"}
{"answer": "The temperature is 267 °C.", "choices": null, "id": "eng_0362", "kind": "worked_example", "lang": "en", "question": "Temperature is 540 K. What is it in Celsius?", "steps": ["T = 540 K.", "C = 540 − 273 = 267 °C.", "Result 267 °C."], "subject": "engineering", "text": "Answer: 267 °C.\nSteps:\n1. T = 540 K.\n2. C = 540 − 273 = 267 °C.\n3. Result 267 °C.", "topic": "thermodynamics"}
{"answer": "The resistance is 29 Ω.", "choices": null, "id": "eng_0363", "kind": "worked_example", "lang": "en", "question": "Voltage 87 V drives 3 A. What is the resistance?", "steps": ["V = 87 V, I = 3 A.", "R = V/I = 29 Ω.", "Result 29 Ω."], "subject": "engineering", "text": "Answer: 29 Ω.\nSteps:\n1. V = 87 V, I = 3 A.\n2. R = V/I = 29 Ω.\n3. Result 29 Ω.", "topic": "circuits"}
{"answer": "The final value is 78 units.", "choices": null, "id": "eng_0364", "kind": "worked_example", "lang": "en", "question": "Gain 26 system gets a step of amplitude 3. What is the final value?", "steps": ["K = 26 (dimensionless), step 3 units.", "Final = 3×26 = 78 units.", "Result 78 units."], "subject": "engineering", "text": "Answer: 78 units.\nSteps:\n1. K = 26 (dimensionless), step 3 units.\n2. Final = 3×26 = 78 units.\n3. Result 78 units.", "topic": "control"}
{"answer": "Hydraulic power is 5493.6 W.", "choices": null, "id": "eng_0365", "kind": "worked_example", "lang": "en", "question": "Pump lifts 0.02 m³/s of water 28 m. What hydraulic power is needed?", "steps": ["Q = 0.02 m³/s, H = 28 m.", "P = ρgQH = 5493.6 W.", "Result 5493.6 W."], "subject": "engineering", "text": "Answer: 5493.6 W.\nSteps:\n1. Q = 0.02 m³/s, H = 28 m.\n2. P = ρgQH = 5493.6 W.\n3. Result 5493.6 W.", "topic": "fluids"}
{"answer": "Elongation is 10 mm.", "choices": {"A": "11 mm", "B": "9 mm", "C": "10 mm", "D": "12 mm"}, "id": "eng_0366", "kind": "multiple_choice", "lang": "en", "question": "Force 100 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation?", "steps": ["F = 100 kN, L = 2 m.", "ΔL = FL/AE = 10 mm.", "Select option C (10 mm)."], "subject": "engineering", "text": "Answer: 10 mm.\nSteps:\n1. F = 100 kN, L = 2 m.\n2. ΔL = FL/AE = 10 mm.\n3. Select option C (10 mm).\nAnswer: (C)", "topic": "materials"}
{"answer": "Reakce v B je 2800 N.", "choices": null, "id": "eng_0367", "kind": "worked_example", "lang": "cs", "question": "Nosník 6 m, břemeno 4200 N ve 4 m od A. Jaká je reakce v B?", "steps": ["F = 4200 N, span 6 m.", "RB = 4200×4/6 = 2800 N.", "Result 2800 N."], "subject": "engineering", "text": "Answer: 2800 N.\nSteps:\n1. F = 4200 N, span 6 m.\n2. RB = 4200×4/6 = 2800 N.\n3. Result 2800 N.", "topic": "statics"}
{"answer": "Internal energy rises 125 kJ.", "choices": {"A": "130 kJ", "B": "120 kJ", "C": "135 kJ", "D": "125 kJ"}, "id": "eng_0368", "kind": "multiple_choice", "lang": "en", "question": "System gains 240 kJ of heat and does 115 kJ of work. What is internal energy change?", "steps": ["Q = 240 kJ, W = 115 kJ.", "ΔU = Q−W = 125 kJ.", "Select option D (125 kJ)."], "subject": "engineering", "text": "Answer: 125 kJ.\nSteps:\n1. Q = 240 kJ, W = 115 kJ.\n2. ΔU = Q−W = 125 kJ.\n3. Select option D (125 kJ).\nAnswer: (D)", "topic": "thermodynamics"}
{"answer": "Elektrický výkon je napětí krát proud, měří se ve wattech.", "choices": null, "id": "eng_0369", "kind": "concept", "lang": "cs", "question": "Co je elektrický výkon?", "steps": ["Volty krát ampéry.", "Watty ven.", "Teplo či práce."], "subject": "engineering", "text": "Answer: U krát I.\nSteps:\n1. Volty krát ampéry.\n2. Watty ven.\n3. Teplo či práce.", "topic": "circuits"}
