data: 120 synthetic physics problems with explicit params; answers machine-verified before publish
349b94a verified | [ | |
| { | |
| "id": "kin-0", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 10.4 m/s and constant acceleration 2.4 m/s^2 for 10.4 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 10.4, | |
| "a": 2.4, | |
| "t": 10.4 | |
| }, | |
| "answer": 237.95, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 10.4*10.4 + 0.5*2.4*10.4^2 = 237.95 m" | |
| }, | |
| { | |
| "id": "kin-1", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 22.3 m/s and constant acceleration 6.8 m/s^2 for 5.7 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 22.3, | |
| "a": 6.8, | |
| "t": 5.7 | |
| }, | |
| "answer": 237.58, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 22.3*5.7 + 0.5*6.8*5.7^2 = 237.58 m" | |
| }, | |
| { | |
| "id": "kin-2", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 7.0 m/s and constant acceleration 3.6 m/s^2 for 4.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 7.0, | |
| "a": 3.6, | |
| "t": 4.3 | |
| }, | |
| "answer": 63.38, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 7.0*4.3 + 0.5*3.6*4.3^2 = 63.38 m" | |
| }, | |
| { | |
| "id": "kin-3", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 11.2 m/s and constant acceleration 5.4 m/s^2 for 7.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 11.2, | |
| "a": 5.4, | |
| "t": 7.3 | |
| }, | |
| "answer": 225.64, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 11.2*7.3 + 0.5*5.4*7.3^2 = 225.64 m" | |
| }, | |
| { | |
| "id": "kin-4", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 28.5 m/s and constant acceleration 3.8 m/s^2 for 7.9 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 28.5, | |
| "a": 3.8, | |
| "t": 7.9 | |
| }, | |
| "answer": 343.73, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 28.5*7.9 + 0.5*3.8*7.9^2 = 343.73 m" | |
| }, | |
| { | |
| "id": "kin-5", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 22.4 m/s and constant acceleration 7.5 m/s^2 for 4.2 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 22.4, | |
| "a": 7.5, | |
| "t": 4.2 | |
| }, | |
| "answer": 160.23, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 22.4*4.2 + 0.5*7.5*4.2^2 = 160.23 m" | |
| }, | |
| { | |
| "id": "kin-6", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 17.8 m/s and constant acceleration 5.0 m/s^2 for 4.1 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 17.8, | |
| "a": 5.0, | |
| "t": 4.1 | |
| }, | |
| "answer": 115.0, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 17.8*4.1 + 0.5*5.0*4.1^2 = 115.0 m" | |
| }, | |
| { | |
| "id": "kin-7", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 28.6 m/s and constant acceleration 2.7 m/s^2 for 9.4 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 28.6, | |
| "a": 2.7, | |
| "t": 9.4 | |
| }, | |
| "answer": 388.13, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 28.6*9.4 + 0.5*2.7*9.4^2 = 388.13 m" | |
| }, | |
| { | |
| "id": "kin-8", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 3.9 m/s and constant acceleration 9.0 m/s^2 for 11.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 3.9, | |
| "a": 9.0, | |
| "t": 11.3 | |
| }, | |
| "answer": 618.68, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 3.9*11.3 + 0.5*9.0*11.3^2 = 618.68 m" | |
| }, | |
| { | |
| "id": "kin-9", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 3.4 m/s and constant acceleration 2.5 m/s^2 for 9.5 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 3.4, | |
| "a": 2.5, | |
| "t": 9.5 | |
| }, | |
| "answer": 145.11, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 3.4*9.5 + 0.5*2.5*9.5^2 = 145.11 m" | |
| }, | |
| { | |
| "id": "kin-10", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 28.4 m/s and constant acceleration 6.2 m/s^2 for 6.8 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 28.4, | |
| "a": 6.2, | |
| "t": 6.8 | |
| }, | |
| "answer": 336.46, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 28.4*6.8 + 0.5*6.2*6.8^2 = 336.46 m" | |
| }, | |
| { | |
| "id": "kin-11", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 27.2 m/s and constant acceleration 1.7 m/s^2 for 7.5 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 27.2, | |
| "a": 1.7, | |
| "t": 7.5 | |
| }, | |
| "answer": 251.81, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 27.2*7.5 + 0.5*1.7*7.5^2 = 251.81 m" | |
| }, | |
| { | |
| "id": "kin-12", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 15.1 m/s and constant acceleration 1.7 m/s^2 for 9.8 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 15.1, | |
| "a": 1.7, | |
| "t": 9.8 | |
| }, | |
| "answer": 229.61, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 15.1*9.8 + 0.5*1.7*9.8^2 = 229.61 m" | |
| }, | |
| { | |
| "id": "kin-13", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 24.5 m/s and constant acceleration 1.2 m/s^2 for 4.7 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 24.5, | |
| "a": 1.2, | |
| "t": 4.7 | |
| }, | |
| "answer": 128.4, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 24.5*4.7 + 0.5*1.2*4.7^2 = 128.4 m" | |
| }, | |
| { | |
