Exam 1: Conservation Laws Constrain Interactions

Suppose you have a spool of thread that can rotate around a fixed axis as you pull thread off it. If you pull the thread with your hand so that the thread always lies along a certain fixed line, how will your hand's speed as it moves compare to $|\vec{\omega}|$ , where $R$ is the spool's radius and $R|\vec{\omega}|$ is angular speed?

Is the specified change in the following objects' thermal energies due to a flow of heat (A), work (B), or some other flow of energy (E)? -Liquid nitrogen poured on a slab of ice boils furiously. (Liquid nitrogen's boiling point is $77 \mathrm{~K}$ .)

An egg will cook no more rapidly in furiously boiling water than in gently simmering water

The letter $\mathrm{N}$ is symmetric (in the sense defined in this chapter) for rotations around an axis going through its center that points in which of the following directions?

Which of the six objects shown below has the largest rotational energy? (All have the same mass.) A. B. C. D. E.

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. - Suppose we know that the system has 5 bondits of kinetic energy when its atoms are separated by $0.2 \mathrm{~nm}$ . What minimum energy is required to break the bond?

Figure C9.12 shows the potential energy function for a certain interaction. This interaction is

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. -Two people riding personal hovercraft tug on each other with a rope.

Substance $A$ has twice the specific "heat" as substance $B$ . Suppose we put $100-g$ blocks of these substances in direct sunlight. Assume both blocks are black and present the same surface area to the incoming sunlight. After a certain period of time, how are the temperature changes $\Delta T_{A}$ and $\Delta T_{B}$ of these blocks related (assuming they lose little heat to their surroundings)?

A reference frame attached to a train is a reasonably good inertial frame if the train is stopped at a station.

In the hypothetical atomic interaction shown in figure C9.13, assume that the atoms initially have zero radial velocity at a separation of $0.25 \mathrm{~nm}$ . If the atoms are jostled slightly so that the system gains a slight amount of energy, what happens to the atoms' separation afterward?

A cylinder rolls, without slipping, down an incline directly toward you. The contact interaction between the cylinder and the incline exerts a frictional torque on the cylinder. What is this torque's direction?

A dark object sitting in sunlight gets warm. The sun radiates light because it is very hot, much hotter than the object. So should we categorize the radiation that the object receives from the sun as being heat $Q$ or energy transferred by electromagnetic radiation $\left[E_{\mathrm{ER}}\right]$ ? Be prepared to justify your answer with an argument (multiple reasonable arguments are possible).

Substance $A$ has twice the specific "heat" as substance $B$ . Suppose we have a $50-g$ block of each substance at a common initial temperature of $100^{\circ} \mathrm{C}$ . We then put both blocks into a well-insulated cup containing $500 \mathrm{~g}$ of water at $20^{\circ} \mathrm{C}$ , and wait until the objects' and the water's temperatures no longer change. -Which has suffered the greater temperature change?

Consider the types of reference frames listed below. (NRF = nonrotating frame) -A NRF attached to Jupiter's center of mass A. A NRF in deep space B. A NRF that is freely floating C. A NRF attached to the earth's center of mass D. A frame attached to the earth's surface (or a similarly slowly rotating object) E. A frame moving at a constant velocity relative to one of the frame types described above F. A noninertial frame

Two rods with the same density and diameter form a cross, as shown below. Where is the system's center of mass? (Hint: Treat each rod as a uniform object, whose center of mass is its geometric center.)

You can be certain that a collision between two objects is elastic if

Consider the types of reference frames listed below. (NRF = nonrotating frame) -A frame attached to a car moving with a fixed speed on a straight road A. A NRF in deep space B. A NRF that is freely floating C. A NRF attached to the earth's center of mass D. A frame attached to the earth's surface (or a similarly slowly rotating object) E. A frame moving at a constant velocity relative to one of the frame types described above F. A noninertial frame

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. - If an object moves at a rate of $5 \mathrm{~m} / \mathrm{s}$ in the $-y$ direction, then $\vec{v}=+5 \mathrm{~m} / \mathrm{s}$ .

Which of the following things is an "extended object"? For each item, answer "A" if the item is an acceptable extended object, " $\mathrm{B}$ " if the definition of an extended object applies badly to the item, and " $\mathrm{D}$ " if it is debatable. -The water in an ocean current