{"answer": "Settling time is about 81 s.", "choices": null, "id": "eng_0370", "kind": "worked_example", "lang": "en", "question": "Time constant 27 s. What is 5% settling time?", "steps": ["τ = 27 s.", "ts ≈ 3τ = 81 s.", "Result 81 s."], "subject": "engineering", "text": "Answer: 81 s.\nSteps:\n1. τ = 27 s.\n2. ts ≈ 3τ = 81 s.\n3. Result 81 s.", "topic": "control"}
{"answer": "Gauge pressure is 215.82 kPa.", "choices": {"A": "215.82 kPa", "B": "210.82 kPa", "C": "220.82 kPa", "D": "225.82 kPa"}, "id": "eng_0371", "kind": "multiple_choice", "lang": "en", "question": "Water depth is 22 m. What is gauge pressure?", "steps": ["ρ = 1000 kg/m³, h = 22 m.", "p = ρgh = 215.82 kPa.", "Select option A (215.82 kPa)."], "subject": "engineering", "text": "Answer: 215.82 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 22 m.\n2. p = ρgh = 215.82 kPa.\n3. Select option A (215.82 kPa).\nAnswer: (A)", "topic": "fluids"}
{"answer": "The factor of safety is 4.", "choices": {"A": "4.5 (dimensionless)", "B": "3.5 (dimensionless)", "C": "5 (dimensionless)", "D": "4 (dimensionless)"}, "id": "eng_0372", "kind": "multiple_choice", "lang": "en", "question": "Yield 300 MPa, working stress 75 MPa. What is the factor of safety?", "steps": ["σy = 300 MPa, σw = 75 MPa.", "n = 4 (dimensionless).", "Select option D (4 (dimensionless))."], "subject": "engineering", "text": "Answer: 4 (dimensionless).\nSteps:\n1. σy = 300 MPa, σw = 75 MPa.\n2. n = 4 (dimensionless).\n3. Select option D (4 (dimensionless)).\nAnswer: (D)", "topic": "materials"}
{"answer": "Each end reaction is 1600 N.", "choices": null, "id": "eng_0373", "kind": "worked_example", "lang": "en", "question": "Uniform beam weighs 3200 N over 8 m. What is each end reaction?", "steps": ["W = 3200 N, midspan 4 m.", "R = W/2 = 1600 N.", "Result 1600 N."], "subject": "engineering", "text": "Answer: 1600 N.\nSteps:\n1. W = 3200 N, midspan 4 m.\n2. R = W/2 = 1600 N.\n3. Result 1600 N.", "topic": "statics"}
{"answer": "The specific volume is 13 m³/kg.", "choices": null, "id": "eng_0374", "kind": "worked_example", "lang": "en", "question": "Gas fills 52 m³ with mass 4 kg. What is the specific volume?", "steps": ["V = 52 m³, m = 4 kg.", "v = V/m = 13 m³/kg.", "Result 13 m³/kg."], "subject": "engineering", "text": "Answer: 13 m³/kg.\nSteps:\n1. V = 52 m³, m = 4 kg.\n2. v = V/m = 13 m³/kg.\n3. Result 13 m³/kg.", "topic": "thermodynamics"}
{"answer": "The tap voltage is 31 V.", "choices": null, "id": "eng_0375", "kind": "worked_example", "lang": "en", "question": "Divider with two 1000 Ω resistors fed 62 V. What is the tap voltage?", "steps": ["Vin = 62 V, halves.", "Vout = 31 V.", "Result 31 V."], "subject": "engineering", "text": "Answer: 31 V.\nSteps:\n1. Vin = 62 V, halves.\n2. Vout = 31 V.\n3. Result 31 V.", "topic": "circuits"}
{"answer": "The integral output is 135 V.", "choices": null, "id": "eng_0376", "kind": "worked_example", "lang": "en", "question": "Error 2 units lasts 135 s with Ki = 0.5 1/s. What is the integral output?", "steps": ["e = 2 units, t = 135 s.", "u = 0.5×2×135 = 135 V.", "Result 135 V."], "subject": "engineering", "text": "Answer: 135 V.\nSteps:\n1. e = 2 units, t = 135 s.\n2. u = 0.5×2×135 = 135 V.\n3. Result 135 V.", "topic": "control"}
{"answer": "Base pressure is 284.49 kPa.", "choices": null, "id": "eng_0377", "kind": "worked_example", "lang": "en", "question": "Still water column 29 m high. What is pressure at the base?", "steps": ["ρ = 1000 kg/m³, h = 29 m.", "p = ρgh = 284.49 kPa.", "Result 284.49 kPa."], "subject": "engineering", "text": "Answer: 284.49 kPa.\nSteps:\n1. ρ = 1000 kg/m³, h = 29 m.\n2. p = ρgh = 284.49 kPa.\n3. Result 284.49 kPa.", "topic": "fluids"}