| "id": "kin-14", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 6.1 m/s and constant acceleration 2.7 m/s^2 for 10.1 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 6.1, | |
| "a": 2.7, | |
| "t": 10.1 | |
| }, | |
| "answer": 199.32, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 6.1*10.1 + 0.5*2.7*10.1^2 = 199.32 m" | |
| }, | |
| { | |
| "id": "kin-15", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 10.5 m/s and constant acceleration 1.6 m/s^2 for 2.5 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 10.5, | |
| "a": 1.6, | |
| "t": 2.5 | |
| }, | |
| "answer": 31.25, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 10.5*2.5 + 0.5*1.6*2.5^2 = 31.25 m" | |
| }, | |
| { | |
| "id": "kin-16", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 27.0 m/s and constant acceleration 5.7 m/s^2 for 10.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 27.0, | |
| "a": 5.7, | |
| "t": 10.3 | |
| }, | |
| "answer": 580.46, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 27.0*10.3 + 0.5*5.7*10.3^2 = 580.46 m" | |
| }, | |
| { | |
| "id": "kin-17", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 10.8 m/s and constant acceleration 8.0 m/s^2 for 4.0 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 10.8, | |
| "a": 8.0, | |
| "t": 4.0 | |
| }, | |
| "answer": 107.2, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 10.8*4.0 + 0.5*8.0*4.0^2 = 107.2 m" | |
| }, | |
| { | |
| "id": "kin-18", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 9.0 m/s and constant acceleration 6.1 m/s^2 for 5.8 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 9.0, | |
| "a": 6.1, | |
| "t": 5.8 | |
| }, | |
| "answer": 154.8, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 9.0*5.8 + 0.5*6.1*5.8^2 = 154.8 m" | |
| }, | |
| { | |
| "id": "kin-19", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 6.8 m/s and constant acceleration 6.5 m/s^2 for 3.9 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 6.8, | |
| "a": 6.5, | |
| "t": 3.9 | |
| }, | |
| "answer": 75.95, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 6.8*3.9 + 0.5*6.5*3.9^2 = 75.95 m" | |
| }, | |
| { | |
| "id": "kin-20", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 2.4 m/s and constant acceleration 3.2 m/s^2 for 10.0 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 2.4, | |
| "a": 3.2, | |
| "t": 10.0 | |
| }, | |
| "answer": 184.0, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 2.4*10.0 + 0.5*3.2*10.0^2 = 184.0 m" | |
| }, | |
| { | |
| "id": "kin-21", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 11.0 m/s and constant acceleration 2.5 m/s^2 for 7.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 11.0, | |
| "a": 2.5, | |
| "t": 7.3 | |
| }, | |
| "answer": 146.91, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 11.0*7.3 + 0.5*2.5*7.3^2 = 146.91 m" | |
| }, | |
| { | |
| "id": "kin-22", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 19.9 m/s and constant acceleration 1.5 m/s^2 for 2.1 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 19.9, | |
| "a": 1.5, | |
| "t": 2.1 | |
| }, | |
| "answer": 45.1, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 19.9*2.1 + 0.5*1.5*2.1^2 = 45.1 m" | |
| }, | |
| { | |
| "id": "kin-23", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 20.9 m/s and constant acceleration 8.7 m/s^2 for 2.9 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 20.9, | |
| "a": 8.7, | |
| "t": 2.9 | |
| }, | |
| "answer": 97.19, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 20.9*2.9 + 0.5*8.7*2.9^2 = 97.19 m" | |
| }, | |
| { | |
| "id": "kin-24", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 3.8 m/s and constant acceleration 7.6 m/s^2 for 2.2 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 3.8, | |
| "a": 7.6, | |
| "t": 2.2 | |
| }, | |
| "answer": 26.75, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 3.8*2.2 + 0.5*7.6*2.2^2 = 26.75 m" | |
| }, | |
| { | |
| "id": "kin-25", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 28.8 m/s and constant acceleration 5.2 m/s^2 for 3.6 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 28.8, | |
| "a": 5.2, | |
| "t": 3.6 | |
| }, | |
| "answer": 137.38, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 28.8*3.6 + 0.5*5.2*3.6^2 = 137.38 m" | |
| }, | |
| { | |
| "id": "kin-26", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 17.9 m/s and constant acceleration 4.2 m/s^2 for 2.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 17.9, | |
| "a": 4.2, | |
| "t": 2.3 | |
| }, | |
| "answer": 52.28, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 17.9*2.3 + 0.5*4.2*2.3^2 = 52.28 m" | |
| }, | |
| { | |
| "id": "kin-27", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 26.6 m/s and constant acceleration 5.5 m/s^2 for 4.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 26.6, | |
| "a": 5.5, | |
| "t": 4.3 | |
| }, | |
| "answer": 165.23, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 26.6*4.3 + 0.5*5.5*4.3^2 = 165.23 m" | |
| }, | |
| { | |
| "id": "kin-28", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 8.4 m/s and constant acceleration 6.7 m/s^2 for 10.2 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 8.4, | |
