trajectory_id stringlengths 39 45 | problem_id stringlengths 12 18 | domain stringclasses 6
values | turn int64 0 0 | accumulated_directives listlengths 0 0 | prompt stringlengths 296 2.32k | target_output stringlengths 22 4.23k | source_candidate_ids listlengths 1 1 | dataset_tier stringclasses 1
value | instruction stringlengths 296 2.32k | input stringclasses 1
value | output stringlengths 22 4.76k |
|---|---|---|---|---|---|---|---|---|---|---|---|
E1_solver_manual_det:physgym_0010:turn0 | physgym_0010 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The region in space where $x > 0$ and $y > 0$ is a vacuum, while... | The infinite conductor and the point at infinity are equipotential, $U{=}0$, with the boundary condition that the tangential electric field $E_{\tau}{=}0$. By the uniqueness theorem of electrostatics, the induced charges on the conductor can be equivalently replaced by image charges to determine the contribution to the... | [
"physgym_0010_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The region in space where $x > 0$ and $y > 0$ is a vacuum, while... | The infinite conductor and the point at infinity are equipotential, $U{=}0$, with the boundary condition that the tangential electric field $E_{\tau}{=}0$. By the uniqueness theorem of electrostatics, the induced charges on the conductor can be equivalently replaced by image charges to determine the contribution to the... | |
E1_solver_manual_det:physgym_0039:turn0 | physgym_0039 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A rectangular wooden block of height $H$ and density $\rho_{1}$ ... | Taking the top at equilibrium as the origin, establish the coordinate system as shown.
Let the position of the top of the block be $y$. The net force on the block is $-\rho_{1}H S g + \rho_{2}(H-h_{0}-y)S g = -\rho_{2}S g y$. The net force on the block is a linear restoring force, and its motion is simple harmonic mot... | [
"physgym_0039_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A rectangular wooden block of height $H$ and density $\rho_{1}$ ... | Taking the top at equilibrium as the origin, establish the coordinate system as shown.
Let the position of the top of the block be $y$. The net force on the block is $-\rho_{1}H S g + \rho_{2}(H-h_{0}-y)S g = -\rho_{2}S g y$. The net force on the block is a linear restoring force, and its motion is simple harmonic mot... | |
E1_solver_manual_det:physgym_0041:turn0 | physgym_0041 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The rocket ascends vertically from the Earth's surface with a co... | At the moment of takeoff, $N_1=(1+k_1)mg_0$, where $m$ is the mass of the tester.
When ascending to a height $h$, the gravitational acceleration changes to $g=g_0(\dfrac{R}{R+h})^2$
The pressure at this time is $N_2=mg_0(\dfrac{R}{R+h})^2+k_1mg_0$
Since $N_2=k_2N_1$, solving the equations together gives
$h=R(\dfrac{1}{... | [
"physgym_0041_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The rocket ascends vertically from the Earth's surface with a co... | At the moment of takeoff, $N_1=(1+k_1)mg_0$, where $m$ is the mass of the tester.
When ascending to a height $h$, the gravitational acceleration changes to $g=g_0(\dfrac{R}{R+h})^2$
The pressure at this time is $N_2=mg_0(\dfrac{R}{R+h})^2+k_1mg_0$
Since $N_2=k_2N_1$, solving the equations together gives
$h=R(\dfrac{1}{... | |
E1_solver_manual_det:physgym_0043:turn0 | physgym_0043 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two dielectric materials with base areas both equal to $\pmb{A}$... | Let the magnitudes of the electric field intensity in the two media be $E_{1}, E_{2}$ respectively, and according to the relationship between the electric potentials, we have
$$
E_{1}h_{1} + E_{2}h_{2} = U_{0}
$$
The magnitudes of the current density in the two media are
$$
\begin{aligned}
j_1 &= \sigma_1 E_1, \\
j_... | [
"physgym_0043_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two dielectric materials with base areas both equal to $\pmb{A}$... | Let the magnitudes of the electric field intensity in the two media be $E_{1}, E_{2}$ respectively, and according to the relationship between the electric potentials, we have
$$
E_{1}h_{1} + E_{2}h_{2} = U_{0}
$$
The magnitudes of the current density in the two media are
$$
\begin{aligned}
j_1 &= \sigma_1 E_1, \\
j_... | |
E1_solver_manual_det:physgym_0072:turn0 | physgym_0072 | THERMODYNAMICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
At time $t=0$, an adiabatic cylinder with a cross-sectional area... | From the proportional relationship between work done and heat absorbed:
$$
\frac{1}{2}\left(p_{1}\mathrm{d}V_{1}+p_{2}\mathrm{d}V_{2}\right)=T_{1}\mathrm{d}S_{1}=T_{2}\mathrm{d}S_{2}
$$
From the first law of thermodynamics:
$$
\mathrm{d}U_{i}=T_{i}\mathrm{d}S_{i}-p_{i}\mathrm{d}V_{i}
$$
And the equation of state:
... | [
"physgym_0072_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
At time $t=0$, an adiabatic cylinder with a cross-sectional area... | From the proportional relationship between work done and heat absorbed:
$$
\frac{1}{2}\left(p_{1}\mathrm{d}V_{1}+p_{2}\mathrm{d}V_{2}\right)=T_{1}\mathrm{d}S_{1}=T_{2}\mathrm{d}S_{2}
$$
From the first law of thermodynamics:
$$
\mathrm{d}U_{i}=T_{i}\mathrm{d}S_{i}-p_{i}\mathrm{d}V_{i}
$$
And the equation of state:
... | |
E1_solver_manual_det:physgym_0250:turn0 | physgym_0250 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
There is now an electrolyte with thickness $L$ in the $z$ direct... | Given the potential difference $u$, it can be seen:
$$
\varphi_{+}=u/2,\varphi_{-}=-u/2,\lambda=\frac{2\pi(\varepsilon_{1}+\varepsilon_{2})\varphi_{+}}{2\xi_{+}}=\frac{\pi(\varepsilon_{1}+\varepsilon_{2})u}{\operatorname{arccosh}(\mathrm{D/R})}
$$
Select a surface encapsulating the cylindrical surface and examine Gau... | [
"physgym_0250_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
There is now an electrolyte with thickness $L$ in the $z$ direct... | Given the potential difference $u$, it can be seen:
$$
\varphi_{+}=u/2,\varphi_{-}=-u/2,\lambda=\frac{2\pi(\varepsilon_{1}+\varepsilon_{2})\varphi_{+}}{2\xi_{+}}=\frac{\pi(\varepsilon_{1}+\varepsilon_{2})u}{\operatorname{arccosh}(\mathrm{D/R})}
$$
Select a surface encapsulating the cylindrical surface and examine Gau... | |
E1_solver_manual_det:physgym_0284:turn0 | physgym_0284 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Fiber-optic communication has greatly advanced our information t... | Considering that the optical signal should propagate without loss, the light transmission in the optical fiber should involve total internal reflection at the interface. Assume the incident electric field is represented by ${\widetilde{E}}_{i}$, and the reflected electric field by $\widetilde{E}_{r}$; we have $\widetil... | [
