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) | |
E1_solver_manual_det:book_mech_0061_a:turn0 | book_mech_0061_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:
Pendulum 2 has a string twice as long as pendulum 1. If
we defin... | Pendulum 2 has then same total force
on it when it is at the same angle, but when the
333
Problem 7-8.
two pendula are at the same angle, pendulum 2
is at twice the distance from equilibrium. Pendulum 2’s F−x graph will therefore look like
pendulum 1’s, but stretched out twice as wide.
Since k is the slope of this grap... | [
"book_mech_0061_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:
Pendulum 2 has a string twice as long as pendulum 1. If
we defin... | Pendulum 2 has then same total force
on it when it is at the same angle, but when the
333
Problem 7-8.
two pendula are at the same angle, pendulum 2
is at twice the distance from equilibrium. Pendulum 2’s F−x graph will therefore look like
pendulum 1’s, but stretched out twice as wide.
Since k is the slope of this grap... | |
E1_solver_manual_det:book_mech_0062_b:turn0 | book_mech_0062_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:
The following is a graph of the height of a water wave as a
func... | Since v = fλ, doubling both velocity and frequency leaves the wavelength unchanged. This is
exactly the same as the orginal wave.
ANSWER: fλ, doubling both velocity and frequency leaves the wavelength unchanged | [
"book_mech_0062_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:
The following is a graph of the height of a water wave as a
func... | Since v = fλ, doubling both velocity and frequency leaves the wavelength unchanged. This is
exactly the same as the orginal wave.
ANSWER: fλ, doubling both velocity and frequency leaves the wavelength unchanged | |
E1_solver_manual_det:book_mech_0062_c:turn0 | book_mech_0062_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:
The following is a graph of the height of a water wave as a
func... | The information about the velocity is irrelevant. We’re
given the wavelength and amplitude directly, so
that’s all we need to show. (The change in velocity implies an additional change in frequency
for the given wavelength, but the wavelength is
1/3 the original, not 1/6.)
original
ANSWER: original | [
"book_mech_0062_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:
The following is a graph of the height of a water wave as a
func... | The information about the velocity is irrelevant. We’re
given the wavelength and amplitude directly, so
that’s all we need to show. (The change in velocity implies an additional change in frequency
for the given wavelength, but the wavelength is
1/3 the original, not 1/6.)
original
ANSWER: original | |
E1_solver_manual_det:book_mech_0065:turn0 | book_mech_0065 | 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 musical note middle C has a frequency of 262 Hz. What
are it... | T = 1 /f = 3 .82 ms, and λ = v/f =
(340 m/s)/f = 1.3 m.
ANSWER: 1.3 m | [
"book_mech_0065_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 musical note middle C has a frequency of 262 Hz. What
are it... | T = 1 /f = 3 .82 ms, and λ = v/f =
(340 m/s)/f = 1.3 m.
ANSWER: 1.3 m | |
E1_solver_manual_det:book_em_0066:turn0 | book_em_0066 | 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 Fullerton, California, the earth’s magnetic field is in the
d... | By/Bx = tan 59 deg = 1.7
ANSWER: 1.7 | [
"book_em_0066_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 Fullerton, California, the earth’s magnetic field is in the
d... | By/Bx = tan 59 deg = 1.7
ANSWER: 1.7 | |
E1_solver_manual_det:book_em_0067_a:turn0 | book_em_0067_a | 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:
Suppose that, as in minilab 1 on p. 38, we have a known ambient ... | Bm/Ba = tanθ
ANSWER: tanθ | [
"book_em_0067_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:
Suppose that, as in minilab 1 on p. 38, we have a known ambient ... | Bm/Ba = tanθ
ANSWER: tanθ | |
E1_solver_manual_det:book_em_0068:turn0 | book_em_0068 | 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:
If you add a magnetic field with magnitude 1 T to a field of
mag... | The maximum is 3 T, which is achieved
when the fields are in the same direction. The
minimum is 1 T, when they are in opposite direction. By varying the angle between the vectors
from 0 to 180 degrees, all values in between can
be achieved as well.