{"answer": "A composite mixes stiff fibers in a matrix for tailored strength and lightness.", "choices": null, "id": "eng_0378", "kind": "concept", "lang": "en", "question": "What is a composite material?", "steps": ["Carbon epoxy.", "Glass boats.", "Rule blends."], "subject": "engineering", "text": "Answer: Fibers in matrix.\nSteps:\n1. Carbon epoxy.\n2. Glass boats.\n3. Rule blends.", "topic": "materials"}
{"answer": "Zero-force members carry no load when a joint has only two non-collinear members unloaded.", "choices": null, "id": "eng_0379", "kind": "concept", "lang": "en", "question": "What characterizes zero-force members?", "steps": ["Two members.", "No load.", "Both zero."], "subject": "engineering", "text": "Answer: Unloaded pair.\nSteps:\n1. Two members.\n2. No load.\n3. Both zero.", "topic": "statics"}
{"answer": "The power is 1400 W.", "choices": null, "id": "eng_0380", "kind": "worked_example", "lang": "en", "question": "Work 14000 J is done in 10 s. What is the power?", "steps": ["W = 14000 J, t = 10 s.", "P = W/t = 1400 W.", "Result 1400 W."], "subject": "engineering", "text": "Answer: 1400 W.\nSteps:\n1. W = 14000 J, t = 10 s.\n2. P = W/t = 1400 W.\n3. Result 1400 W.", "topic": "thermodynamics"}
{"answer": "Energy used is 2100 Wh.", "choices": {"A": "2000 Wh", "B": "2200 Wh", "C": "2150 Wh", "D": "2100 Wh"}, "id": "eng_0381", "kind": "multiple_choice", "lang": "en", "question": "A 1050 W bulb burns 2 h. How much energy is used?", "steps": ["P = 1050 W, t = 2 h.", "E = Pt = 2100 Wh.", "Select option D (2100 Wh)."], "subject": "engineering", "text": "Answer: 2100 Wh.\nSteps:\n1. P = 1050 W, t = 2 h.\n2. E = Pt = 2100 Wh.\n3. Select option D (2100 Wh).\nAnswer: (D)", "topic": "circuits"}
{"answer": "The steady value is 105 units.", "choices": {"A": "105 units", "B": "100 units", "C": "110 units", "D": "115 units"}, "id": "eng_0382", "kind": "multiple_choice", "lang": "en", "question": "System K/(10s+1) with K = 105 gets a unit step. What is the steady value?", "steps": ["DC gain K = 105 (dimensionless).", "Step final = 105 units.", "Select option A (105 units)."], "subject": "engineering", "text": "Answer: 105 units.\nSteps:\n1. DC gain K = 105 (dimensionless).\n2. Step final = 105 units.\n3. Select option A (105 units).\nAnswer: (A)", "topic": "control"}
{"answer": "Flow is treated compressible when speed nears sound speed or density shifts matter.", "choices": null, "id": "eng_0383", "kind": "concept", "lang": "en", "question": "When is flow treated compressible?", "steps": ["Mach over 0.3.", "Density moves.", "Air fast."], "subject": "engineering", "text": "Answer: Near sound speed.\nSteps:\n1. Mach over 0.3.\n2. Density moves.\n3. Air fast.", "topic": "fluids"}
{"answer": "Teplotní napětí je 324 MPa.", "choices": null, "id": "eng_0384", "kind": "worked_example", "lang": "cs", "question": "Ocelová tyč (E = 200 GPa, α = 12e-6/K) chladne o 135 K vetknutá. Jaké vznikne napětí?", "steps": ["E = 200 GPa, ΔT = 135 K.", "σ = EαΔT = 324 MPa.", "Result 324 MPa."], "subject": "engineering", "text": "Answer: 324 MPa.\nSteps:\n1. E = 200 GPa, ΔT = 135 K.\n2. σ = EαΔT = 324 MPa.\n3. Result 324 MPa.", "topic": "materials"}