"physgym_0284_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Fiber-optic communication has greatly advanced our information t... | Considering that the optical signal should propagate without loss, the light transmission in the optical fiber should involve total internal reflection at the interface. Assume the incident electric field is represented by ${\widetilde{E}}_{i}$, and the reflected electric field by $\widetilde{E}_{r}$; we have $\widetil... | |
E1_solver_manual_det:physgym_0636:turn0 | physgym_0636 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Establish a Cartesian coordinate system Oxyz, with a hypothetica... | Consider the case of a single circular loop, establishing a spherical coordinate system $(r, \alpha)$ with the loop axis as the polar axis. Then: $$ V = {\frac{1}{4\pi\varepsilon_{0}}}\int_{0}^{2\pi}{\frac{Q d\theta}{2\pi}}{\frac{1}{\sqrt{r^{2}+R^{2}-2R r \sin\alpha \cos\Theta}}}={\frac{Q}{4\pi\varepsilon_{0}}}\left({\... | [
"physgym_0636_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Establish a Cartesian coordinate system Oxyz, with a hypothetica... | Consider the case of a single circular loop, establishing a spherical coordinate system $(r, \alpha)$ with the loop axis as the polar axis. Then: $$ V = {\frac{1}{4\pi\varepsilon_{0}}}\int_{0}^{2\pi}{\frac{Q d\theta}{2\pi}}{\frac{1}{\sqrt{r^{2}+R^{2}-2R r \sin\alpha \cos\Theta}}}={\frac{Q}{4\pi\varepsilon_{0}}}\left({... | |
E1_solver_manual_det:physgym_0649:turn0 | physgym_0649 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In modern plasma physics experiments, negative particles are oft... | Analyzing the magnetic field at a small displacement $z$ along the $z$-axis away from the coordinate origin $$ \vec{B_{z}}={\frac{\mu_{0}Q\Omega R}{4\pi}}\left({\frac{R}{[R^{2}+(l+z)^{2}]^{\frac{3}{2}}}}+{\frac{R}{[R^{2}+(l-z)^{2}]^{\frac{3}{2}}}}\right) $$ yields $$ \vec{B_{z}}=\frac{\mu_{0}Q\Omega}{2\pi}\frac{R^{2}}{... | [
"physgym_0649_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In modern plasma physics experiments, negative particles are oft... | Analyzing the magnetic field at a small displacement $z$ along the $z$-axis away from the coordinate origin $$ \vec{B_{z}}={\frac{\mu_{0}Q\Omega R}{4\pi}}\left({\frac{R}{[R^{2}+(l+z)^{2}]^{\frac{3}{2}}}}+{\frac{R}{[R^{2}+(l-z)^{2}]^{\frac{3}{2}}}}\right) $$ yields $$ \vec{B_{z}}=\frac{\mu_{0}Q\Omega}{2\pi}\fra... | |
E1_solver_manual_det:physgym_0653:turn0 | physgym_0653 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A massless insulating string of length $a$ is fixed at one end, ... | If the ring is a superconducting ring, when it moves in a magnetic field, due to the properties of the superconductor, the magnetic flux in the ring remains unchanged, i.e.: $$ L I + B S = B \cdot \pi r^2 $$ Thus, the current in the ring is: $$ \begin{array}{l}{I = \displaystyle\frac{B}{L}(\pi r^{2} - S)}\ = \displayst... | [
"physgym_0653_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A massless insulating string of length $a$ is fixed at one end, ... | If the ring is a superconducting ring, when it moves in a magnetic field, due to the properties of the superconductor, the magnetic flux in the ring remains unchanged, i.e.: $$ L I + B S = B \cdot \pi r^2 $$ Thus, the current in the ring is: $$ \begin{array}{l}{I = \displaystyle\frac{B}{L}(\pi r^{2} - S)}\ = \displa... | |
E1_solver_manual_det:physgym_0654:turn0 | physgym_0654 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The forty-second batch of Trisolarian immigrants arrived on Eart... | There are two reference frames; let's set up the agreements first. The reference frame of the Earth observer is called the $\Sigma$ frame, and the reference frame of the spaceship is called the $\Sigma$ frame. We agree that: $$\beta_{1}=\frac{v_{1}}{c},\gamma_{1}=\frac{1}{\sqrt{1-\beta_{1}^{2}}},\beta_{2}=\frac{v_{2}}{... | [
"physgym_0654_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The forty-second batch of Trisolarian immigrants arrived on Eart... | There are two reference frames; let's set up the agreements first. The reference frame of the Earth observer is called the $\Sigma$ frame, and the reference frame of the spaceship is called the $\Sigma$ frame. We agree that: $$\beta_{1}=\frac{v_{1}}{c},\gamma_{1}=\frac{1}{\sqrt{1-\beta_{1}^{2}}},\beta_{2}=\frac{v_{2}}... | |
E1_solver_manual_det:physgym_0702:turn0 | physgym_0702 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
To establish a rectangular coordinate system in an infinitely la... | Near the origin, the electric potential can be expressed as $$ \begin{array}{r l} U&=-\displaystyle\frac\lambda{2\pi\varepsilon_{0}}\ln\displaystyle\frac{\sqrt{(a-x)^{2}+y^{2}}}{a}-\displaystyle\frac\lambda{2\pi\varepsilon_{0}}\ln\displaystyle\frac{\sqrt{(a+x)^{2}+y^{2}}}{a}\\ &+\displaystyle\frac\lambda{2\pi\varepsilo... | [
"physgym_0702_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
To establish a rectangular coordinate system in an infinitely la... | Near the origin, the electric potential can be expressed as $$ \begin{array}{r l} U&=-\displaystyle\frac\lambda{2\pi\varepsilon_{0}}\ln\displaystyle\frac{\sqrt{(a-x)^{2}+y^{2}}}{a}-\displaystyle\frac\lambda{2\pi\varepsilon_{0}}\ln\displaystyle\frac{\sqrt{(a+x)^{2}+y^{2}}}{a}\\ &+\displaystyle\frac\lambda{2\pi\varepsil... | |
E1_solver_manual_det:book_mech_0001_b:turn0 | book_mech_0001_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Compute the following things. If they don’t make sense because o... | 1.33 m;
ANSWER: 1.33 m; | [
"book_mech_0001_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Compute the following things. If they don’t make sense because o... | 1.33 m;
ANSWER: 1.33 m; | |
E1_solver_manual_det:book_mech_0001_c:turn0 | book_mech_0001_c | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Compute the following things. If they don’t make sense because o... | doesn’t make
sense;
ANSWER: sense; | [
"book_mech_0001_c_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Compute the following things. If they don’t make sense because o... | doesn’t make
sense;
ANSWER: sense; | |
E1_solver_manual_det:book_mech_0001_d:turn0 | book_mech_0001_d | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Compute the following things. If they don’t make sense because o... | 60 miles/hour
ANSWER: 60 miles/hour | [
"book_mech_0001_d_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Compute the following things. If they don’t make sense because o... | 60 miles/hour