ANSWER: be achieved as well. | [
"book_em_0068_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 you add a magnetic field with magnitude 1 T to a field of
mag... | The maximum is 3 T, which is achieved
when the fields are in the same direction. The
minimum is 1 T, when they are in opposite direction. By varying the angle between the vectors
from 0 to 180 degrees, all values in between can
be achieved as well.
ANSWER: be achieved as well. | |
E1_solver_manual_det:book_em_0069:turn0 | book_em_0069 | 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 electric fields, both lying in the x-y plane, are superposed... | This problem has to be done analytically,
not graphically, because it requires such high
precision. The two given angles are both measured counterclockwise from the right, which is
convenient; for angles defined this way, we can
always find x components using a cosine, and y
components using a sine, and the plus and mi... | [
"book_em_0069_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 electric fields, both lying in the x-y plane, are superposed... | This problem has to be done analytically,
not graphically, because it requires such high
precision. The two given angles are both measured counterclockwise from the right, which is
convenient; for angles defined this way, we can
always find x components using a cosine, and y
components using a sine, and the plus and mi... | |
E1_solver_manual_det:book_em_0070_a:turn0 | book_em_0070_a | 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:
Which of the following expressions make sense, and which are
non... | The cross product inside the parentheses results in a vector, and the second cross product results in a vector.
ANSWER: The cross product inside the parentheses results in a vector, and the second cross product results in a vector. | [
"book_em_0070_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:
Which of the following expressions make sense, and which are
non... | The cross product inside the parentheses results in a vector, and the second cross product results in a vector.
ANSWER: The cross product inside the parentheses results in a vector, and the second cross product results in a vector. | |
E1_solver_manual_det:book_em_0070_b:turn0 | book_em_0070_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:
Which of the following expressions make sense, and which are
non... | The cross product
gives a vector, and then dotting it with the other
vector gives a scalar.
ANSWER: vector gives a scalar. | [
"book_em_0070_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:
Which of the following expressions make sense, and which are
non... | The cross product
gives a vector, and then dotting it with the other
vector gives a scalar.
ANSWER: vector gives a scalar. | |
E1_solver_manual_det:book_em_0070_c:turn0 | book_em_0070_c | 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:
Which of the following expressions make sense, and which are
non... | The dot product gives
a scalar, but you can’t take a cross product of a
scalar with a vector. This one is nonsense.
ANSWER: scalar with a vector. This one is nonsense. | [
"book_em_0070_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:
Which of the following expressions make sense, and which are
non... | The dot product gives
a scalar, but you can’t take a cross product of a
scalar with a vector. This one is nonsense.
ANSWER: scalar with a vector. This one is nonsense. | |
E1_solver_manual_det:book_em_0071:turn0 | book_em_0071 | 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:
Find the angle between the following two vectors:
ˆx + 2ˆy + 3ˆz... | a· b =|a||b| cosθab
θab = cos−1
( a· b
|a||b|
)
= 12.9◦
ANSWER: 12.9◦ | [
"book_em_0071_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:
Find the angle between the following two vectors:
ˆx + 2ˆy + 3ˆz... | a· b =|a||b| cosθab
θab = cos−1
( a· b
|a||b|
)
= 12.9◦
ANSWER: 12.9◦ | |
E1_solver_manual_det:book_em_0072:turn0 | book_em_0072 | 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:
Find a vector that is perpendicular to both of the following
two... | The easiest way to find such a vector is to
take the cross product.
(A× B)x =AyBz−ByAz =−3
(A× B)y =AzBx−BzAx = 6
(A× B)z =AxBy−BxAy =−3
335
So our vector is −3ˆx + 6ˆy− 3ˆz. We could also
use any other vector lying along the same line,
i.e., any scalar multiple of this one. I checked my
result by computing its dot pro... | [
"book_em_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:
Find a vector that is perpendicular to both of the following
two... | The easiest way to find such a vector is to
take the cross product.
(A× B)x =AyBz−ByAz =−3
(A× B)y =AzBx−BzAx = 6
(A× B)z =AxBy−BxAy =−3
335
So our vector is −3ˆx + 6ˆy− 3ˆz. We could also
use any other vector lying along the same line,
i.e., any scalar multiple of this one. I checked my
result by computing its dot pro... | |
E1_solver_manual_det:book_em_0073_a:turn0 | book_em_0073_a | 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 earth’s magnetic field measured inside a certain classroom
i... | Applying the Pythagorean theorem
gives 30.0 µT.
