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?

(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.)

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.

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 $\left|\vec{F}_{2}\right|=\left|\vec{F}_{\text {tot }}\right|-\left|\vec{F}_{1}\right|$ .

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?

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.)

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.

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

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.) -

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.

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.

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

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