ANSWER: 60 miles/hour | |
E1_solver_manual_det:book_mech_0002:turn0 | book_mech_0002 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Your backyard has brick walls on both ends. You measure a
distan... | 23.4 m + 2× 0.294 m = 23 .988 m, which
should be rounded to 24 .0 m (3 significant figures)
ANSWER: 23 .988 m, which should be rounded to 24 .0 m (3 significant figures) | [
"book_mech_0002_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Your backyard has brick walls on both ends. You measure a
distan... | 23.4 m + 2× 0.294 m = 23 .988 m, which
should be rounded to 24 .0 m (3 significant figures)
ANSWER: 23 .988 m, which should be rounded to 24 .0 m (3 significant figures) | |
E1_solver_manual_det:book_mech_0003:turn0 | book_mech_0003 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The speed of light is 3.0 × 108 m/s. Convert this to furlongs
pe... | 3.0× 108 m/s
×
(100 cm
1 m
)( 1 inch
2.54 cm
)( 1 foot
12 inches
)
×
(1 yard
3 feet
)( 1 furlong
220 yards
)
×
( 60 s
1 min
)( 60 min
1 hr
)( 24 hr
1 day
)( 14 days
1 forthnight
)
= 1.8× 1012 furlongs/fortnight
ANSWER: 1.8× 1012 furlongs/fortnight | [
"book_mech_0003_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The speed of light is 3.0 × 108 m/s. Convert this to furlongs
pe... | 3.0× 108 m/s
×
(100 cm
1 m
)( 1 inch
2.54 cm
)( 1 foot
12 inches
)
×
(1 yard
3 feet
)( 1 furlong
220 yards
)
×
( 60 s
1 min
)( 60 min
1 hr
)( 24 hr
1 day
)( 14 days
1 forthnight
)
= 1.8× 1012 furlongs/fortnight
ANSWER: 1.8× 1012 furlongs/fortnight | |
E1_solver_manual_det:book_mech_0004:turn0 | book_mech_0004 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Express each of the following quantities in micrograms:
(a) 10 m... | (a) 10 4 µg; (b) 10 10 µg; (c) 10 10 µg; (d)
1011 µg; (e) 1 µg
ANSWER: 1011 µg; (e) 1 µg | [
"book_mech_0004_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Express each of the following quantities in micrograms:
(a) 10 m... | (a) 10 4 µg; (b) 10 10 µg; (c) 10 10 µg; (d)
1011 µg; (e) 1 µg
ANSWER: 1011 µg; (e) 1 µg | |
E1_solver_manual_det:book_mech_0005_a:turn0 | book_mech_0005_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In the last century, the average age of the onset of puberty for... | 0.5 mg
0.2 ng/hamburger = 0.5× 10−3 g0.2× 10−9 g hamburgers
= 2 million hamburgers!
(Note how the fake units of “hamburgers” help
to reassure us that dividing the first number by
the second one gives the right result.)
ANSWER: the second one gives the right result.) | [
"book_mech_0005_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In the last century, the average age of the onset of puberty for... | 0.5 mg
0.2 ng/hamburger = 0.5× 10−3 g0.2× 10−9 g hamburgers
= 2 million hamburgers!
(Note how the fake units of “hamburgers” help
to reassure us that dividing the first number by
the second one gives the right result.)
ANSWER: the second one gives the right result.) | |
E1_solver_manual_det:book_mech_0005_b:turn0 | book_mech_0005_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In the last century, the average age of the onset of puberty for... | (0.5 mg)/(300 ng/serving)=2000 servings
ANSWER: 2000 servings | [
"book_mech_0005_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In the last century, the average age of the onset of puberty for... | (0.5 mg)/(300 ng/serving)=2000 servings
ANSWER: 2000 servings | |
E1_solver_manual_det:book_mech_0006:turn0 | book_mech_0006 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You jump up straight up in the air. When do you have the
greates... | Gravitational energy depends on how far
apart the masses are. When you’re at the top
of your jump, your mass is as far as it’s ever going to be from the mass of the planet, so that’s
when your gravitational energy is the greatest.
Energy is conserved, so your greatest kinetic energy must be when your gravitational ener... | [
"book_mech_0006_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You jump up straight up in the air. When do you have the
greates... | Gravitational energy depends on how far
apart the masses are. When you’re at the top
of your jump, your mass is as far as it’s ever going to be from the mass of the planet, so that’s
when your gravitational energy is the greatest.
Energy is conserved, so your greatest kinetic energy must be when your gravitational ener... | |
E1_solver_manual_det:book_mech_0007:turn0 | book_mech_0007 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Anya and Ivan lean over a balcony side by side. Anya throws a
pe... | Kinetic energy doesn’t depend on the direction of the motion, so since both pennies start
out at the same speed, they both start out with
the same kinetic energy. They also start out at
the same height, so they have the same gravitational energy and the same total energy. Energy
is conserved, so if they start out with ... | [
"book_mech_0007_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Anya and Ivan lean over a balcony side by side. Anya throws a
pe... | Kinetic energy doesn’t depend on the direction of the motion, so since both pennies start
out at the same speed, they both start out with
the same kinetic energy. They also start out at
the same height, so they have the same gravitational energy and the same total energy. Energy
is conserved, so if they start out with ... | |
E1_solver_manual_det:book_mech_0008_a:turn0 | book_mech_0008_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If weight B moves down by a certain amount, how much
does weight... | The piece of string connected to B has
three vertical parts: one connecting to the ceiling, one between the two pulleys, and one going
down to B. If the part connecting to B lengthens
by, say 2 cm, then this extra 2 cm has to come
out of the other two segments. In other words,
1 cm of string is lost from the part conne... | [
"book_mech_0008_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If weight B moves down by a certain amount, how much
does weight... | The piece of string connected to B has
three vertical parts: one connecting to the ceiling, one between the two pulleys, and one going
down to B. If the part connecting to B lengthens
by, say 2 cm, then this extra 2 cm has to come
out of the other two segments. In other words,
1 cm of string is lost from the part conne... | |
E1_solver_manual_det:book_mech_0008_b:turn0 | book_mech_0008_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
What should the ratio of the two weights be if they are to balan... | If they move, one will lose gravitational energy while the other gains gravitational energy.