ANSWER: gives 30.0 µT. | [
"book_em_0073_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:
The earth’s magnetic field measured inside a certain classroom
i... | Applying the Pythagorean theorem
gives 30.0 µT.
ANSWER: gives 30.0 µT. | |
E1_solver_manual_det:book_em_0073_b:turn0 | book_em_0073_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:
The earth’s magnetic field measured inside a certain classroom
i... | For a uniform field, the relationship
dUB = ( c2/8πk)B2dv is equivalent to UB =
(c2/8πk)B2v, which gives 1.43× 10−2 J.
ANSWER: (c2/8πk)B2v, which gives 1.43× 10−2 J | [
"book_em_0073_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:
The earth’s magnetic field measured inside a certain classroom
i... | For a uniform field, the relationship
dUB = ( c2/8πk)B2dv is equivalent to UB =
(c2/8πk)B2v, which gives 1.43× 10−2 J.
ANSWER: (c2/8πk)B2v, which gives 1.43× 10−2 J | |
E1_solver_manual_det:book_em_0074:turn0 | book_em_0074 | 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 nuclei 3H (hydrogen-3, or tritium) and 3He (helium-3)
have a... | The energy density is proportional to the
square of the field, so if the field patterns are
identical except for a scaling up by a factor of 2,
the energy in 3He is greater by a factor of 4.
ANSWER: the energy in 3He is greater by a factor of 4. | [
"book_em_0074_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 nuclei 3H (hydrogen-3, or tritium) and 3He (helium-3)
have a... | The energy density is proportional to the
square of the field, so if the field patterns are
identical except for a scaling up by a factor of 2,
the energy in 3He is greater by a factor of 4.
ANSWER: the energy in 3He is greater by a factor of 4. | |
E1_solver_manual_det:book_em_0075:turn0 | book_em_0075 | 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 strongest magnetic field at the earth’s surface is 66 µT,
of... | The energy density of the magnetic
field is proportional to the square of the
field, so the ratio of the energy densities is
[(66 µT)/(23 µT)]2 = 8.2.
ANSWER: 8.2 | [
"book_em_0075_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 strongest magnetic field at the earth’s surface is 66 µT,
of... | The energy density of the magnetic
field is proportional to the square of the
field, so the ratio of the energy densities is
[(66 µT)/(23 µT)]2 = 8.2.
ANSWER: 8.2 | |
E1_solver_manual_det:book_em_0076:turn0 | book_em_0076 | 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 electric and magnetic fields have different units, so we
can... | Setting (c2/8πk)B2 = (1/8πk)E2 gives
E/B =c.
ANSWER: c | [
"book_em_0076_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 electric and magnetic fields have different units, so we
can... | Setting (c2/8πk)B2 = (1/8πk)E2 gives
E/B =c.
ANSWER: c | |
E1_solver_manual_det:book_em_0077_a:turn0 | book_em_0077_a | 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 an electrical storm, an electric field builds up in the space... | The energy per unit volume is
E
V = 18πk|E|2 .
(E is energy, E is electric field.) At the moment
when the lightning strikes, the field equals Ec.
The volume of the air in which the field exists is
L2h.
E = 18πkE2cL2h
ANSWER: 18πkE2cL2h | [
"book_em_0077_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 an electrical storm, an electric field builds up in the space... | The energy per unit volume is
E
V = 18πk|E|2 .
(E is energy, E is electric field.) At the moment
when the lightning strikes, the field equals Ec.
The volume of the air in which the field exists is
L2h.
E = 18πkE2cL2h
ANSWER: 18πkE2cL2h | |
E1_solver_manual_det:book_em_0079_a:turn0 | book_em_0079_a | 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:
Throughout this problem, we will use the standard notation
ρ (Gr... | The energy depends on the square of
the field, so we have
α = (E1 + E2)2
E21
= (E1 + E2)· E1 + E2)E21
= E21 + 2E1· E2 +E22
E21
= 2 + 2 cosθ
θ = cos−1
(α
2− 1
)
.