{"answer": "The couple moment is 720 N·m.", "choices": {"A": "750 N·m", "B": "690 N·m", "C": "780 N·m", "D": "720 N·m"}, "id": "eng_0385", "kind": "multiple_choice", "lang": "en", "question": "A couple has forces 240 N spaced 3 m apart. What is its moment?", "steps": ["F = 240 N, d = 3 m.", "M = Fd = 720 N·m.", "Select option D (720 N·m)."], "subject": "engineering", "text": "Answer: 720 N·m.\nSteps:\n1. F = 240 N, d = 3 m.\n2. M = Fd = 720 N·m.\n3. Select option D (720 N·m).\nAnswer: (D)", "topic": "statics"}
{"answer": "The temperature is 393 K.", "choices": {"A": "393 K", "B": "388 K", "C": "398 K", "D": "403 K"}, "id": "eng_0386", "kind": "multiple_choice", "lang": "en", "question": "Temperature is 120 °C. What is it in kelvin?", "steps": ["T = 120 °C.", "K = 120 + 273 = 393 K.", "Select option A (393 K)."], "subject": "engineering", "text": "Answer: 393 K.\nSteps:\n1. T = 120 °C.\n2. K = 120 + 273 = 393 K.\n3. Select option A (393 K).\nAnswer: (A)", "topic": "thermodynamics"}
{"answer": "Napětí je 264 V.", "choices": {"A": "264 V", "B": "252 V", "C": "276 V", "D": "288 V"}, "id": "eng_0387", "kind": "multiple_choice", "lang": "cs", "question": "Proud 22 A teče odporem 12 Ω. Jaké je napětí?", "steps": ["I = 22 A, R = 12 Ω.", "V = IR = 264 V.", "Vyber možnost A (264 V)."], "subject": "engineering", "text": "Answer: 264 V.\nSteps:\n1. I = 22 A, R = 12 Ω.\n2. V = IR = 264 V.\n3. Vyber možnost A (264 V).\nAnswer: (A)", "topic": "circuits"}
{"answer": "Gain margin is how much gain can rise before instability, in decibels.", "choices": null, "id": "eng_0388", "kind": "concept", "lang": "en", "question": "What is gain margin?", "steps": ["dB headroom.", "Phase 180 mark.", "Bigger safer."], "subject": "engineering", "text": "Answer: Room to grow.\nSteps:\n1. dB headroom.\n2. Phase 180 mark.\n3. Bigger safer.", "topic": "control"}
{"answer": "The exit velocity is 30 m/s.", "choices": null, "id": "eng_0389", "kind": "worked_example", "lang": "en", "question": "Tank head 45 m (take g = 10 m/s²). What is the Torricelli velocity?", "steps": ["h = 45 m, g = 10 m/s².", "v = √(2gh) = 30 m/s.", "Result 30 m/s."], "subject": "engineering", "text": "Answer: 30 m/s.\nSteps:\n1. h = 45 m, g = 10 m/s².\n2. v = √(2gh) = 30 m/s.\n3. Result 30 m/s.", "topic": "fluids"}
{"answer": "Transverse strain is -1860 microstrain.", "choices": null, "id": "eng_0390", "kind": "worked_example", "lang": "en", "question": "Bar stretches 6200 microstrain, Poisson ratio 0.3. What is transverse strain?", "steps": ["εa = 6200 microstrain, ν = 0.3.", "εt = −νεa = -1860 microstrain.", "Result -1860 microstrain."], "subject": "engineering", "text": "Answer: -1860 microstrain.\nSteps:\n1. εa = 6200 microstrain, ν = 0.3.\n2. εt = −νεa = -1860 microstrain.\n3. Result -1860 microstrain.", "topic": "materials"}
{"answer": "A statically determinate structure solves reactions from equilibrium equations alone.", "choices": null, "id": "eng_0391", "kind": "concept", "lang": "en", "question": "What is a statically determinate structure?", "steps": ["Count unknowns.", "Match equations.", "No deformation."], "subject": "engineering", "text": "Answer: Equilibrium suffices.\nSteps:\n1. Count unknowns.\n2. Match equations.\n3. No deformation.", "topic": "statics"}
{"answer": "The efficiency is 37%.", "choices": null, "id": "eng_0392", "kind": "worked_example", "lang": "en", "question": "Engine turns 370 J of 1000 J heat into work. What is the efficiency?", "steps": ["W = 370 J, Q = 1000 J.", "η = W/Q = 37%.", "Result 37%."], "subject": "engineering", "text": "Answer: 37%.\nSteps:\n1. W = 370 J, Q = 1000 J.\n2. η = W/Q = 37%.\n3. Result 37%.", "topic": "thermodynamics"}
