Question 1

A glider on an air track is connected by a spring to the end of the air track. If it takes $0.30 \mathrm{~s}$ for the glider to travel the distance of $12 \mathrm{~cm}$ from one turning point to the other, its amplitude is

Accepted Answer

The amplitude of a simple harmonic motion is the maximum displacement from the equilibrium position. The distance given (12 cm) is the total round trip from one turning point to the other and back to the starting point, which means the amplitude (half the round trip) is 6 cm.

Question 2

Consider the glider described in problem N10T.4. Its phase rate is

Accepted Answer

The answer of Consider the glider described in problem N10T.4....

Question 3

Suppose the $\mathrm{x}$-position of an oscillating object is given by $x(t)=A \cos (\omega t+\theta)$. What is the object's speed at time $\mathrm{t}=0$ ?

Accepted Answer

The speed of the object is the magnitude of the derivative of its position with respect to time. Differentiating $x(t)=A \cos (\omega t+\theta)$ with respect to $t$ gives the velocity $v(t) = -A\omega \sin(\omega t + \theta)$. At $t=0$, $v(0) = -A\omega \sin(\theta)$, and the speed, being the magnitude of velocity, is $|A\omega \sin(\theta)|$.

Question 4

A glider on an air track is connected by a spring to the end of the air track. If it is pulled $3.5 \mathrm{~cm}$ in the $+x$ direction away from its equilibrium point and then released from rest at $t=0$, what is the initial phase $\theta$ ?

Accepted Answer

The initial phase is 0 because the glider is released from rest at the equilibrium point.

Question 5

A glider on an air track is connected by a spring to the end of the air track. If it is pulled $3.5 \mathrm{~cm}$ in the $-x$ direction away from its equilibrium point and then released from rest at $t=0$, what is the initial phase $\theta$ ?

Accepted Answer

The answer of A glider on an air track is...

Question 6

A mass hanging from the end of a spring has a phase rate of $\omega=6.3 \mathrm{~s}^{-1} \approx 1$ cycle/s. Let's define $t=0$ to be when the mass passes $x=0$ going up. If its speed as it passes is $1.0 \mathrm{~m} / \mathrm{s}$, what is its amplitude $A$ ?

Accepted Answer

The amplitude $A$ can be found using the relationship between the maximum speed $v_{max}$, the angular frequency $\omega$, and the amplitude $A$, which is given by $v_{max} = \omega A$. Given that the speed as it passes $x=0$ is $1.0 \mathrm{~m/s}$ and $\omega = 6.3 \mathrm{~s}^{-1}$, we can solve for $A$ as $A = \frac{v_{max}}{\omega} = \frac{1.0}{6.3} \approx 0.16 \mathrm{~m}$.

Question 7

Suppose we know the value of $\omega$ for a simple harmonic oscillator. What further information do we need to know to fix the amplitude $A$ and the initial phase $\theta$ in the solution to the simple harmonic oscillator equation? (If more than one item is needed, feel free to indicate more than one answer.)

Accepted Answer

The answer of Suppose we know the value of $\omega$...

Question 8

To double the period of a pendulum, you need to multiply its length by a factor of:

Accepted Answer

The period of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity. To double the period, the new period $T'$ is $2T$, so $2T = 2\pi\sqrt{\frac{L'}{g}}$. Solving for $L'$ in terms of $L$ gives $L' = 4L$, meaning the length must be multiplied by 4.

Question 9

For a swinging pendulum, the maximum angle that the pendulum's string makes with the vertical corresponds to what in the pendulum solution $\phi=A \cos (\omega t+\theta)$ ?

Accepted Answer

The maximum angle $\phi$ that the pendulum's string makes with the vertical corresponds to the amplitude $A$ in the solution $\phi=A \cos (\omega t+\theta)$. The amplitude $A$ represents the maximum displacement from the equilibrium position, which in the context of a pendulum, is the maximum angular displacement from the vertical.

Question 10

Kepler's second law implies that as a planet's distance from the sun increases in an elliptical orbit, its orbital speed

Accepted Answer

The answer of Kepler's second law implies that as a...

