Question 1

Two hockey pucks are initially at rest on a horizontal plane of frictionless ice. Puck $A$ has twice the mass of puck $B$. Suppose we apply the same constant force on each puck for the same interval of time $d t$. How do the puck's kinetic energies compare at the end of the interval?

Accepted Answer

A)  $K_{A}=4 K_{B}$ 
B)  $K_{A}=2 K_{B}$ 
C)  $K_{A}=K_{B}$ 
D)  $K_{B}=2 K_{A}$ 
E)  $K_{B}=4 K_{A}$
F) Some other relationship (specify)

Question 2

Assume that $D$ and $R$ have units of meters, $T$ has units of seconds, $m$ and $M$ have units of kilograms, $V$ has units of meters per second, and $g$ has units of $\mathrm{m} / \mathrm{s}^{2}$. Which of the following equations has selfconsistent units?

Accepted Answer

A)  $\mathrm{D}=m \mathrm{R}^{2}$ 
B)  $m=M\left[1+R^{2}\right]$ 
C)  $\mathrm{D}=[1-\mathrm{m} / \mathrm{M}] g \mathrm{~T}^{2}$ 
D)  $g=m v^{2} / \mathrm{R}$ 
E)  $\mathrm{D}=v^{2} / \mathrm{R} T$
F) None of these can be correct.

Question 3

(Tricky!) A bowling ball rolls on the floor at a constant velocity away from you. What is the approximate direction of the ball's total angular momentum around your head? (Hint: How fast do the ball's particles move about the ball's center of mass compared to the speed of the ball's center of mass as it moves away from you? Think about it.)

Accepted Answer

A)  Upward. 
B)  Downward. 
C)  To your left. 
D)  To your right. 
E)  Away from you.
F) It depends on the ball's moment of inertia.
G) It depends on the ball's rotation rate.

Question 4

To which of the following two-object systems can we apply conservation of momentum, and why? In each case, answer "A" if we can apply conservation of momentum because the system floats in space, "F" if it's because the system is functionally isolated, " $C$ " if it's because the system undergoes a collision, and " $\mathrm{D}$ " if momentum is not conserved at all because the system is not isolated.
-An asteroid imbeds itself in a planet.

Accepted Answer

The answer of To which of the following two-object systems...

Question 5

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.
-$\vec{F}_{\text {tot }}=\vec{F}_{1}+\vec{F}_{2}$ implies that $\left|\vec{F}_{2}\right|=\left|\vec{F}_{\text {tot }}\right|-\left|\vec{F}_{1}\right|$.

Accepted Answer

The answer of Which of the following statements involve notation,...

Question 6

In the hypothetical atomic interaction shown in figure C9.13, suppose that initially the system's kinetic energy is $\frac{1}{2} \mu|\vec{v}|^{2}=5 \times 10^{-21} J$ at an initial separation of $0.1 \mathrm{~nm}$. About how much energy would we have to add to the system for the atoms to fly off to infinite separation?

Accepted Answer

A)  $1 \times 10^{-21} \mathrm{~J}$ 
B)  $6 \times 10^{-21} \mathrm{~J}$ 
C)  $11 \times 10^{-21} \mathrm{~J}$ 
D)  $16 \times 10^{-21} \mathrm{~J}$ 
E)  None. The atoms will do so without adding energy.

Question 7

A cylinder rolls, without slipping, down an incline directly toward you. The cylinder's angular velocity $\vec{\omega}$ points in which direction?

Accepted Answer

A)  Toward you 
B)  Away from you 
C)  To your right 
D)  To your left 
E)  Some other direction (specify)

Question 8

Suppose you climb about 10 stories worth of stairs. Roughly what is the minimum number of food calories you have burned? (Select the closest.)

Accepted Answer

A)  $70,000 \mathrm{Cal}$ 
B)  $4,000 \mathrm{Cal}$ 
C)  $70 \mathrm{Cal}$ 
D)  4 Cal 
E)  Less than 1 Cal

Question 9

To which of the following two-object systems can we apply conservation of momentum, and why? In each case, answer "A" if we can apply conservation of momentum because the system floats in space, "F" if it's because the system is functionally isolated, " $C$ " if it's because the system undergoes a collision, and " $\mathrm{D}$ " if momentum is not conserved at all because the system is not isolated.
-A cannonball drops to the earth and lands with a thud, burying itself in the ground.