If A was a boulder and B was a feather, then A
could release more gravitational energy by dropping than B would consume by rising. Likewise if
B was ridiculously heavy compared to A, you’d
release gravitational energy by lettin... | [
"book_mech_0008_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
What should the ratio of the two weights be if they are to balan... | If they move, one will lose gravitational energy while the other gains gravitational energy.
If A was a boulder and B was a feather, then A
could release more gravitational energy by dropping than B would consume by rising. Likewise if
B was ridiculously heavy compared to A, you’d
release gravitational energy by lettin... | |
E1_solver_manual_det:book_mech_0009_a:turn0 | book_mech_0009_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You release a magnet on a tabletop near a big piece of
iron, and... | Magnetic energy plus kinetic energy
stays the same, so if it’s speeding up, the KE
is increasing and the magnetic energy must be
decreasing.
ANSWER: decreasing. | [
"book_mech_0009_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You release a magnet on a tabletop near a big piece of
iron, and... | Magnetic energy plus kinetic energy
stays the same, so if it’s speeding up, the KE
is increasing and the magnetic energy must be
decreasing.
ANSWER: decreasing. | |
E1_solver_manual_det:book_mech_0009_b:turn0 | book_mech_0009_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Suppose instead that you have two repelling magnets. You give
th... | By similar reasoning, magnetic
energy must be increasing as they approach each
other.
ANSWER: other. | [
"book_mech_0009_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Suppose instead that you have two repelling magnets. You give
th... | By similar reasoning, magnetic
energy must be increasing as they approach each
other.
ANSWER: other. | |
E1_solver_manual_det:book_mech_0010:turn0 | book_mech_0010 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
For an astronaut sealed inside a space suit, getting rid of body... | To raise her body temperature by six degrees, the amount of energy required will be
6× 200 kJ, or 1200 kJ. Converting to the basic units of joules, this is 1 .2× 106 J. A watt
is a joule per second, so every second, the heat
energy added to her body will be 200 J. That
means that the time it will take for her to die
wi... | [
"book_mech_0010_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
For an astronaut sealed inside a space suit, getting rid of body... | To raise her body temperature by six degrees, the amount of energy required will be
6× 200 kJ, or 1200 kJ. Converting to the basic units of joules, this is 1 .2× 106 J. A watt
is a joule per second, so every second, the heat
energy added to her body will be 200 J. That
means that the time it will take for her to die
wi... | |
E1_solver_manual_det:book_mech_0012:turn0 | book_mech_0012 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
How high above the surface of the earth should a rocket be
in or... | First we take Newton’s law of gravity,
F = Gm1m2/r2, and throw out the constant
factor of Gm1m2, turning it into the proportionality F ∝ 1/r2, or r ∝ 1/√F . Changing this into a statement about ratios, we have
r1/r2 =
F2/F1 = 10. At the earth’s surface, r
equals the earth’s radius. To make it ten times
bigger, we have ... | [
"book_mech_0012_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
How high above the surface of the earth should a rocket be
in or... | First we take Newton’s law of gravity,
F = Gm1m2/r2, and throw out the constant
factor of Gm1m2, turning it into the proportionality F ∝ 1/r2, or r ∝ 1/√F . Changing this into a statement about ratios, we have
r1/r2 =
F2/F1 = 10. At the earth’s surface, r
equals the earth’s radius. To make it ten times
bigger, we have ... | |
E1_solver_manual_det:book_mech_0013:turn0 | book_mech_0013 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
As suggested on page 28, imagine that the mass of the electron
r... | One method for exploiting the changing
mass of the electrons would be the same as the
method given in the text for exploiting a change
in G: raise a large weight on a day when the
electrons’ mass was small, then lower it and get
back the energy on a day when it was high. Energy would not be conserved. The amount of
ene... | [
"book_mech_0013_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
As suggested on page 28, imagine that the mass of the electron
r... | One method for exploiting the changing
mass of the electrons would be the same as the
method given in the text for exploiting a change
in G: raise a large weight on a day when the
electrons’ mass was small, then lower it and get
back the energy on a day when it was high. Energy would not be conserved. The amount of
ene... | |
E1_solver_manual_det:book_mech_0014:turn0 | book_mech_0014 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A typical balance like the ones used in school classes can be
re... | The mass change in that example came
out to be so small because we were dividing by
c2, which is big. To make it an easily measurable mass change, we’d have to make the decimal
325
place move over by about 8 places on the final result, i.e., make c2 about 108 times smaller. That
means making c about 10 4 times smaller.... | [
"book_mech_0014_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A typical balance like the ones used in school classes can be
re... | The mass change in that example came
out to be so small because we were dividing by
c2, which is big. To make it an easily measurable mass change, we’d have to make the decimal
325
place move over by about 8 places on the final result, i.e., make c2 about 108 times smaller. That
means making c about 10 4 times smaller.... | |
E1_solver_manual_det:book_mech_0015_a:turn0 | book_mech_0015_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A free neutron (as opposed to a neutron bound into an
atomic nuc... | In units of 10 −27 kg, the amount of
mass lost is
1.67495− 1.67265− 0.00091 = 0.00139 ,
i.e., 0.00139× 10−27 kg. This mass has been
converted into energy:
E =mc2
= (0.00139× 10−27)(3× 108)2
= 1.25× 10−13 joules .
(In the meter-kilogram-second system of units,
kilograms multiplied velocity squared give units
of joules.)... | [
"book_mech_0015_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A free neutron (as opposed to a neutron bound into an
atomic nuc... | In units of 10 −27 kg, the amount of
mass lost is
1.67495− 1.67265− 0.00091 = 0.00139 ,
i.e., 0.00139× 10−27 kg. This mass has been
converted into energy:
E =mc2
= (0.00139× 10−27)(3× 108)2
= 1.25× 10−13 joules .