Question 11

The sun's mass is about 1000 times that of Jupiter, and the radius of Jupiter's orbit is about 1100 times the sun's radius. The center of mass of the sun/Jupiter system is inside the sun.

Accepted Answer

The answer of The sun's mass is about 1000 times...

Question 12

Two stars, one with radius $r$ and the other with radius $3 r$, orbit each other so that their centers of mass are $25 r$ apart. Assume that the stars have the same uniform density. This system's center of mass is inside the larger star.

Accepted Answer

The center of mass of a system is closer to the more massive object. Since both stars have the same density, the larger star (with radius $3r$) has a greater volume and thus a greater mass. Given the uniform density, the mass of the larger star is proportional to its volume, which is $3^3 = 27$ times the volume (and thus the mass) of the smaller star. Therefore, the center of mass, being influenced more by the larger mass, will be located closer to the larger star, and given the distances involved (with the stars' centers only $25r$ apart), it is indeed inside the larger star.

Question 13

The speed of a satellite in a circular orbit of radius $R$ around the earth is $3.0 \mathrm{~km} / \mathrm{s}$. The speed of another satellite in a different circular orbit around the earth is one-half this value. What is the radius of that satellite's orbit?

Accepted Answer

The speed of a satellite in orbit is proportional to the square root of the inverse of the radius of the orbit ($v \propto \sqrt{1/R}$). If the speed of the second satellite is half that of the first ($v_2 = 0.5v_1$), then its orbital radius must be four times larger ($R_2 = 4R_1$) to maintain this relationship, as $(0.5)^2 = 1/4$, inversely relating speed to radius.

Question 14

A satellite orbits the earth once every $2.0 \mathrm{~h}$. What is the orbital period of another satellite whose orbital radius is 4.0 times larger?

Accepted Answer

According to Kepler's third law, the orbital period $T$ is proportional to the $3/2$ power of the orbital radius $r$. If the radius is 4 times larger, the period is $4^{3/2} = 8$ times longer. Thus, $2.0 \mathrm{~h} \times 8 = 16 \mathrm{~h}$.

Question 15

The radius of the earth's (almost circular) orbit around the sun is $150,000,000 \mathrm{~km}$, and it takes $1 \mathrm{y}$ for the earth to go around the sun. Imagine that a certain satellite goes in an almost circular orbit of radius $15,000 \mathrm{~km}$ around the earth (this radius is 10,000 times smaller than the earth's orbital radius around the sun). What is the period of this orbit?

Accepted Answer

The answer of The radius of the earth's (almost circular)...

Question 16

Imagine that we launch a spaceship from the earth so its speed is 6 AU/y relative to the earth in the direction that the earth orbits the sun. This spaceship's subsequent orbit around the sun is:

Accepted Answer

The spaceship's speed of 6 AU/y exceeds the escape velocity from the solar system, resulting in a hyperbolic trajectory.

Question 17

Consider an orbit where $r_{c}=1 \mathrm{AU}$ and $b=2 \mathrm{AU}$. What kind of orbit is this?

Accepted Answer

The answer of Consider an orbit where $r_{c}=1 \mathrm{AU}$ and...

Question 18

Consider an asteroid in an elliptical orbit whose closest point to the sun is $r_{c}=1 \mathrm{AU}$ and farthest point is $7 \mathrm{AU}$ from the sun. Its orbital period is

Accepted Answer

The answer of Consider an asteroid in an elliptical orbit...

Question 19

Is the work energy flowing into or out of the gas in process $B \rightarrow C$ positive $(A)$ or negative (B)?
A) Positive}
B) Negative

Accepted Answer

The work energy flowing into the gas in process $B \rightarrow C$ is positive because work is done on the gas, increasing its internal energy.

Question 20

Kepler's 2nd law applies to hyperbolic orbits.

Accepted Answer

Kepler's 2nd law, which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time, applies specifically to elliptical orbits in the context of Kepler's laws of planetary motion, not hyperbolic orbits.