ANSWER: . | [
"book_em_0079_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:
Throughout this problem, we will use the standard notation
ρ (Gr... | The energy depends on the square of
the field, so we have
α = (E1 + E2)2
E21
= (E1 + E2)· E1 + E2)E21
= E21 + 2E1· E2 +E22
E21
= 2 + 2 cosθ
θ = cos−1
(α
2− 1
)
.
ANSWER: . | |
E1_solver_manual_det:book_em_0080:turn0 | book_em_0080 | 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:
Prove the anticommutative property of the vector cross product, ... | The definition of the vector cross product
in terms of the components is (A×B)x =AyBz−
ByAz, and similarly for y and z. Reversing the
roles of A and B interchanges the positive and
negative terms on the right, so the sign flips.
ANSWER: negative terms on the right, so the sign flips. | [
"book_em_0080_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:
Prove the anticommutative property of the vector cross product, ... | The definition of the vector cross product
in terms of the components is (A×B)x =AyBz−
ByAz, and similarly for y and z. Reversing the
roles of A and B interchanges the positive and
negative terms on the right, so the sign flips.
ANSWER: negative terms on the right, so the sign flips. | |
E1_solver_manual_det:book_em_0081:turn0 | book_em_0081 | 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:
Find three vectors with which you can demonstrate that the
vecto... | Since it’s not associative in general, we
expect that almost any set of three vectors, chosen at random, will provide a suitable counterexample. I decided to use combinations of the
unit vectors ˆx, ˆy, and ˆz, since they’re easy to
calculate with. The first example I tried was
ˆx×(ˆy׈z), which demonstrated Murphy’s l... | [
"book_em_0081_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:
Find three vectors with which you can demonstrate that the
vecto... | Since it’s not associative in general, we
expect that almost any set of three vectors, chosen at random, will provide a suitable counterexample. I decided to use combinations of the
unit vectors ˆx, ˆy, and ˆz, since they’re easy to
calculate with. The first example I tried was
ˆx×(ˆy׈z), which demonstrated Murphy’s l... | |
E1_solver_manual_det:book_em_0082:turn0 | book_em_0082 | 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:
Let a and b be any two numbers (not both zero), and let
u = aˆx ... | Let v = cˆx +dˆy, where c and d are to
be found. We don’t expect to be able to determine both c and d uniquely, because for any v
that works, so will any nonzero scalar multiple
of it. That is, we only expect to be able to find
the ratio c/d, which expresses how big c is in
proportion to d.
We want v to be perpendicula... | [
"book_em_0082_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:
Let a and b be any two numbers (not both zero), and let
u = aˆx ... | Let v = cˆx +dˆy, where c and d are to
be found. We don’t expect to be able to determine both c and d uniquely, because for any v
that works, so will any nonzero scalar multiple
of it. That is, we only expect to be able to find
the ratio c/d, which expresses how big c is in
proportion to d.
We want v to be perpendicula... | |
E1_solver_manual_det:book_em_0086_a:turn0 | book_em_0086_a | 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 gravitational field g of a typical asteroid is so weak that ... | The total force acting on the particle
is mg +qE, so by Newton’s second law its acceleration is a =g + (q/m)E. This makes sense
because when q = 0, we get a =g. Applying the
constant-acceleration equation v2f = v20 + 2a∆x
gives h =−v2/2(g +qE/m). In the case where
gravity is dominant, the negative value ofg gives
h> 0,... | [
"book_em_0086_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:
The gravitational field g of a typical asteroid is so weak that ... | The total force acting on the particle
is mg +qE, so by Newton’s second law its acceleration is a =g + (q/m)E. This makes sense
because when q = 0, we get a =g. Applying the
constant-acceleration equation v2f = v20 + 2a∆x
gives h =−v2/2(g +qE/m). In the case where
gravity is dominant, the negative value ofg gives
h> 0,... | |
E1_solver_manual_det:book_em_0086_b:turn0 | book_em_0086_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:
The gravitational field g of a typical asteroid is so weak that ... | Plugging in gives 83 m. This is comparable to the asteroid’s “football-field” size, so the
approximation ofg as a constant may not be correct. Our result should probably be taken as a
lower bound.
ANSWER: lower bound. | [
"book_em_0086_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:
The gravitational field g of a typical asteroid is so weak that ... | Plugging in gives 83 m. This is comparable to the asteroid’s “football-field” size, so the
approximation ofg as a constant may not be correct. Our result should probably be taken as a
lower bound.