(In the meter-kilogram-second system of units,
kilograms multiplied velocity squared give units
of joules.)... | |
E1_solver_manual_det:book_mech_0015_b:turn0 | book_mech_0015_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Neutrons and protons make up essentially all of the mass of the
... | For this process, the total mass changes
from 1.67265 to 1.67586 (again in units of 10−27
kg). This is an increase in mass, which means
that we would have to have a source of energy to
make the reaction happen. A free proton has no
such source of energy; it’s all by itself, so there’s
nothing for it to get energy from.... | [
"book_mech_0015_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Neutrons and protons make up essentially all of the mass of the
... | For this process, the total mass changes
from 1.67265 to 1.67586 (again in units of 10−27
kg). This is an increase in mass, which means
that we would have to have a source of energy to
make the reaction happen. A free proton has no
such source of energy; it’s all by itself, so there’s
nothing for it to get energy from.... | |
E1_solver_manual_det:book_mech_0017:turn0 | book_mech_0017 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You’re a passenger in the open basket hanging under a hotair bal... | If the balloon is being carried along by the
wind at constant velocity, then it’s at rest with
respect to the air. Only relative motion can
cause a physical effect — absolute motion isn’t
even a well-defined concept. Since there is no
relative motion between the balloon and the air,
there can’t be any physical effect. ... | [
"book_mech_0017_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You’re a passenger in the open basket hanging under a hotair bal... | If the balloon is being carried along by the
wind at constant velocity, then it’s at rest with
respect to the air. Only relative motion can
cause a physical effect — absolute motion isn’t
even a well-defined concept. Since there is no
relative motion between the balloon and the air,
there can’t be any physical effect. ... | |
E1_solver_manual_det:book_mech_0018:turn0 | book_mech_0018 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Driving along in your car, you take your foot off the gas, and
y... | Suppose you’re being observed by a cop in
a car that was initially next to you and matching
your speed. Let’s say that as you take your foot
off the gas, the cop car continues at the same
speed, so you fall behind. In the cop’s frame
of reference, you were initially at rest, and then
started moving backward, so you wer... | [
"book_mech_0018_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Driving along in your car, you take your foot off the gas, and
y... | Suppose you’re being observed by a cop in
a car that was initially next to you and matching
your speed. Let’s say that as you take your foot
off the gas, the cop car continues at the same
speed, so you fall behind. In the cop’s frame
of reference, you were initially at rest, and then
started moving backward, so you wer... | |
E1_solver_manual_det:book_mech_0019:turn0 | book_mech_0019 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If all the air molecules in the room settled down in a thin
film... | It would only violate conservation of energy. Momentum has a direction in space, and
momenta in opposite directions can cancel out.
Since all the air molecules are moving in different, random directions, their total momentum is
initially zero. After settling down on the floor,
their total momentum is still zero. There’... | [
"book_mech_0019_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If all the air molecules in the room settled down in a thin
film... | It would only violate conservation of energy. Momentum has a direction in space, and
momenta in opposite directions can cancel out.
Since all the air molecules are moving in different, random directions, their total momentum is
initially zero. After settling down on the floor,
their total momentum is still zero. There’... | |
E1_solver_manual_det:book_mech_0020:turn0 | book_mech_0020 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A bullet flies through the air, passes through a paperback
book,... | Force is a transfer of momentum from one
object to another. Equivalently, we can describe force as an interaction between two objects. Whichever way we say it, it takes two to
tango — you can’t have a force unless two objects are involved. There is no force when the
bullet is in the air. There is a force when the
bulle... | [
"book_mech_0020_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A bullet flies through the air, passes through a paperback
book,... | Force is a transfer of momentum from one
object to another. Equivalently, we can describe force as an interaction between two objects. Whichever way we say it, it takes two to
tango — you can’t have a force unless two objects are involved. There is no force when the
bullet is in the air. There is a force when the
bulle... | |
E1_solver_manual_det:book_mech_0024_a:turn0 | book_mech_0024_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two cars with different masses each have the same kinetic
energy... | The amount of KE to be converted into
heat is the same in both cases, so the amount of
work that has to be done is the same in both
cases. Since work equals force times distance,
and the work and force are the same, the stopping distance is the same.
ANSWER: and the work and force are the same, the stopping distance is... | [
"book_mech_0024_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two cars with different masses each have the same kinetic
energy... | The amount of KE to be converted into
heat is the same in both cases, so the amount of
work that has to be done is the same in both
cases. Since work equals force times distance,
and the work and force are the same, the stopping distance is the same.
ANSWER: and the work and force are the same, the stopping distance is... | |
E1_solver_manual_det:book_mech_0024_b:turn0 | book_mech_0024_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two cars with different masses each have the same kinetic
energy... | Since the stopping distances are equal, if you
watched videos of the two boats stopping, the
videos would look exactly the same except for a
rescaling of the time. That is, the slower boat’s
motion would look like the faster one’s, but in
slow motion. Therefore the time for the slower
boat to stop will be greater.
ANSW... | [
"book_mech_0024_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two cars with different masses each have the same kinetic
energy... | Since the stopping distances are equal, if you
watched videos of the two boats stopping, the
videos would look exactly the same except for a
rescaling of the time. That is, the slower boat’s
motion would look like the faster one’s, but in
slow motion. Therefore the time for the slower
boat to stop will be greater.
ANSW... | |
E1_solver_manual_det:book_mech_0025_a:turn0 | book_mech_0025_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In each of the following situations, is the work being done
posi... | +, foot moves same direction as foot’s
force on ground
ANSWER: force on ground | [
"book_mech_0025_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In each of the following situations, is the work being done
posi... | +, foot moves same direction as foot’s
force on ground
ANSWER: force on ground | |
E1_solver_manual_det:book_mech_0025_b:turn0 | book_mech_0025_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In each of the following situations, is the work being done
posi... | +, force and motion are both forward
(c)−, force is backward, motion is forward
(d)−, force is up and motion is down
ANSWER: (d)−, force is up and motion is down | [
"book_mech_0025_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
In each of the following situations, is the work being done
posi... | +, force and motion are both forward
(c)−, force is backward, motion is forward
(d)−, force is up and motion is down
ANSWER: (d)−, force is up and motion is down | |
E1_solver_manual_det:book_mech_0026_a:turn0 | book_mech_0026_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Weiping lifts a rock with a weight of 1.0 N through a height
of ... | As Weiping raises the rock, the sign
of the force and the sign of d are the same (both
are up), so she does 1 joule of work. On the way
down, her force is up and the motion is down, so
she does−1 joule of work. The total is zero.
