Problem 1 (30 points) - Solution
(a) (10 pts) For a gas, the molar heat capacity CV is the heat required to increase the temperature of 1
mole of gas at constant volume by 1 K. Table 15.4 shows experimental measurements of C V for
various types of gas. You notice a value
of ~12.5 J/(mol . K) for monatomic
molecule gas, being consistent with a
theoretical prediction of 3/2 R. However
it is ~20.8 J/(mol . K) for diatomic
molecule gas, being consistent with a
theoretical prediction of 5/2 R. Explain
what causes the difference?
Diatomic molecules can store heat energy in three modes of translation, rotation and
vibration,, while it is done in one mode of translation for monatomic molecules.
(b) (5 pts) In the system shown in the figure, M > m, the surface of the bench is horizontal and
frictionless, and the connecting string pulls horizontally on m. As more and more weight is gradually
added to m, which of the following statements best describes the behavior of the system after it is
released?
(A) The acceleration remains the same all cases, since there is no friction
and pull of gravity on M is the same.
(B) The acceleration gets smaller and smaller and becomes zero when
enough weight is added so that m = M.
(C) The velocity remains the same in all cases.
(D) The velocity becomes zero when m = M.
(E) None of the preceding statements is correct.
(c) (10 pts) The x-t graph in the right represents the motion of a
mass attached to a horizontal spring undergoing simple harmonic
motion. Which graph below is the acceleration versus time graph
for the mass?
a
a
(A)
x
a
(B)
(C)
(D) None of the above
(d) (5 pts) You are Captain of the US Starship P-201 with a broken engine and waiting for a rescue
from National Aggie and Space Administration (NASA). You have three identical spare oxygen
tanks in the ship, but with same weights measured on three different planets, Moon, Earth, Jupiter.
The ship system is designed, so that you can connect only one tank to your crew’s living quarter.
Which would you rather pick:
(A) A tank that weights 100 N on Earth.
(B) A tank that weights 100 N on Jupiter.
(C) A tank that weights 100 N on Earth’s Moon.
(D) Any tank, because the weight of oxygen is the same in all
three tanks.
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Problem 2 (30 points) - Solution
A cart carrying a vertical missile launcher moves horizontally at a constant velocity of 30.0 m/s to
the right. It launches a rocket vertically upward. The missile has an initial vertical velocity of 40.0
m/s relative to the cart.
(a) (15 pts) How high does the rocket go? What is the speed of the rocket at the highest point?
(b) (10 pts) How far does that cart travel while the rocket is in the air?
(c) (5 pts) Where does the rocket land relative to the cart?
vA = 30.0 m/s
Problem 3 (35 points)
A bullet is fired vertically into 1.40-kg block of wood at rest on a thin horizontal sheet directly above
it (see the figure below). If the bullet has a mass of 20.0 g and a speed of 310 m/s, how high will the
block rise into the air after the bullet becomes embedded in it? Note that the gravitational
acceleration near Earth’s surface is g = 9.80 m/s2.
10 pts
20 pts
5 pts
Problem 4 (35 points) - Solution
If you were in the class, you saw several demonstrations during the lectures. Pick (a) four
demonstrations that were done or close to what we did in this semester; (b) two demonstrations of
testing the angular momentum conservation.
(a) … A, B, C, F
(b) … A, C
(A) Gyroscopic Motion
(C) Professor’s Spinning
(E) Newton’s Cradle
(B) Race of Rolling Objects w/o Slipping
(D) Loop the Loop
(F) Wave Machine - Transverse Waves
Problem 5 (35 points) - Solution
Problem 6 (25 points) - Solution
Problem 6 (35 points) - Solution