ANSWER: lower bound. | |
E1_solver_manual_det:book_em_0087_a:turn0 | book_em_0087_a | 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 an inkjet printer, a series of droplets of ink, each with
mas... | Let thex axis be in the initial direction
of motion andy the direction of the electric field.
Newton’s laws tell us that thex andy motion are
independent, so the x velocity is constant, and
the time taken to pass through the capacitor is
t = w/u. The final velocity in the y diection is
v = at = (q/m)Et = qEw/mu. The de... | [
"book_em_0087_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 an inkjet printer, a series of droplets of ink, each with
mas... | Let thex axis be in the initial direction
of motion andy the direction of the electric field.
Newton’s laws tell us that thex andy motion are
independent, so the x velocity is constant, and
the time taken to pass through the capacitor is
t = w/u. The final velocity in the y diection is
v = at = (q/m)Et = qEw/mu. The de... | |
E1_solver_manual_det:book_em_0087_b:turn0 | book_em_0087_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:
Evaluate your result, in radians, for m = 2.0 × 10−10 kg, u =
20... | Converting the given data to SI and plugging
in, the result is θ = 0.98 radians, or a little more
than a 45 degree angle.
ANSWER: 0.98 radians, or a little more than a 45 degree angle | [
"book_em_0087_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:
Evaluate your result, in radians, for m = 2.0 × 10−10 kg, u =
20... | Converting the given data to SI and plugging
in, the result is θ = 0.98 radians, or a little more
than a 45 degree angle.
ANSWER: 0.98 radians, or a little more than a 45 degree angle | |
E1_solver_manual_det:book_em_0088_a:turn0 | book_em_0088_a | 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:
At time t = 0, a positively charged particle is placed,
at rest,... | F = ma and F = qE, and since the
field is uniform, the force and acceleration will be
constant. For motion with constant acceleration,
we havev =at, and eliminating the unknown F
givesv =qEt/m.
ANSWER: qEt/m | [
"book_em_0088_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:
At time t = 0, a positively charged particle is placed,
at rest,... | F = ma and F = qE, and since the
field is uniform, the force and acceleration will be
constant. For motion with constant acceleration,
we havev =at, and eliminating the unknown F
givesv =qEt/m.
ANSWER: qEt/m | |
E1_solver_manual_det:book_em_0088_b:turn0 | book_em_0088_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:
If this is done with two different objects and they are observed... | You can conclude that they have the same
ratio of q/m, but you can’t tell whether they
have the sameq and the samem. One could have
twice the charge and twice the mass compared to
the other, for instance.
ANSWER: the other, for instance. | [
"book_em_0088_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:
If this is done with two different objects and they are observed... | You can conclude that they have the same
ratio of q/m, but you can’t tell whether they
have the sameq and the samem. One could have
twice the charge and twice the mass compared to
the other, for instance.
ANSWER: the other, for instance. | |
E1_solver_manual_det:book_em_0089:turn0 | book_em_0089 | 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:
Suppose that at some instant in time, a wire extending from
x = ... | q =
∫ x=∞
x=0
dq
=
∫ ∞
0
dq
dx dx
=
∫ ∞
0
ae−bx dx
= ab
ANSWER: ab | [
"book_em_0089_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 that at some instant in time, a wire extending from
x = ... | q =
∫ x=∞
x=0
dq
=
∫ ∞
0
dq
dx dx
=
∫ ∞
0
ae−bx dx
= ab
ANSWER: ab | |
E1_solver_manual_det:book_em_0090_a:turn0 | book_em_0090_a | 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:
Example 3 on p. 51 calculated the field of a dipole in its midpl... | If positive is the direction from the negative charge to the positive charge, and we pick a
point on the positive side, then adding the fields
of the two charges gives
E =kq
[
(r−𝓁/2)−2− (r +𝓁/2)−2].
This is an odd function of r, but in fact the field
is physically an even function of r. If we had
evaluated the field... | [
"book_em_0090_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:
Example 3 on p. 51 calculated the field of a dipole in its midpl... | If positive is the direction from the negative charge to the positive charge, and we pick a
point on the positive side, then adding the fields
of the two charges gives
E =kq
[
(r−𝓁/2)−2− (r +𝓁/2)−2].