Bubba’s force was in the same direction as the
motion during both halves of his motion, si... | [
"book_mech_0026_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Weiping lifts a rock with a weight of 1.0 N through a height
of ... | As Weiping raises the rock, the sign
of the force and the sign of d are the same (both
are up), so she does 1 joule of work. On the way
down, her force is up and the motion is down, so
she does−1 joule of work. The total is zero.
Bubba’s force was in the same direction as the
motion during both halves of his motion, si... | |
E1_solver_manual_det:book_mech_0027:turn0 | book_mech_0027 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You are trying to loosen a stuck bolt on your R V using a big
wr... | You can get the maximum torque by setting everything up with θ=90◦, giving
τ =rF sinθ
=rmg
= 270 N·m .
ANSWER: 270 N·m | [
"book_mech_0027_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You are trying to loosen a stuck bolt on your R V using a big
wr... | You can get the maximum torque by setting everything up with θ=90◦, giving
τ =rF sinθ
=rmg
= 270 N·m .
ANSWER: 270 N·m | |
E1_solver_manual_det:book_mech_0028:turn0 | book_mech_0028 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A physical therapist wants her patient to rehabilitate his injur... | The total torque required is the torque
needed to lift his arm plus the torque needed
to lift the weight. Since his arm is not changing,
she needs to tell him to set things up so that the
torque needed to lift the weight is also the same
as before. Torque is rF sinθ, and since he is decreasing r by a factor of 17/33, s... | [
"book_mech_0028_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A physical therapist wants her patient to rehabilitate his injur... | The total torque required is the torque
needed to lift his arm plus the torque needed
to lift the weight. Since his arm is not changing,
she needs to tell him to set things up so that the
torque needed to lift the weight is also the same
as before. Torque is rF sinθ, and since he is decreasing r by a factor of 17/33, s... | |
E1_solver_manual_det:book_mech_0029:turn0 | book_mech_0029 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
An object is observed to have constant angular momentum.
Can you... | No, it just means that any torques that do
act are adding up to produce zero total torque.
For instance, a merry-go-round rotating with
constant angular velocity has torques acting on
it, but the motor’s torque and the torque due
to friction are just canceling out to produce zero
total torque. Of course it is also poss... | [
"book_mech_0029_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
An object is observed to have constant angular momentum.
Can you... | No, it just means that any torques that do
act are adding up to produce zero total torque.
For instance, a merry-go-round rotating with
constant angular velocity has torques acting on
it, but the motor’s torque and the torque due
to friction are just canceling out to produce zero
total torque. Of course it is also poss... | |
E1_solver_manual_det:book_mech_0030:turn0 | book_mech_0030 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two horizontal tree branches on the same tree have equal
diamete... | For the purpose of calculating gravitational torques, we can treat each branch as if its
weight were concentrated at its center of mass.
The longer branch’s center of mass is twice as far
from the trunk, so the r is doubled. The gravitational force is also twice as much, so τ =rF is
four times greater.
ANSWER: rF is fo... | [
"book_mech_0030_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Two horizontal tree branches on the same tree have equal
diamete... | For the purpose of calculating gravitational torques, we can treat each branch as if its
weight were concentrated at its center of mass.
The longer branch’s center of mass is twice as far
from the trunk, so the r is doubled. The gravitational force is also twice as much, so τ =rF is
four times greater.
ANSWER: rF is fo... | |
E1_solver_manual_det:book_mech_0031_a:turn0 | book_mech_0031_a | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Alice says Cathy’s body has zero momentum, but Bob
says Cathy’s ... | Alice could be in a frame of reference in
which Cathy isn’t moving. For instance, if Alice
and Cathy were in an airplane together, it would
be natural for both of them to adopt the frame
of reference of the plane. Bob could be using the
frame of reference of the dirt.
ANSWER: frame of reference of the dirt. | [
"book_mech_0031_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Alice says Cathy’s body has zero momentum, but Bob
says Cathy’s ... | Alice could be in a frame of reference in
which Cathy isn’t moving. For instance, if Alice
and Cathy were in an airplane together, it would
be natural for both of them to adopt the frame
of reference of the plane. Bob could be using the
frame of reference of the dirt.
ANSWER: frame of reference of the dirt. | |
E1_solver_manual_det:book_mech_0031_b:turn0 | book_mech_0031_b | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Alice and Bob agree that Dong’s body has nonzero momentum,
but d... | Your opinions about angular momentum will
depend on what point in space you arbitrarily
chose as the axis. Let’s say Dong is sitting on
some grass. Bob might be using the center of
the spinning Earth is his axis, while Alice uses
the spot Dong is sitting on.
ANSWER: the spot Dong is sitting on. | [
"book_mech_0031_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Alice and Bob agree that Dong’s body has nonzero momentum,
but d... | Your opinions about angular momentum will
depend on what point in space you arbitrarily
chose as the axis. Let’s say Dong is sitting on
some grass. Bob might be using the center of
the spinning Earth is his axis, while Alice uses
the spot Dong is sitting on.
ANSWER: the spot Dong is sitting on. | |
E1_solver_manual_det:book_mech_0032:turn0 | book_mech_0032 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A person of weight W stands on the ball of one foot. Find
the te... | Basically we have a situation with two
equations in two unknowns. There is an equation that says the total torque on the foot is
zero, and another equation that says the total
force on the foot is zero. The two unknowns
are the tension in the calf muscle, T , and the
force exerted by the shinbone, Fs. We can however si... | [
"book_mech_0032_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A person of weight W stands on the ball of one foot. Find
the te... | Basically we have a situation with two
equations in two unknowns. There is an equation that says the total torque on the foot is
zero, and another equation that says the total
force on the foot is zero. The two unknowns
are the tension in the calf muscle, T , and the
force exerted by the shinbone, Fs. We can however si... | |
E1_solver_manual_det:book_rel_0034_a:turn0 | book_rel_0034_a | RELATIVITY | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | She says her own velocity is zero.
Time dilation happens because of relative motion. We can conclude that A and B are not in
motion relative to one another, but that there is
relative motion between them and C.
ANSWER: relative motion between them and C. | [
"book_rel_0034_a_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | She says her own velocity is zero.
Time dilation happens because of relative motion. We can conclude that A and B are not in
motion relative to one another, but that there is
relative motion between them and C.
ANSWER: relative motion between them and C. | |
E1_solver_manual_det:book_rel_0034_b:turn0 | book_rel_0034_b | RELATIVITY | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | Alice says B is at rest, but C is moving.