Accepted Answer

The answer of To which of the following two-object systems...

Question 10

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.
-$\vec{F}_{A} \equiv[\Delta \vec{p}]_{A} / \Delta t$ implies that $\Delta t=[\Delta \vec{p}]_{A} / \vec{F}_{A}$.

Accepted Answer

The answer of Which of the following statements involve notation,...

Question 11

Consider a three-particle system. The center of mass of this system must lie on the plane that contains all three particles. Be prepared to explain why or why not. (Hint: A clever choice of reference frame makes answering this question easier.)

Accepted Answer

A) True 
 B)False

Question 12

We cannot experimentally determine the actual value of a system's total energy

Accepted Answer

A) True 
 B)False

Question 13

Suppose you are looking down on a disk that is spinning counterclockwise. If we apply an upward torque to the disk, its angular speed

Accepted Answer

A)  Increases. 
B)  Decreases. 
C)  Remains the same

Question 14

An object of mass $m$ traveling at speed $\vec{v}_{0}$ in the $+x$ direction hits an identical object at rest. Characterize each of the collision outcomes shown below as being (A) absurd or (C) credible. (The collisions are not necessarily elastic, but they are not super-elastic.)
-

Accepted Answer

The answer of An object of mass $m$ traveling at...

Question 15

A friend is running clockwise at a constant speed on a circular track. At the instant your friend is running due east, your friend is due west of you. What is the direction of your friend's angular momentum around you at that instant? Choose from the possible directions presented in problem C7T.3, remembering that this is a top view, with $\mathrm{A}$ corresponding to north, $\mathrm{C}$ to east, and so on.

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  Upward
F) Downward
G) (The vector is zero)

Question 16

Suppose the interaction between two atoms has the effective potential energy curve shown below:
  
I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits.
-If the atoms have 10 bondits of kinetic energy at infinity, what energy must we remove to form a bond?

Accepted Answer

A)  Only a smidgen (less than a bondit) 
B)  5 bondits 
C)  10 bondits 
D)  15 bondits 
E)  20 bondits
F) The bond is already broken (or we can't form a bond).

Question 17

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous.
- The speed at the end of the interval is $v=v_{0}+1$.

Accepted Answer

The answer of Which of the following statements involve notation,...

Question 18

Figure C9.12 shows the potential energy function for a certain interaction between two objects. As their separation $r$ increases, the magnitude of the force each exerts on the other (A) increases or (B) decreases.

Accepted Answer

A)  Increases. 
B)  Decreases.

Question 19

The following diagrams show hypothetical results for collisions between identical balls floating in space. One ball was originally moving to the right along the dashed line before striking the other ball at rest. (The collision was not necessarily head-on.) The arrows depict the balls' final velocities. Which outcomes are physically believable? 
-
A) if it is absurd.
B)if the outcome is believable

Accepted Answer

The answer of The following diagrams show hypothetical results for...

Question 20

In the hypothetical atomic interaction shown in figure C9.13, assume that initially the atoms have a total energy of $3 \times$ $10^{-21} \mathrm{~J}$ at $r=0.1 \mathrm{~nm}$. These atoms are

Accepted Answer

A)  Unbound (they will separate to infinity). 
B)  Bound (they will not separate to infinity). 
C)  The answer depends on whether the atoms are initially moving toward or away from each other.

Exam 1: Conservation Laws Constrain Interactions

Two hockey pucks are initially at rest on a horizontal plane of frictionless ice. Puck $A$ has twice the mass of puck $B$ . Suppose we apply the same constant force on each puck for the same interval of time $d t$ . How do the puck's kinetic energies compare at the end of the interval?

Assume that $D$ and $R$ have units of meters, $T$ has units of seconds, $m$ and $M$ have units of kilograms, $V$ has units of meters per second, and $g$ has units of $\mathrm{m} / \mathrm{s}^{2}$ . Which of the following equations has selfconsistent units?

A cylinder rolls, without slipping, down an incline directly toward you. The cylinder's angular velocity $\vec{\omega}$ points in which direction?

Suppose you climb about 10 stories worth of stairs. Roughly what is the minimum number of food calories you have burned? (Select the closest.)