This is an odd function of r, but in fact the field
is physically an even function of r. If we had
evaluated the field... | |
E1_solver_manual_det:book_em_0092:turn0 | book_em_0092 | 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:
Three charges are arranged on a square as shown. All three
charg... | Let the square’s sides be of length a. The
field at the center is the vector sum of the fields
that would have been produced individually by
the three charges. Each of these individual fields
iskq/r2, wherer1 =a/√2 for the two chargesq1,
andr2 =a/2 forq2. Vector addition can be done
by adding components. Letx be horizo... | [
"book_em_0092_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:
Three charges are arranged on a square as shown. All three
charg... | Let the square’s sides be of length a. The
field at the center is the vector sum of the fields
that would have been produced individually by
the three charges. Each of these individual fields
iskq/r2, wherer1 =a/√2 for the two chargesq1,
andr2 =a/2 forq2. Vector addition can be done
by adding components. Letx be horizo... | |
E1_solver_manual_det:book_em_0093_a:turn0 | book_em_0093_a | 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:
Use Gauss’ law to find the field inside an infinite cylinder
wit... | The setup is similar to the preceding problem. We again choose as our Gaussian
surface a finite cylinder of length 𝓁 and radius
R. Gauss’s law gives 2 πR𝓁E = 4πkqin, where
qin = πR2𝓁ρ. Solving for the field, we have
E = 2πkRρ.
ANSWER: 2πkRρ | [
"book_em_0093_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:
Use Gauss’ law to find the field inside an infinite cylinder
wit... | The setup is similar to the preceding problem. We again choose as our Gaussian
surface a finite cylinder of length 𝓁 and radius
R. Gauss’s law gives 2 πR𝓁E = 4πkqin, where
qin = πR2𝓁ρ. Solving for the field, we have
E = 2πkRρ.
ANSWER: 2πkRρ | |
E1_solver_manual_det:book_em_0093_b:turn0 | book_em_0093_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:
Check that your answer makes sense on the axis. | At R = 0, we get E = 0. This makes sense,
because the field has to vanish on the axis by
symmetry. If it were to be nonzero, there would
be no way to decide which direction it should
point.
ANSWER: point. | [
"book_em_0093_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:
Check that your answer makes sense on the axis. | At R = 0, we get E = 0. This makes sense,
because the field has to vanish on the axis by
symmetry. If it were to be nonzero, there would
be no way to decide which direction it should
point.
ANSWER: point. | |
E1_solver_manual_det:book_em_0093_c:turn0 | book_em_0093_c | 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:
Check that the units of your answer make sense. | The units of E = 2πkRρ are
N
C =?
(N·m2
C2
)
(m)
( C
m3
)
,
which does check out.
ANSWER: which does check out. | [
"book_em_0093_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:
Check that the units of your answer make sense. | The units of E = 2πkRρ are
N
C =?
(N·m2
C2
)
(m)
( C
m3
)
,
which does check out.
ANSWER: which does check out. | |
E1_solver_manual_det:book_em_0095_a:turn0 | book_em_0095_a | 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:
Several pointlike, interacting particles are released, all initi... | The two particles are already at the
greatest distance from one another that is allowed by conservation of energy, so neither can
escape.
ANSWER: escape. | [
"book_em_0095_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:
Several pointlike, interacting particles are released, all initi... | The two particles are already at the
greatest distance from one another that is allowed by conservation of energy, so neither can
escape.
ANSWER: escape. | |
E1_solver_manual_det:book_em_0095_b:turn0 | book_em_0095_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:
Several pointlike, interacting particles are released, all initi... | By bringing two of the particles close together, we can reduce the gravitational potential energy to an arbitrarily large negative value.
This allows the third particle to escape without
violating conservation of energy. By similar reasoning, we expect that systems such as our solar
339
system may, over long time scale... | [
"book_em_0095_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:
Several pointlike, interacting particles are released, all initi... | By bringing two of the particles close together, we can reduce the gravitational potential energy to an arbitrarily large negative value.
This allows the third particle to escape without
violating conservation of energy. By similar reasoning, we expect that systems such as our solar
339
system may, over long time scale... |
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