Exam 1: Conservation Laws Constrain Interactions

An external interaction exerts a force $\vec{F}$ on a certain system as the place where the force is applied moves a displacement $\overrightarrow{d r}=[d x, d y, d z]$ . Which of the following is the correct component expression for the work done by the interaction on the system?

A baseball player slides into third base. Why, according to the modern model of mechanics, does the player eventually come to rest?

A cup sitting on a table constantly receives upward momentum from the table

The angular momentum (around a rotating rigid object's center of mass) of an arbitrary particle in that object points directly along the object's rotation axis

Suppose an unpowered but moving railroad car receives some coal (basically at rest) from a stationary conveyor belt. This coal therefore only carries chemical energy into the car. This mass transfer will

A given object always has a specific moment of inertia $l$ , independent of the axis around which it rotates (as long as the axis goes through the object's center of mass)

When an object slides down a frictionless incline, the contact interaction between the object and incline does no work on the object

Consider a satellite (whose mass is $m$ ) orbiting the earth (whose mass is $M$ ). If we use the formula $V_{g}=-$ $G M m / r$ for the gravitational potential energy in this situation, the earth/satellite system's total energy $E$ turns out to be negative. With respect to the total energy of what situation is $E$ negative?

The lengths of the hour and minute hands of a clock are $4 \mathrm{~cm}$ and $6 \mathrm{~cm}$ , respectively. If the vectors $\vec{u}$ and $\vec{w}$ represent the hour and minute hands, respectively, then $\vec{u} \times \vec{w}$ at 5:00 pm is closest to

Suppose two identical objects traveling toward each other with the same speed collide. According to the momentum-transfer principle, if we observe one of the objects to be at rest after the collision, the other object:

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. -An atom

Consider the types of reference frames listed below. (NRF = nonrotating frame) -A reference frame constructed in a sports stadium 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 frames would be an appropriate inertial reference frame for analyzing the effects on the earth of its gravitational interaction with the moon? -A frame attached to the earth's center of mass (CM) A) if the frame is appropriate B) if it would be bad for this purpose.

In example C4.2, if we had modeled the atoms as solid spheres instead of modeling the nuclei as pointlike particles, we would have gotten the same result for the system's center of mass

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 forces on the object cancel, so $\vec{F}_{\text {tot }}=0$ .

(Tricky!) Suppose that a batter hits a foul ball almost exactly vertically in the air. As the ball rises, the magnitude of the torque that the gravitational interaction exerts on the ball around the pitcher:

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. -An electron

A person throws three rocks off a cliff of height $h$ at exactly the same speed $\left|\vec{v}_{i}\right|$ , each time, but throwing rock $A$ almost vertically upward, rock $B$ horizontally, and rock $C$ almost vertically downward (see the diagram below). Which rock hits the ground with the greatest speed? (Ignore air friction.)

If a change in nozzle design increases a given rocket engine's exhaust speed by a factor of two, by what factor does this increase or decrease the amount of propellant needed to get its payload to a specific final velocity? (Assume the payload and engine mass is small compared to that of the fuel, and choose the closest answer.)

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)? -A hot cup of tea on a table becomes cooler with time.