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous. - $\vec{F}_{A} \equiv[\Delta \vec{p}]_{A} / \Delta t$ implies that $\Delta t=[\Delta \vec{p}]_{A} / \vec{F}_{A}$ .

Consider a three-particle system. The center of mass of this system must lie on the plane that contains all three particles. Be prepared to explain why or why not. (Hint: A clever choice of reference frame makes answering this question easier.)

We cannot experimentally determine the actual value of a system's total energy

Suppose you are looking down on a disk that is spinning counterclockwise. If we apply an upward torque to the disk, its angular speed

Suppose the interaction between two atoms has the effective potential energy curve shown below: I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits. -If the atoms have 10 bondits of kinetic energy at infinity, what energy must we remove to form a bond?

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous. - The speed at the end of the interval is $v=v_{0}+1$ .

Figure C9.12 shows the potential energy function for a certain interaction between two objects. As their separation $r$ increases, the magnitude of the force each exerts on the other (A) increases or (B) decreases.

Exam 1: Conservation Laws Constrain Interactions

Two hockey pucks are initially at rest on a horizontal plane of frictionless ice. Puck AAA has twice the mass of puck BBB . Suppose we apply the same constant force on each puck for the same interval of time dtd tdt . How do the puck's kinetic energies compare at the end of the interval?

Assume that DDD and RRR have units of meters, TTT has units of seconds, mmm and MMM have units of kilograms, VVV has units of meters per second, and ggg has units of m/s2\mathrm{m} / \mathrm{s}^{2}m/s2 . Which of the following equations has selfconsistent units?

A cylinder rolls, without slipping, down an incline directly toward you. The cylinder's angular velocity ω⃗\vec{\omega}ω points in which direction?

Suppose you climb about 10 stories worth of stairs. Roughly what is the minimum number of food calories you have burned? (Select the closest.)

Consider a three-particle system. The center of mass of this system must lie on the plane that contains all three particles. Be prepared to explain why or why not. (Hint: A clever choice of reference frame makes answering this question easier.)

We cannot experimentally determine the actual value of a system's total energy

Suppose you are looking down on a disk that is spinning counterclockwise. If we apply an upward torque to the disk, its angular speed

An object of mass mmm traveling at speed v⃗0\vec{v}_{0}v0​ in the +x+x+x direction hits an identical object at rest. Characterize each of the collision outcomes shown below as being (A) absurd or (C) credible. (The collisions are not necessarily elastic, but they are not super-elastic.) -

Suppose the interaction between two atoms has the effective potential energy curve shown below: I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits. -If the atoms have 10 bondits of kinetic energy at infinity, what energy must we remove to form a bond?

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer AAA if the statement is acceptable, or EEE if it is erroneous. - The speed at the end of the interval is v=v0+1v=v_{0}+1v=v0​+1 .

Figure C9.12 shows the potential energy function for a certain interaction between two objects. As their separation rrr increases, the magnitude of the force each exerts on the other (A) increases or (B) decreases.

In the hypothetical atomic interaction shown in figure C9.13, assume that initially the atoms have a total energy of 3×3 \times3× 10−21 J10^{-21} \mathrm{~J}10−21 J at r=0.1 nmr=0.1 \mathrm{~nm}r=0.1 nm . These atoms are

Two hockey pucks are initially at rest on a horizontal plane of frictionless ice. Puck $A$ has twice the mass of puck $B$ . Suppose we apply the same constant force on each puck for the same interval of time $d t$ . How do the puck's kinetic energies compare at the end of the interval?

Assume that $D$ and $R$ have units of meters, $T$ has units of seconds, $m$ and $M$ have units of kilograms, $V$ has units of meters per second, and $g$ has units of $\mathrm{m} / \mathrm{s}^{2}$ . Which of the following equations has selfconsistent units?

A cylinder rolls, without slipping, down an incline directly toward you. The cylinder's angular velocity $\vec{\omega}$ points in which direction?

Which of the following statements involve notation, unit, or conceptual errors? For each statement, answer $A$ if the statement is acceptable, or $E$ if it is erroneous. - The speed at the end of the interval is $v=v_{0}+1$ .

Figure C9.12 shows the potential energy function for a certain interaction between two objects. As their separation $r$ increases, the magnitude of the force each exerts on the other (A) increases or (B) decreases.