ANSWER: Alice says B is at rest, but C is moving. | [
"book_rel_0034_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | Alice says B is at rest, but C is moving.
ANSWER: Alice says B is at rest, but C is moving. | |
E1_solver_manual_det:book_rel_0034_c:turn0 | book_rel_0034_c | RELATIVITY | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | Betty says A is at rest, but C is moving.
ANSWER: Betty says A is at rest, but C is moving. | [
"book_rel_0034_c_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | Betty says A is at rest, but C is moving.
ANSWER: Betty says A is at rest, but C is moving. | |
E1_solver_manual_det:book_rel_0034_d:turn0 | book_rel_0034_d | RELATIVITY | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | Cathy says both A and B are moving, and she
sees them moving in the same direction at the
same speed.
ANSWER: same speed. | [
"book_rel_0034_d_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Astronauts in three different spaceships are communicating
with ... | Cathy says both A and B are moving, and she
sees them moving in the same direction at the
same speed.
ANSWER: same speed. | |
E1_solver_manual_det:book_em_0036:turn0 | book_em_0036 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A hydrogen atom consists of an electron and a proton. For our
pr... | Electricity is an inverse square force, so if
r is smaller by a factor of 206.77, the force will
be greater by a factor of 206 .772 = 42754.
ANSWER: 42754 | [
"book_em_0036_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A hydrogen atom consists of an electron and a proton. For our
pr... | Electricity is an inverse square force, so if
r is smaller by a factor of 206.77, the force will
be greater by a factor of 206 .772 = 42754.
ANSWER: 42754 | |
E1_solver_manual_det:book_em_0041:turn0 | book_em_0041 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Physicist Richard Feynman originated a new way of thinking
about... | Replacing either charge in p/1 with a lightcolored charge moving backward in time gives
a diagram like p/2, which is still an attraction.
Doing something similar to p/4 results in p/3,
which is still a repulsion. It also works the other
way around, e.g., you can do it to the bottom
charge in p/2, which gives something ... | [
"book_em_0041_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Physicist Richard Feynman originated a new way of thinking
about... | Replacing either charge in p/1 with a lightcolored charge moving backward in time gives
a diagram like p/2, which is still an attraction.
Doing something similar to p/4 results in p/3,
which is still a repulsion. It also works the other
way around, e.g., you can do it to the bottom
charge in p/2, which gives something ... | |
E1_solver_manual_det:book_em_0043_b:turn0 | book_em_0043_b | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You can’t use a light wave to see things that are smaller than
t... | No, because the wavelength of visible light
is thousands of times bigger than the size of an
atom.
ANSWER: atom. | [
"book_em_0043_b_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
You can’t use a light wave to see things that are smaller than
t... | No, because the wavelength of visible light
is thousands of times bigger than the size of an
atom.
ANSWER: atom. | |
E1_solver_manual_det:book_em_0045:turn0 | book_em_0045 | ELECTROMAGNETISM | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
This book begins and ends with the topic of light. Give an
examp... | The correspondence principle says that
new models have to be backward-compatible
with old ones, i.e., the new model has to explain
successfully all the same observations that the
old model was able to deal with. The beginning of the book used the ray model, but now
we’ve learned about the wave model. The ray
model was ... | [
"book_em_0045_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
This book begins and ends with the topic of light. Give an
examp... | The correspondence principle says that
new models have to be backward-compatible
with old ones, i.e., the new model has to explain
successfully all the same observations that the
old model was able to deal with. The beginning of the book used the ray model, but now
we’ve learned about the wave model. The ray
model was ... | |
E1_solver_manual_det:book_optics_0051:turn0 | book_optics_0051 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A man is walking at 1.0 m/s directly towards a flat mirror.
At w... | The image is at an equal distance behind
the mirror, so the distance between the man and
his image is twice his distance from the mirror,
and his separation from his image is reducing at
a rate of 2.0 m/s.
ANSWER: a rate of 2.0 m/s. | [
"book_optics_0051_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A man is walking at 1.0 m/s directly towards a flat mirror.
At w... | The image is at an equal distance behind
the mirror, so the distance between the man and
his image is twice his distance from the mirror,
and his separation from his image is reducing at
a rate of 2.0 m/s.
ANSWER: a rate of 2.0 m/s. | |
E1_solver_manual_det:book_optics_0052:turn0 | book_optics_0052 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If a mirror on a wall is only big enough for you to see yourself... | If you’re going to see a particular part of
your body, then rays from that part of your body
have to be able to go to the mirror, be reflected,
and go into your eye. If we’re trying to find the
lowest part you can see, then we’re interested in
the case where the ray hits the very bottom of
the mirror. Backing up doesn’... | [
"book_optics_0052_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If a mirror on a wall is only big enough for you to see yourself... | If you’re going to see a particular part of
your body, then rays from that part of your body
have to be able to go to the mirror, be reflected,
and go into your eye. If we’re trying to find the
lowest part you can see, then we’re interested in
the case where the ray hits the very bottom of
the mirror. Backing up doesn’... | |
E1_solver_manual_det:book_optics_0055:turn0 | book_optics_0055 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If the user of an astronomical telescope moves her head
closer t... | The magnification is the ratio of the image’s size to the object’s size. It has nothing
to do with the person’s location. The angular
magnification, however, does depend on the person’s location, because things farther away subtend smaller angles. The distance to the actual
object is not changed significantly, since it... | [
"book_optics_0055_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
If the user of an astronomical telescope moves her head
closer t... | The magnification is the ratio of the image’s size to the object’s size. It has nothing
to do with the person’s location. The angular
magnification, however, does depend on the person’s location, because things farther away subtend smaller angles. The distance to the actual
object is not changed significantly, since it... | |
E1_solver_manual_det:book_optics_0056:turn0 | book_optics_0056 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Here’s a game my kids like to play. I sit next to a sunny
window... | The problem can be simplified conceptually by replacing the hypothetical square watch
with a square hole in a piece of paper. This version is also easy to construct and test experimentally. The bundle of rays transmitted through
the hole is identical to the bundle that would be
reflected by a specular-reflecting square... | [
"book_optics_0056_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Here’s a game my kids like to play. I sit next to a sunny
window... | The problem can be simplified conceptually by replacing the hypothetical square watch
with a square hole in a piece of paper. This version is also easy to construct and test experimentally. The bundle of rays transmitted through
the hole is identical to the bundle that would be
reflected by a specular-reflecting square... | |
E1_solver_manual_det:book_optics_0057:turn0 | book_optics_0057 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A Global Positioning System (GPS) receiver is a device that
lets... | The time it takes light to travel a few meters, say 3 m, is (3 m)/(3× 108 m/s) = 10−8 s.