Quiz 2: The Laws of Physics Are Universal Newtonian Mechanics

A glider on an air track is connected by a spring to the end of the air track. If it takes $0.30 \mathrm{~s}$ for the glider to travel the distance of $12 \mathrm{~cm}$ from one turning point to the other, its amplitude is

Consider the glider described in problem N10T.4. Its phase rate is

Suppose the $\mathrm{x}$ -position of an oscillating object is given by $x(t) =A \cos (\omega t+\theta)$ . What is the object's speed at time $\mathrm{t}=0$ ?

A glider on an air track is connected by a spring to the end of the air track. If it is pulled $3.5 \mathrm{~cm}$ in the $+x$ direction away from its equilibrium point and then released from rest at $t=0$ , what is the initial phase $\theta$ ?

A glider on an air track is connected by a spring to the end of the air track. If it is pulled $3.5 \mathrm{~cm}$ in the $-x$ direction away from its equilibrium point and then released from rest at $t=0$ , what is the initial phase $\theta$ ?

A mass hanging from the end of a spring has a phase rate of $\omega=6.3 \mathrm{~s}^{-1} \approx 1$ cycle/s. Let's define $t=0$ to be when the mass passes $x=0$ going up. If its speed as it passes is $1.0 \mathrm{~m} / \mathrm{s}$ , what is its amplitude $A$ ?

To double the period of a pendulum, you need to multiply its length by a factor of:

For a swinging pendulum, the maximum angle that the pendulum's string makes with the vertical corresponds to what in the pendulum solution $\phi=A \cos (\omega t+\theta)$ ?

Kepler's second law implies that as a planet's distance from the sun increases in an elliptical orbit, its orbital speed

The sun's mass is about 1000 times that of Jupiter, and the radius of Jupiter's orbit is about 1100 times the sun's radius. The center of mass of the sun/Jupiter system is inside the sun.

Two stars, one with radius $r$ and the other with radius $3 r$ , orbit each other so that their centers of mass are $25 r$ apart. Assume that the stars have the same uniform density. This system's center of mass is inside the larger star.

The speed of a satellite in a circular orbit of radius $R$ around the earth is $3.0 \mathrm{~km} / \mathrm{s}$ . The speed of another satellite in a different circular orbit around the earth is one-half this value. What is the radius of that satellite's orbit?

A satellite orbits the earth once every $2.0 \mathrm{~h}$ . What is the orbital period of another satellite whose orbital radius is 4.0 times larger?

Imagine that we launch a spaceship from the earth so its speed is 6 AU/y relative to the earth in the direction that the earth orbits the sun. This spaceship's subsequent orbit around the sun is:

Consider an orbit where $r_{c}=1 \mathrm{AU}$ and $b=2 \mathrm{AU}$ . What kind of orbit is this?

Consider an asteroid in an elliptical orbit whose closest point to the sun is $r_{c}=1 \mathrm{AU}$ and farthest point is $7 \mathrm{AU}$ from the sun. Its orbital period is

Is the work energy flowing into or out of the gas in process $B \rightarrow C$ positive $(A)$ or negative (B)? A) Positive} B) Negative

Kepler's 2nd law applies to hyperbolic orbits.

Quiz 2: The Laws of Physics Are Universal Newtonian Mechanics

A glider on an air track is connected by a spring to the end of the air track. If it takes 0.30 s0.30 \mathrm{~s}0.30 s for the glider to travel the distance of 12 cm12 \mathrm{~cm}12 cm from one turning point to the other, its amplitude is

Consider the glider described in problem N10T.4. Its phase rate is

Suppose the x\mathrm{x}x -position of an oscillating object is given by x(t) =Acos⁡(ωt+θ) x(t) =A \cos (\omega t+\theta) x(t) =Acos(ωt+θ) . What is the object's speed at time t=0\mathrm{t}=0t=0 ?

A glider on an air track is connected by a spring to the end of the air track. If it is pulled 3.5 cm3.5 \mathrm{~cm}3.5 cm in the +x+x+x direction away from its equilibrium point and then released from rest at t=0t=0t=0 , what is the initial phase θ\thetaθ ?

A glider on an air track is connected by a spring to the end of the air track. If it is pulled 3.5 cm3.5 \mathrm{~cm}3.5 cm in the −x-x−x direction away from its equilibrium point and then released from rest at t=0t=0t=0 , what is the initial phase θ\thetaθ ?