| "a": 6.7, | |
| "t": 10.2 | |
| }, | |
| "answer": 434.21, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 8.4*10.2 + 0.5*6.7*10.2^2 = 434.21 m" | |
| }, | |
| { | |
| "id": "kin-29", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 14.5 m/s and constant acceleration 1.3 m/s^2 for 7.6 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 14.5, | |
| "a": 1.3, | |
| "t": 7.6 | |
| }, | |
| "answer": 147.74, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 14.5*7.6 + 0.5*1.3*7.6^2 = 147.74 m" | |
| }, | |
| { | |
| "id": "kin-30", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 24.1 m/s and constant acceleration 7.0 m/s^2 for 4.2 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 24.1, | |
| "a": 7.0, | |
| "t": 4.2 | |
| }, | |
| "answer": 162.96, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 24.1*4.2 + 0.5*7.0*4.2^2 = 162.96 m" | |
| }, | |
| { | |
| "id": "kin-31", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 8.8 m/s and constant acceleration 3.6 m/s^2 for 2.8 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 8.8, | |
| "a": 3.6, | |
| "t": 2.8 | |
| }, | |
| "answer": 38.75, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 8.8*2.8 + 0.5*3.6*2.8^2 = 38.75 m" | |
| }, | |
| { | |
| "id": "kin-32", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 18.7 m/s and constant acceleration 6.5 m/s^2 for 6.2 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 18.7, | |
| "a": 6.5, | |
| "t": 6.2 | |
| }, | |
| "answer": 240.87, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 18.7*6.2 + 0.5*6.5*6.2^2 = 240.87 m" | |
| }, | |
| { | |
| "id": "kin-33", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 18.3 m/s and constant acceleration 7.5 m/s^2 for 9.8 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 18.3, | |
| "a": 7.5, | |
| "t": 9.8 | |
| }, | |
| "answer": 539.49, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 18.3*9.8 + 0.5*7.5*9.8^2 = 539.49 m" | |
| }, | |
| { | |
| "id": "kin-34", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 28.8 m/s and constant acceleration 6.5 m/s^2 for 11.2 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 28.8, | |
| "a": 6.5, | |
| "t": 11.2 | |
| }, | |
| "answer": 730.24, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 28.8*11.2 + 0.5*6.5*11.2^2 = 730.24 m" | |
| }, | |
| { | |
| "id": "kin-35", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 22.7 m/s and constant acceleration 5.9 m/s^2 for 7.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 22.7, | |
| "a": 5.9, | |
| "t": 7.3 | |
| }, | |
| "answer": 322.92, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 22.7*7.3 + 0.5*5.9*7.3^2 = 322.92 m" | |
| }, | |
| { | |
| "id": "kin-36", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 18.0 m/s and constant acceleration 2.9 m/s^2 for 6.3 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 18.0, | |
| "a": 2.9, | |
| "t": 6.3 | |
| }, | |
| "answer": 170.95, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 18.0*6.3 + 0.5*2.9*6.3^2 = 170.95 m" | |
| }, | |
| { | |
| "id": "kin-37", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 26.7 m/s and constant acceleration 2.5 m/s^2 for 7.0 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 26.7, | |
| "a": 2.5, | |
| "t": 7.0 | |
| }, | |
| "answer": 248.15, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 26.7*7.0 + 0.5*2.5*7.0^2 = 248.15 m" | |
| }, | |
| { | |
| "id": "kin-38", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 8.5 m/s and constant acceleration 5.3 m/s^2 for 2.8 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 8.5, | |
| "a": 5.3, | |
| "t": 2.8 | |
| }, | |
| "answer": 44.58, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 8.5*2.8 + 0.5*5.3*2.8^2 = 44.58 m" | |
| }, | |
| { | |
| "id": "kin-39", | |
| "topic": "kinematics", | |
| "problem": "A particle moves with initial velocity 10.9 m/s and constant acceleration 6.5 m/s^2 for 7.9 s. What is its displacement? Answer in meters.", | |
| "params": { | |
| "v0": 10.9, | |
| "a": 6.5, | |
| "t": 7.9 | |
| }, | |
| "answer": 288.94, | |
| "solution": "x = v0*t + 0.5*a*t^2 = 10.9*7.9 + 0.5*6.5*7.9^2 = 288.94 m" | |
| }, | |
| { | |
| "id": "en-0", | |
| "topic": "energy", | |
| "problem": "A 75.5 kg object is raised 79.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 75.5, | |
| "h": 79.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 58659.88, | |
| "solution": "PE = m*g*h = 75.5*9.81*79.2 = 58659.88 J" | |
| }, | |
| { | |
| "id": "en-1", | |
| "topic": "energy", | |
| "problem": "A 62.4 kg object is raised 31.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 62.4, | |
| "h": 31.8, | |
| "g": 9.81 | |
| }, | |
| "answer": 19466.18, | |
| "solution": "PE = m*g*h = 62.4*9.81*31.8 = 19466.18 J" | |
| }, | |
| { | |
| "id": "en-2", | |
| "topic": "energy", | |
| "problem": "A 42.2 kg object is raised 29.5 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 42.2, | |
| "h": 29.5, | |
| "g": 9.81 | |
| }, | |
| "answer": 12212.47, | |
| "solution": "PE = m*g*h = 42.2*9.81*29.5 = 12212.47 J" | |
| }, | |
| { | |
| "id": "en-3", | |
| "topic": "energy", | |