ANSWER: 10−8 s | [
"book_optics_0057_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
A Global Positioning System (GPS) receiver is a device that
lets... | The time it takes light to travel a few meters, say 3 m, is (3 m)/(3× 108 m/s) = 10−8 s.
ANSWER: 10−8 s | |
E1_solver_manual_det:book_optics_0059:turn0 | book_optics_0059 | OPTICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The Stealth Bomber is designed with flat, smooth surfaces.
Why w... | Because the surfaces are flat, you get
specular reflection. In specular reflection, all the
reflected rays go in one direction. Unless the
plane is directly overhead, that direction won’t
be the right direction to make the rays come back
to the radar station.
This is different from a normal plane, which
has complicated... | [
"book_optics_0059_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
The Stealth Bomber is designed with flat, smooth surfaces.
Why w... | Because the surfaces are flat, you get
specular reflection. In specular reflection, all the
reflected rays go in one direction. Unless the
plane is directly overhead, that direction won’t
be the right direction to make the rays come back
to the radar station.
This is different from a normal plane, which
has complicated... | |
E1_solver_manual_det:book_mech_0060:turn0 | book_mech_0060 | MECHANICS | 0 | [] | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Many single-celled organisms propel themselves through water
wit... | 0.07 to 0.10 s
( 1
15 Hz to 110 Hz)
ANSWER: 15 Hz to 110 Hz) | [
"book_mech_0060_sol1"
] | E1_solver_manual_det | Solve the following physics problem step by step (in at most 10 logical steps). State the governing physical equations, perform algebraic substitutions clearly, include SI units, and end with the final answer on a new line prefixed with ANSWER:.
PROBLEM:
Many single-celled organisms propel themselves through water
wit... | 0.07 to 0.10 s
( 1
15 Hz to 110 Hz)
ANSWER: 15 Hz to 110 Hz) |
End of preview. Expand in Data Studio
Adversarial Physics Solver — Experiment E1 (solver_e1_manual_det)
Codebase & Pipeline Repository: vital-ar/adversarial_physics_problems_solver
Dataset Overview
solver_e1_manual_det is Dataset 1 (Model 1 / E1) in the 4-stage Lexsi AI (CuratorKIT + AlignTune + AuditKIT) progressive data-curation ablation study for the Adversarial Physics Problem Solver–Verifier system.
This dataset represents the pre-CuratorKIT manual deterministic baseline: it contains all university-level physics problems that passed handwritten Python regex and rule-based filtering immediately before any CuratorKIT normalizers, deduplicators, or quality gates were applied.
- Role in Ablation Ladder: Isolates the baseline performance of
CohereLabs/tiny-aya-globalwhen fine-tuned withAlignTuneon data filtered solely by manual Python rules (1,076training problems), directly comparable againstE2(CuratorKITwithout LLM tools,728problems),E3(CuratorKIT+CohereForAI/aya-expanse-8bcanonical normalization,681problems), andE4(full Stage 2 adversarial multi-trajectory & hint-conditioned SFT,1,444examples). - Target Student Model:
CohereLabs/tiny-aya-global(fine-tuned viaAlignTune). - Evaluation Benchmark: Evaluated with
AuditKIT(18-metric suite) on the locked 38-problem Validation and 38-problem Test splits from PhysGym.
Splits & Domain Distribution
| Split | File | Examples | Source | Description |
|---|---|---|---|---|
train |
train.jsonl |
1,076 | 12 PhysGym seeds + 1,064 Crowell textbook problems |
Manual-rule-filtered Turn-0 Solver training pool before CuratorKIT |
validation |
validation.jsonl |
38 | PhysGym (validation split) |
Locked held-out validation benchmark for early stopping & hyperparameter selection |
test |
test.jsonl |
38 | PhysGym (test split) |
Locked held-out test benchmark for final AuditKIT evaluation |
Training Split Domain Breakdown (1,076 Examples)
| Physics Domain | Count | Share |
|---|---|---|
MECHANICS |
645 | 59.9% |
ELECTROMAGNETISM |
228 | 21.2% |
MODERN_PHYSICS |
105 | 9.8% |
RELATIVITY |
51 | 4.7% |
OPTICS |
24 | 2.2% |
THERMODYNAMICS |
23 | 2.1% |
| Total | 1,076 | 100.0% |
What Manual Filtering Was Applied (Before CuratorKIT)
- PhysGym Seed Step-Count Filter: Retained
12of the21PhysGym training seeds solvable within1–10logical reasoning operations (9multi-page competition derivations with11–20steps were excluded). - Independent Multi-Part Subproblem Splitting: Extracted standalone single-target subproblems (
(a),(b)) from the986Crowell textbook problems (1,163split candidates). - Manual Regex Hygiene & Self-Containment Rules: Removed running PDF headers/footers, ensured an explicit
ANSWER: <value_or_expression>sentinel line, and filtered out99subproblems with visual figure dependencies ("in the figure","from the graph"), external cross-references ("see problem 2 on p. 1028"), or> 10logical steps. - What Is Still Present (Addressed in
E2byCuratorKIT): Near-duplicate textbook formulations, within-pool semantic overlap, and un-normalized raw textbook prose (348redundant/overlapping entries thatCuratorKIT'sEmbeddingDeduplicator,MinHashDeduplicator, andDiversityGateremove inE2).
Schema
Each record in train.jsonl, validation.jsonl, and test.jsonl follows the canonical SolverTrajectory JSON schema:
{
"trajectory_id": "E1_solver_manual_det:physgym_0010:turn0",
"problem_id": "physgym_0010",
"domain": "ELECTROMAGNETISM",
"turn": 0,
"accumulated_directives": [],
"prompt": "### Physics Problem:\n...\n\n### Instructions:\nSolve the problem step-by-step in 1 to 10 concise logical steps and end with `ANSWER: <final_value_or_expression>`.",
"target_output": "...\nANSWER: ...",
"source_candidate_ids": ["physgym_0010_sol1"],
"dataset_tier": "E1_solver_manual_det"
}
Provenance & Integrity Files
manifest.json—CuratorKITpipeline execution manifest.lexsi_provenance.json—lexsi.provenance/1lineage record consumed byAlignTuneandAuditKIT.checksums.txt— SHA-256 digests of all split and metadata files.- Project Repository & Codebase: https://github.com/vital-ar/adversarial_physics_problems_solver
- Downloads last month
- 102