To double the period of a pendulum, you need to multiply its length by a factor of:

For a swinging pendulum, the maximum angle that the pendulum's string makes with the vertical corresponds to what in the pendulum solution ϕ=Acos⁡(ωt+θ) \phi=A \cos (\omega t+\theta) ϕ=Acos(ωt+θ) ?

Kepler's second law implies that as a planet's distance from the sun increases in an elliptical orbit, its orbital speed

The sun's mass is about 1000 times that of Jupiter, and the radius of Jupiter's orbit is about 1100 times the sun's radius. The center of mass of the sun/Jupiter system is inside the sun.

Two stars, one with radius rrr and the other with radius 3r3 r3r , orbit each other so that their centers of mass are 25r25 r25r apart. Assume that the stars have the same uniform density. This system's center of mass is inside the larger star.

The speed of a satellite in a circular orbit of radius RRR around the earth is 3.0 km/s3.0 \mathrm{~km} / \mathrm{s}3.0 km/s . The speed of another satellite in a different circular orbit around the earth is one-half this value. What is the radius of that satellite's orbit?

A satellite orbits the earth once every 2.0 h2.0 \mathrm{~h}2.0 h . What is the orbital period of another satellite whose orbital radius is 4.0 times larger?

Imagine that we launch a spaceship from the earth so its speed is 6 AU/y relative to the earth in the direction that the earth orbits the sun. This spaceship's subsequent orbit around the sun is:

Consider an orbit where rc=1AUr_{c}=1 \mathrm{AU}rc​=1AU and b=2AUb=2 \mathrm{AU}b=2AU . What kind of orbit is this?

Consider an asteroid in an elliptical orbit whose closest point to the sun is rc=1AUr_{c}=1 \mathrm{AU}rc​=1AU and farthest point is 7AU7 \mathrm{AU}7AU from the sun. Its orbital period is

Is the work energy flowing into or out of the gas in process B→CB \rightarrow CB→C positive (A)(A)(A) or negative (B)? A) Positive} B) Negative

Kepler's 2nd law applies to hyperbolic orbits.

A glider on an air track is connected by a spring to the end of the air track. If it takes $0.30 \mathrm{~s}$ for the glider to travel the distance of $12 \mathrm{~cm}$ from one turning point to the other, its amplitude is

Suppose the $\mathrm{x}$ -position of an oscillating object is given by $x(t) =A \cos (\omega t+\theta)$ . What is the object's speed at time $\mathrm{t}=0$ ?

A glider on an air track is connected by a spring to the end of the air track. If it is pulled $3.5 \mathrm{~cm}$ in the $+x$ direction away from its equilibrium point and then released from rest at $t=0$ , what is the initial phase $\theta$ ?

A glider on an air track is connected by a spring to the end of the air track. If it is pulled $3.5 \mathrm{~cm}$ in the $-x$ direction away from its equilibrium point and then released from rest at $t=0$ , what is the initial phase $\theta$ ?

For a swinging pendulum, the maximum angle that the pendulum's string makes with the vertical corresponds to what in the pendulum solution $\phi=A \cos (\omega t+\theta)$ ?

Two stars, one with radius $r$ and the other with radius $3 r$ , orbit each other so that their centers of mass are $25 r$ apart. Assume that the stars have the same uniform density. This system's center of mass is inside the larger star.

The speed of a satellite in a circular orbit of radius $R$ around the earth is $3.0 \mathrm{~km} / \mathrm{s}$ . The speed of another satellite in a different circular orbit around the earth is one-half this value. What is the radius of that satellite's orbit?

A satellite orbits the earth once every $2.0 \mathrm{~h}$ . What is the orbital period of another satellite whose orbital radius is 4.0 times larger?

Consider an orbit where $r_{c}=1 \mathrm{AU}$ and $b=2 \mathrm{AU}$ . What kind of orbit is this?

Consider an asteroid in an elliptical orbit whose closest point to the sun is $r_{c}=1 \mathrm{AU}$ and farthest point is $7 \mathrm{AU}$ from the sun. Its orbital period is

Is the work energy flowing into or out of the gas in process $B \rightarrow C$ positive $(A)$ or negative (B)? A) Positive} B) Negative