| "problem": "A 65.1 kg object is raised 86.1 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 65.1, | |
| "h": 86.1, | |
| "g": 9.81 | |
| }, | |
| "answer": 54986.13, | |
| "solution": "PE = m*g*h = 65.1*9.81*86.1 = 54986.13 J" | |
| }, | |
| { | |
| "id": "en-4", | |
| "topic": "energy", | |
| "problem": "A 18.2 kg object is raised 5.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 18.2, | |
| "h": 5.7, | |
| "g": 9.81 | |
| }, | |
| "answer": 1017.69, | |
| "solution": "PE = m*g*h = 18.2*9.81*5.7 = 1017.69 J" | |
| }, | |
| { | |
| "id": "en-5", | |
| "topic": "energy", | |
| "problem": "A 25.3 kg object is raised 91.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 25.3, | |
| "h": 91.8, | |
| "g": 9.81 | |
| }, | |
| "answer": 22784.12, | |
| "solution": "PE = m*g*h = 25.3*9.81*91.8 = 22784.12 J" | |
| }, | |
| { | |
| "id": "en-6", | |
| "topic": "energy", | |
| "problem": "A 55.5 kg object is raised 16.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 55.5, | |
| "h": 16.9, | |
| "g": 9.81 | |
| }, | |
| "answer": 9201.29, | |
| "solution": "PE = m*g*h = 55.5*9.81*16.9 = 9201.29 J" | |
| }, | |
| { | |
| "id": "en-7", | |
| "topic": "energy", | |
| "problem": "A 53.6 kg object is raised 42.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 53.6, | |
| "h": 42.8, | |
| "g": 9.81 | |
| }, | |
| "answer": 22504.92, | |
| "solution": "PE = m*g*h = 53.6*9.81*42.8 = 22504.92 J" | |
| }, | |
| { | |
| "id": "en-8", | |
| "topic": "energy", | |
| "problem": "A 19.5 kg object is raised 47.6 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 19.5, | |
| "h": 47.6, | |
| "g": 9.81 | |
| }, | |
| "answer": 9105.64, | |
| "solution": "PE = m*g*h = 19.5*9.81*47.6 = 9105.64 J" | |
| }, | |
| { | |
| "id": "en-9", | |
| "topic": "energy", | |
| "problem": "A 41.1 kg object is raised 59.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 41.1, | |
| "h": 59.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 23868.91, | |
| "solution": "PE = m*g*h = 41.1*9.81*59.2 = 23868.91 J" | |
| }, | |
| { | |
| "id": "en-10", | |
| "topic": "energy", | |
| "problem": "A 59.6 kg object is raised 48.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 59.6, | |
| "h": 48.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 28239.85, | |
| "solution": "PE = m*g*h = 59.6*9.81*48.3 = 28239.85 J" | |
| }, | |
| { | |
| "id": "en-11", | |
| "topic": "energy", | |
| "problem": "A 40.4 kg object is raised 105.6 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 40.4, | |
| "h": 105.6, | |
| "g": 9.81 | |
| }, | |
| "answer": 41851.81, | |
| "solution": "PE = m*g*h = 40.4*9.81*105.6 = 41851.81 J" | |
| }, | |
| { | |
| "id": "en-12", | |
| "topic": "energy", | |
| "problem": "A 36.9 kg object is raised 10.4 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 36.9, | |
| "h": 10.4, | |
| "g": 9.81 | |
| }, | |
| "answer": 3764.69, | |
| "solution": "PE = m*g*h = 36.9*9.81*10.4 = 3764.69 J" | |
| }, | |
| { | |
| "id": "en-13", | |
| "topic": "energy", | |
| "problem": "A 0.6 kg object is raised 93.0 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 0.6, | |
| "h": 93.0, | |
| "g": 9.81 | |
| }, | |
| "answer": 547.4, | |
| "solution": "PE = m*g*h = 0.6*9.81*93.0 = 547.4 J" | |
| }, | |
| { | |
| "id": "en-14", | |
| "topic": "energy", | |
| "problem": "A 59.8 kg object is raised 93.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 59.8, | |
| "h": 93.7, | |
| "g": 9.81 | |
| }, | |
| "answer": 54967.98, | |
| "solution": "PE = m*g*h = 59.8*9.81*93.7 = 54967.98 J" | |
| }, | |
| { | |
| "id": "en-15", | |
| "topic": "energy", | |
| "problem": "A 61.0 kg object is raised 45.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 61.0, | |
| "h": 45.7, | |
| "g": 9.81 | |
| }, | |
| "answer": 27347.34, | |
| "solution": "PE = m*g*h = 61.0*9.81*45.7 = 27347.34 J" | |
| }, | |
| { | |
| "id": "en-16", | |
| "topic": "energy", | |
| "problem": "A 58.7 kg object is raised 102.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 58.7, | |
| "h": 102.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 58909.15, | |
| "solution": "PE = m*g*h = 58.7*9.81*102.3 = 58909.15 J" | |
| }, | |
| { | |
| "id": "en-17", | |
| "topic": "energy", | |
| "problem": "A 59.5 kg object is raised 97.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 59.5, | |
| "h": 97.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 56735.15, | |
| "solution": "PE = m*g*h = 59.5*9.81*97.2 = 56735.15 J" | |
| }, | |
| { | |
| "id": "en-18", | |
| "topic": "energy", | |
| "problem": "A 64.7 kg object is raised 18.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 64.7, | |
| "h": 18.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 11615.14, | |
| "solution": "PE = m*g*h = 64.7*9.81*18.3 = 11615.14 J" | |
| }, | |
| { | |
| "id": "en-19", | |
| "topic": "energy", | |
| "problem": "A 49.2 kg object is raised 53.7 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 49.2, | |
| "h": 53.7, | |
| "g": 9.81 | |
| }, | |
| "answer": 25918.41, | |
| "solution": "PE = m*g*h = 49.2*9.81*53.7 = 25918.41 J" | |
| }, | |
| { | |
| "id": "en-20", | |
| "topic": "energy", | |