{"answer": "The leaving current is 32 A.", "choices": null, "id": "eng_0393", "kind": "worked_example", "lang": "en", "question": "Currents 2 A and 30 A enter a node. What current leaves?", "steps": ["I1 = 2 A, I2 = 30 A.", "I3 = 32 A.", "Result 32 A."], "subject": "engineering", "text": "Answer: 32 A.\nSteps:\n1. I1 = 2 A, I2 = 30 A.\n2. I3 = 32 A.\n3. Result 32 A.", "topic": "circuits"}
{"answer": "Saturation caps actuator output, stalling control effort at a limit.", "choices": null, "id": "eng_0394", "kind": "concept", "lang": "en", "question": "What is actuator saturation?", "steps": ["Valve full open.", "Motor max volts.", "Windup risk."], "subject": "engineering", "text": "Answer: Capped effort.\nSteps:\n1. Valve full open.\n2. Motor max volts.\n3. Windup risk.", "topic": "control"}
{"answer": "The mass flow is 28 kg/s.", "choices": null, "id": "eng_0395", "kind": "worked_example", "lang": "en", "question": "Water flows 28 L/s. What is the mass flow in kg/s?", "steps": ["Q = 28 L/s, ρ = 1000 kg/m³.", "ṁ = 28 kg/s.", "Result 28 kg/s."], "subject": "engineering", "text": "Answer: 28 kg/s.\nSteps:\n1. Q = 28 L/s, ρ = 1000 kg/m³.\n2. ṁ = 28 kg/s.\n3. Result 28 kg/s.", "topic": "fluids"}
{"answer": "The stress is 220 MPa.", "choices": {"A": "220 MPa", "B": "210 MPa", "C": "230 MPa", "D": "240 MPa"}, "id": "eng_0396", "kind": "multiple_choice", "lang": "en", "question": "Tensile force 22 kN on 100 mm² bar. What is the stress?", "steps": ["F = 22 kN, A = 100 mm².", "σ = F/A = 220 MPa.", "Select option A (220 MPa)."], "subject": "engineering", "text": "Answer: 220 MPa.\nSteps:\n1. F = 22 kN, A = 100 mm².\n2. σ = F/A = 220 MPa.\n3. Select option A (220 MPa).\nAnswer: (A)", "topic": "materials"}
{"answer": "The resultant is 1050 N.", "choices": {"A": "1050 N", "B": "1000 N", "C": "1100 N", "D": "1150 N"}, "id": "eng_0397", "kind": "multiple_choice", "lang": "en", "question": "Forces 630 N east and 840 N north act on a bolt. What is the resultant?", "steps": ["Fx = 630 N, Fy = 840 N.", "R = √(630²+840²) = 1050 N.", "Select option A (1050 N)."], "subject": "engineering", "text": "Answer: 1050 N.\nSteps:\n1. Fx = 630 N, Fy = 840 N.\n2. R = √(630²+840²) = 1050 N.\n3. Select option A (1050 N).\nAnswer: (A)", "topic": "statics"}
{"answer": "Heat moves by conduction through solids, convection in fluids, and radiation by waves.", "choices": null, "id": "eng_0398", "kind": "concept", "lang": "en", "question": "What are the heat transfer modes?", "steps": ["Solid touch.", "Fluid carry.", "Wave shine."], "subject": "engineering", "text": "Answer: Conduction convection radiation.\nSteps:\n1. Solid touch.\n2. Fluid carry.\n3. Wave shine.", "topic": "thermodynamics"}
{"answer": "Superposition solves linear circuits by adding each source effect alone.", "choices": null, "id": "eng_0399", "kind": "concept", "lang": "en", "question": "What is superposition?", "steps": ["One source on.", "Others zeroed.", "Sum results."], "subject": "engineering", "text": "Answer: Add source effects.\nSteps:\n1. One source on.\n2. Others zeroed.\n3. Sum results.", "topic": "circuits"}
{"answer": "The D output is 56 V.", "choices": null, "id": "eng_0400", "kind": "worked_example", "lang": "en", "question": "Error jumps 0 to 280 units in 2 s with Kd = 0.4 s. What is the D output?", "steps": ["Slope = 280/2 units/s.", "u = 0.4×slope = 56 V.", "Result 56 V."], "subject": "engineering", "text": "Answer: 56 V.\nSteps:\n1. Slope = 280/2 units/s.\n2. u = 0.4×slope = 56 V.\n3. Result 56 V.", "topic": "control"}