| "problem": "A 16.1 kg object is raised 51.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 16.1, | |
| "h": 51.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 8086.58, | |
| "solution": "PE = m*g*h = 16.1*9.81*51.2 = 8086.58 J" | |
| }, | |
| { | |
| "id": "en-21", | |
| "topic": "energy", | |
| "problem": "A 43.4 kg object is raised 14.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 43.4, | |
| "h": 14.9, | |
| "g": 9.81 | |
| }, | |
| "answer": 6343.73, | |
| "solution": "PE = m*g*h = 43.4*9.81*14.9 = 6343.73 J" | |
| }, | |
| { | |
| "id": "en-22", | |
| "topic": "energy", | |
| "problem": "A 10.8 kg object is raised 103.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 10.8, | |
| "h": 103.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 10933.83, | |
| "solution": "PE = m*g*h = 10.8*9.81*103.2 = 10933.83 J" | |
| }, | |
| { | |
| "id": "en-23", | |
| "topic": "energy", | |
| "problem": "A 35.2 kg object is raised 81.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 35.2, | |
| "h": 81.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 28039.33, | |
| "solution": "PE = m*g*h = 35.2*9.81*81.2 = 28039.33 J" | |
| }, | |
| { | |
| "id": "en-24", | |
| "topic": "energy", | |
| "problem": "A 60.5 kg object is raised 20.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 60.5, | |
| "h": 20.8, | |
| "g": 9.81 | |
| }, | |
| "answer": 12344.9, | |
| "solution": "PE = m*g*h = 60.5*9.81*20.8 = 12344.9 J" | |
| }, | |
| { | |
| "id": "en-25", | |
| "topic": "energy", | |
| "problem": "A 75.0 kg object is raised 30.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 75.0, | |
| "h": 30.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 22293.23, | |
| "solution": "PE = m*g*h = 75.0*9.81*30.3 = 22293.23 J" | |
| }, | |
| { | |
| "id": "en-26", | |
| "topic": "energy", | |
| "problem": "A 48.6 kg object is raised 24.8 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 48.6, | |
| "h": 24.8, | |
| "g": 9.81 | |
| }, | |
| "answer": 11823.8, | |
| "solution": "PE = m*g*h = 48.6*9.81*24.8 = 11823.8 J" | |
| }, | |
| { | |
| "id": "en-27", | |
| "topic": "energy", | |
| "problem": "A 76.5 kg object is raised 48.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 76.5, | |
| "h": 48.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 36247.46, | |
| "solution": "PE = m*g*h = 76.5*9.81*48.3 = 36247.46 J" | |
| }, | |
| { | |
| "id": "en-28", | |
| "topic": "energy", | |
| "problem": "A 67.1 kg object is raised 114.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 67.1, | |
| "h": 114.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 75238.09, | |
| "solution": "PE = m*g*h = 67.1*9.81*114.3 = 75238.09 J" | |
| }, | |
| { | |
| "id": "en-29", | |
| "topic": "energy", | |
| "problem": "A 10.1 kg object is raised 108.0 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 10.1, | |
| "h": 108.0, | |
| "g": 9.81 | |
| }, | |
| "answer": 10700.75, | |
| "solution": "PE = m*g*h = 10.1*9.81*108.0 = 10700.75 J" | |
| }, | |
| { | |
| "id": "en-30", | |
| "topic": "energy", | |
| "problem": "A 60.0 kg object is raised 100.3 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 60.0, | |
| "h": 100.3, | |
| "g": 9.81 | |
| }, | |
| "answer": 59036.58, | |
| "solution": "PE = m*g*h = 60.0*9.81*100.3 = 59036.58 J" | |
| }, | |
| { | |
| "id": "en-31", | |
| "topic": "energy", | |
| "problem": "A 9.7 kg object is raised 59.4 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 9.7, | |
| "h": 59.4, | |
| "g": 9.81 | |
| }, | |
| "answer": 5652.33, | |
| "solution": "PE = m*g*h = 9.7*9.81*59.4 = 5652.33 J" | |
| }, | |
| { | |
| "id": "en-32", | |
| "topic": "energy", | |
| "problem": "A 65.4 kg object is raised 87.5 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 65.4, | |
| "h": 87.5, | |
| "g": 9.81 | |
| }, | |
| "answer": 56137.73, | |
| "solution": "PE = m*g*h = 65.4*9.81*87.5 = 56137.73 J" | |
| }, | |
| { | |
| "id": "en-33", | |
| "topic": "energy", | |
| "problem": "A 22.9 kg object is raised 101.6 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 22.9, | |
| "h": 101.6, | |
| "g": 9.81 | |
| }, | |
| "answer": 22824.34, | |
| "solution": "PE = m*g*h = 22.9*9.81*101.6 = 22824.34 J" | |
| }, | |
| { | |
| "id": "en-34", | |
| "topic": "energy", | |
| "problem": "A 16.2 kg object is raised 20.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 16.2, | |
| "h": 20.9, | |
| "g": 9.81 | |
| }, | |
| "answer": 3321.47, | |
| "solution": "PE = m*g*h = 16.2*9.81*20.9 = 3321.47 J" | |
| }, | |
| { | |
| "id": "en-35", | |
| "topic": "energy", | |
| "problem": "A 68.5 kg object is raised 64.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 68.5, | |
| "h": 64.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 43141.44, | |
| "solution": "PE = m*g*h = 68.5*9.81*64.2 = 43141.44 J" | |
| }, | |
| { | |
| "id": "en-36", | |
| "topic": "energy", | |
| "problem": "A 7.6 kg object is raised 56.4 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 7.6, | |
| "h": 56.4, | |
| "g": 9.81 | |
| }, | |
| "answer": 4204.96, | |
| "solution": "PE = m*g*h = 7.6*9.81*56.4 = 4204.96 J" | |
| }, | |
| { | |
| "id": "en-37", | |
| "topic": "energy", | |
| "problem": "A 58.2 kg object is raised 119.2 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 58.2, | |
| "h": 119.2, | |
| "g": 9.81 | |
| }, | |
| "answer": 68056.29, | |
| "solution": "PE = m*g*h = 58.2*9.81*119.2 = 68056.29 J" | |
| }, | |
| { | |
| "id": "en-38", | |
| "topic": "energy", | |
| "problem": "A 2.9 kg object is raised 89.1 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 2.9, | |
| "h": 89.1, | |
| "g": 9.81 | |
| }, | |
| "answer": 2534.81, | |
| "solution": "PE = m*g*h = 2.9*9.81*89.1 = 2534.81 J" | |
| }, | |
| { | |
| "id": "en-39", | |
| "topic": "energy", | |
| "problem": "A 43.1 kg object is raised 115.9 m at standard gravity (g=9.81). What is its gravitational potential energy? Answer in joules.", | |
| "params": { | |
| "m": 43.1, | |
| "h": 115.9, | |
| "g": 9.81 | |
| }, | |
| "answer": 49003.79, | |
| "solution": "PE = m*g*h = 43.1*9.81*115.9 = 49003.79 J" | |
| }, | |
| { | |
| "id": "cir-0", | |
| "topic": "circuits", | |
| "problem": "A 9.7 V source drives two resistors in parallel: 299 ohm and 469 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 9.7, | |
| "r1": 299, | |
| "r2": 469 | |
| }, | |
| "answer": 0.0531, | |
| "solution": "Rp = 299*469/(299+469) = 182.59 ohm; I = V/Rp = 9.7/182.59 = 0.0531 A" | |
| }, | |
| { | |
| "id": "cir-1", | |
| "topic": "circuits", | |
| "problem": "A 7.0 V source drives two resistors in parallel: 380 ohm and 324 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 7.0, | |
| "r1": 380, | |
| "r2": 324 | |
| }, | |
| "answer": 0.04, | |
| "solution": "Rp = 380*324/(380+324) = 174.89 ohm; I = V/Rp = 7.0/174.89 = 0.04 A" | |
| }, | |
| { | |
| "id": "cir-2", | |
| "topic": "circuits", | |
| "problem": "A 16.4 V source drives two resistors in parallel: 356 ohm and 290 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 16.4, | |
| "r1": 356, | |
| "r2": 290 | |
| }, | |
| "answer": 0.1026, | |
| "solution": "Rp = 356*290/(356+290) = 159.81 ohm; I = V/Rp = 16.4/159.81 = 0.1026 A" | |
| }, | |
| { | |
| "id": "cir-3", | |
| "topic": "circuits", | |
| "problem": "A 16.2 V source drives two resistors in parallel: 219 ohm and 99 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 16.2, | |
| "r1": 219, | |
| "r2": 99 | |
| }, | |
| "answer": 0.2376, | |
| "solution": "Rp = 219*99/(219+99) = 68.18 ohm; I = V/Rp = 16.2/68.18 = 0.2376 A" | |
| }, | |
| { | |
| "id": "cir-4", | |
| "topic": "circuits", | |
| "problem": "A 14.2 V source drives two resistors in parallel: 386 ohm and 286 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 14.2, | |
| "r1": 386, | |
| "r2": 286 | |
| }, | |
| "answer": 0.0864, | |
| "solution": "Rp = 386*286/(386+286) = 164.28 ohm; I = V/Rp = 14.2/164.28 = 0.0864 A" | |
| }, | |
| { | |
| "id": "cir-5", | |
| "topic": "circuits", | |
| "problem": "A 6.6 V source drives two resistors in parallel: 179 ohm and 95 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 6.6, | |
| "r1": 179, | |
| "r2": 95 | |
| }, | |
| "answer": 0.1063, | |
| "solution": "Rp = 179*95/(179+95) = 62.06 ohm; I = V/Rp = 6.6/62.06 = 0.1063 A" | |
| }, | |
| { | |
| "id": "cir-6", | |
| "topic": "circuits", | |
| "problem": "A 22.1 V source drives two resistors in parallel: 38 ohm and 498 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 22.1, | |
| "r1": 38, | |
| "r2": 498 | |
| }, | |
| "answer": 0.6259, | |
| "solution": "Rp = 38*498/(38+498) = 35.31 ohm; I = V/Rp = 22.1/35.31 = 0.6259 A" | |
| }, | |
| { | |
| "id": "cir-7", | |
| "topic": "circuits", | |
| "problem": "A 14.7 V source drives two resistors in parallel: 266 ohm and 193 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 14.7, | |
| "r1": 266, | |
| "r2": 193 | |
| }, | |
| "answer": 0.1314, | |
| "solution": "Rp = 266*193/(266+193) = 111.85 ohm; I = V/Rp = 14.7/111.85 = 0.1314 A" | |
| }, | |
| { | |
| "id": "cir-8", | |
| "topic": "circuits", | |
| "problem": "A 14.7 V source drives two resistors in parallel: 63 ohm and 404 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 14.7, | |
| "r1": 63, | |
| "r2": 404 | |
| }, | |
| "answer": 0.2697, | |
| "solution": "Rp = 63*404/(63+404) = 54.5 ohm; I = V/Rp = 14.7/54.5 = 0.2697 A" | |
| }, | |
| { | |
| "id": "cir-9", | |
| "topic": "circuits", | |
| "problem": "A 8.2 V source drives two resistors in parallel: 463 ohm and 148 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 8.2, | |
| "r1": 463, | |
| "r2": 148 | |
| }, | |
| "answer": 0.0731, | |
| "solution": "Rp = 463*148/(463+148) = 112.15 ohm; I = V/Rp = 8.2/112.15 = 0.0731 A" | |
| }, | |
| { | |
| "id": "cir-10", | |
| "topic": "circuits", | |
| "problem": "A 10.4 V source drives two resistors in parallel: 251 ohm and 15 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 10.4, | |
| "r1": 251, | |
| "r2": 15 | |
| }, | |
| "answer": 0.735, | |
| "solution": "Rp = 251*15/(251+15) = 14.15 ohm; I = V/Rp = 10.4/14.15 = 0.735 A" | |
| }, | |
| { | |
| "id": "cir-11", | |
| "topic": "circuits", | |
| "problem": "A 5.8 V source drives two resistors in parallel: 335 ohm and 456 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 5.8, | |
| "r1": 335, | |
| "r2": 456 | |
| }, | |
| "answer": 0.03, | |
| "solution": "Rp = 335*456/(335+456) = 193.12 ohm; I = V/Rp = 5.8/193.12 = 0.03 A" | |
| }, | |
| { | |
| "id": "cir-12", | |
| "topic": "circuits", | |
| "problem": "A 11.2 V source drives two resistors in parallel: 289 ohm and 278 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 11.2, | |
| "r1": 289, | |
| "r2": 278 | |
| }, | |
| "answer": 0.079, | |
| "solution": "Rp = 289*278/(289+278) = 141.7 ohm; I = V/Rp = 11.2/141.7 = 0.079 A" | |
| }, | |
| { | |
| "id": "cir-13", | |
| "topic": "circuits", | |
| "problem": "A 19.8 V source drives two resistors in parallel: 470 ohm and 156 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 19.8, | |
| "r1": 470, | |
| "r2": 156 | |
| }, | |
| "answer": 0.1691, | |
| "solution": "Rp = 470*156/(470+156) = 117.12 ohm; I = V/Rp = 19.8/117.12 = 0.1691 A" | |
| }, | |
| { | |
| "id": "cir-14", | |
| "topic": "circuits", | |
| "problem": "A 6.6 V source drives two resistors in parallel: 454 ohm and 176 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 6.6, | |
| "r1": 454, | |
| "r2": 176 | |
| }, | |
| "answer": 0.052, | |
| "solution": "Rp = 454*176/(454+176) = 126.83 ohm; I = V/Rp = 6.6/126.83 = 0.052 A" | |
| }, | |
| { | |
| "id": "cir-15", | |
| "topic": "circuits", | |
| "problem": "A 12.4 V source drives two resistors in parallel: 142 ohm and 377 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 12.4, | |
| "r1": 142, | |
| "r2": 377 | |
| }, | |
| "answer": 0.1202, | |
| "solution": "Rp = 142*377/(142+377) = 103.15 ohm; I = V/Rp = 12.4/103.15 = 0.1202 A" | |
| }, | |
| { | |
| "id": "cir-16", | |
| "topic": "circuits", | |
| "problem": "A 17.6 V source drives two resistors in parallel: 199 ohm and 406 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 17.6, | |
| "r1": 199, | |
| "r2": 406 | |
| }, | |
| "answer": 0.1318, | |
| "solution": "Rp = 199*406/(199+406) = 133.54 ohm; I = V/Rp = 17.6/133.54 = 0.1318 A" | |
| }, | |
| { | |
| "id": "cir-17", | |
| "topic": "circuits", | |
| "problem": "A 22.2 V source drives two resistors in parallel: 249 ohm and 434 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 22.2, | |
| "r1": 249, | |
| "r2": 434 | |
| }, | |
| "answer": 0.1403, | |
| "solution": "Rp = 249*434/(249+434) = 158.22 ohm; I = V/Rp = 22.2/158.22 = 0.1403 A" | |
| }, | |
| { | |
| "id": "cir-18", | |
| "topic": "circuits", | |
| "problem": "A 3.3 V source drives two resistors in parallel: 412 ohm and 11 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 3.3, | |
| "r1": 412, | |
| "r2": 11 | |
| }, | |
| "answer": 0.3081, | |
| "solution": "Rp = 412*11/(412+11) = 10.71 ohm; I = V/Rp = 3.3/10.71 = 0.3081 A" | |
| }, | |
| { | |
| "id": "cir-19", | |
| "topic": "circuits", | |
| "problem": "A 14.9 V source drives two resistors in parallel: 54 ohm and 250 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 14.9, | |
| "r1": 54, | |
| "r2": 250 | |
| }, | |
| "answer": 0.3355, | |
| "solution": "Rp = 54*250/(54+250) = 44.41 ohm; I = V/Rp = 14.9/44.41 = 0.3355 A" | |
| }, | |
| { | |
| "id": "cir-20", | |
| "topic": "circuits", | |
| "problem": "A 6.7 V source drives two resistors in parallel: 86 ohm and 458 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 6.7, | |
| "r1": 86, | |
| "r2": 458 | |
| }, | |
| "answer": 0.0925, | |
| "solution": "Rp = 86*458/(86+458) = 72.4 ohm; I = V/Rp = 6.7/72.4 = 0.0925 A" | |
| }, | |
| { | |
| "id": "cir-21", | |
| "topic": "circuits", | |
| "problem": "A 11.6 V source drives two resistors in parallel: 297 ohm and 60 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 11.6, | |
| "r1": 297, | |
| "r2": 60 | |
| }, | |
| "answer": 0.2324, | |
| "solution": "Rp = 297*60/(297+60) = 49.92 ohm; I = V/Rp = 11.6/49.92 = 0.2324 A" | |
| }, | |
| { | |
| "id": "cir-22", | |
| "topic": "circuits", | |
| "problem": "A 15.6 V source drives two resistors in parallel: 479 ohm and 184 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 15.6, | |
| "r1": 479, | |
| "r2": 184 | |
| }, | |
| "answer": 0.1173, | |
| "solution": "Rp = 479*184/(479+184) = 132.94 ohm; I = V/Rp = 15.6/132.94 = 0.1173 A" | |
| }, | |
| { | |
| "id": "cir-23", | |
| "topic": "circuits", | |
| "problem": "A 22.9 V source drives two resistors in parallel: 177 ohm and 260 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 22.9, | |
| "r1": 177, | |
| "r2": 260 | |
| }, | |
| "answer": 0.2175, | |
| "solution": "Rp = 177*260/(177+260) = 105.31 ohm; I = V/Rp = 22.9/105.31 = 0.2175 A" | |
| }, | |
| { | |
| "id": "cir-24", | |
| "topic": "circuits", | |
| "problem": "A 21.4 V source drives two resistors in parallel: 144 ohm and 172 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 21.4, | |
| "r1": 144, | |
| "r2": 172 | |
| }, | |
| "answer": 0.273, | |
| "solution": "Rp = 144*172/(144+172) = 78.38 ohm; I = V/Rp = 21.4/78.38 = 0.273 A" | |
| }, | |
| { | |
| "id": "cir-25", | |
| "topic": "circuits", | |
| "problem": "A 12.1 V source drives two resistors in parallel: 56 ohm and 20 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 12.1, | |
| "r1": 56, | |
| "r2": 20 | |
| }, | |
| "answer": 0.8209, | |
| "solution": "Rp = 56*20/(56+20) = 14.74 ohm; I = V/Rp = 12.1/14.74 = 0.8209 A" | |
| }, | |
| { | |
| "id": "cir-26", | |
| "topic": "circuits", | |
| "problem": "A 21.8 V source drives two resistors in parallel: 401 ohm and 252 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 21.8, | |
| "r1": 401, | |
| "r2": 252 | |
| }, | |
| "answer": 0.1409, | |
| "solution": "Rp = 401*252/(401+252) = 154.75 ohm; I = V/Rp = 21.8/154.75 = 0.1409 A" | |
| }, | |
| { | |
| "id": "cir-27", | |
| "topic": "circuits", | |
| "problem": "A 7.5 V source drives two resistors in parallel: 377 ohm and 330 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 7.5, | |
| "r1": 377, | |
| "r2": 330 | |
| }, | |
| "answer": 0.0426, | |
| "solution": "Rp = 377*330/(377+330) = 175.97 ohm; I = V/Rp = 7.5/175.97 = 0.0426 A" | |
| }, | |
| { | |
| "id": "cir-28", | |
| "topic": "circuits", | |
| "problem": "A 3.7 V source drives two resistors in parallel: 63 ohm and 298 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 3.7, | |
| "r1": 63, | |
| "r2": 298 | |
| }, | |
| "answer": 0.0711, | |
| "solution": "Rp = 63*298/(63+298) = 52.01 ohm; I = V/Rp = 3.7/52.01 = 0.0711 A" | |
| }, | |
| { | |
| "id": "cir-29", | |
| "topic": "circuits", | |
| "problem": "A 9.7 V source drives two resistors in parallel: 223 ohm and 473 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 9.7, | |
| "r1": 223, | |
| "r2": 473 | |
| }, | |
| "answer": 0.064, | |
| "solution": "Rp = 223*473/(223+473) = 151.55 ohm; I = V/Rp = 9.7/151.55 = 0.064 A" | |
| }, | |
| { | |
| "id": "cir-30", | |
| "topic": "circuits", | |
| "problem": "A 15.5 V source drives two resistors in parallel: 181 ohm and 174 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 15.5, | |
| "r1": 181, | |
| "r2": 174 | |
| }, | |
| "answer": 0.1747, | |
| "solution": "Rp = 181*174/(181+174) = 88.72 ohm; I = V/Rp = 15.5/88.72 = 0.1747 A" | |
| }, | |
| { | |
| "id": "cir-31", | |
| "topic": "circuits", | |
| "problem": "A 13.5 V source drives two resistors in parallel: 426 ohm and 81 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 13.5, | |
| "r1": 426, | |
| "r2": 81 | |
| }, | |
| "answer": 0.1984, | |
| "solution": "Rp = 426*81/(426+81) = 68.06 ohm; I = V/Rp = 13.5/68.06 = 0.1984 A" | |
| }, | |
| { | |
| "id": "cir-32", | |
| "topic": "circuits", | |
| "problem": "A 14.9 V source drives two resistors in parallel: 386 ohm and 372 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 14.9, | |
| "r1": 386, | |
| "r2": 372 | |
| }, | |
| "answer": 0.0787, | |
| "solution": "Rp = 386*372/(386+372) = 189.44 ohm; I = V/Rp = 14.9/189.44 = 0.0787 A" | |
| }, | |
| { | |
| "id": "cir-33", | |
| "topic": "circuits", | |
| "problem": "A 9.6 V source drives two resistors in parallel: 183 ohm and 270 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 9.6, | |
| "r1": 183, | |
| "r2": 270 | |
| }, | |
| "answer": 0.088, | |
| "solution": "Rp = 183*270/(183+270) = 109.07 ohm; I = V/Rp = 9.6/109.07 = 0.088 A" | |
| }, | |
| { | |
| "id": "cir-34", | |
| "topic": "circuits", | |
| "problem": "A 6.5 V source drives two resistors in parallel: 58 ohm and 450 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 6.5, | |
| "r1": 58, | |
| "r2": 450 | |
| }, | |
| "answer": 0.1265, | |
| "solution": "Rp = 58*450/(58+450) = 51.38 ohm; I = V/Rp = 6.5/51.38 = 0.1265 A" | |
| }, | |
| { | |
| "id": "cir-35", | |
| "topic": "circuits", | |
| "problem": "A 15.7 V source drives two resistors in parallel: 79 ohm and 456 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 15.7, | |
| "r1": 79, | |
| "r2": 456 | |
| }, | |
| "answer": 0.2332, | |
| "solution": "Rp = 79*456/(79+456) = 67.33 ohm; I = V/Rp = 15.7/67.33 = 0.2332 A" | |
| }, | |
| { | |
| "id": "cir-36", | |
| "topic": "circuits", | |
| "problem": "A 14.3 V source drives two resistors in parallel: 449 ohm and 248 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 14.3, | |
| "r1": 449, | |
| "r2": 248 | |
| }, | |
| "answer": 0.0895, | |
| "solution": "Rp = 449*248/(449+248) = 159.76 ohm; I = V/Rp = 14.3/159.76 = 0.0895 A" | |
| }, | |
| { | |
| "id": "cir-37", | |
| "topic": "circuits", | |
| "problem": "A 8.1 V source drives two resistors in parallel: 301 ohm and 449 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 8.1, | |
| "r1": 301, | |
| "r2": 449 | |
| }, | |
| "answer": 0.045, | |
| "solution": "Rp = 301*449/(301+449) = 180.2 ohm; I = V/Rp = 8.1/180.2 = 0.045 A" | |
| }, | |
| { | |
| "id": "cir-38", | |
| "topic": "circuits", | |
| "problem": "A 12.8 V source drives two resistors in parallel: 39 ohm and 414 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 12.8, | |
| "r1": 39, | |
| "r2": 414 | |
| }, | |
| "answer": 0.3591, | |
| "solution": "Rp = 39*414/(39+414) = 35.64 ohm; I = V/Rp = 12.8/35.64 = 0.3591 A" | |
| }, | |
| { | |
| "id": "cir-39", | |
| "topic": "circuits", | |
| "problem": "A 12.1 V source drives two resistors in parallel: 191 ohm and 421 ohm. What total current flows? Answer in amperes, 4 decimals.", | |
| "params": { | |
| "v": 12.1, | |
| "r1": 191, | |
| "r2": 421 | |
| }, | |
| "answer": 0.0921, | |
| "solution": "Rp = 191*421/(191+421) = 131.39 ohm; I = V/Rp = 12.1/131.39 = 0.0921 A" | |
| } | |
| ] |