AJM:4/11/05 Score /100
Physics 132 Final Exam Spring 2002
Name
!
PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the front. Read each
problem carefully. The credit you receive on each problem will depend at least as much on how you get your answer as on what
answer you get. There is no need to be as “wordy” as I ask you to be on homework, but you must show your work or give at
least a brief explanation for every answer. I give no credit for unsupported answers. I give partial credit for partially correct
solutions, but only when I can figure out what you are doing, so be as clear as possible. Make certain that all numerical answers
are given with a reasonable number of significant digits (when in doubt, three is usually a good compromise) and that you have
included appropriate and simplified units. Check your answers for physical reasonableness whenever possible; I do deduct points
for ridiculous answers that go uncommented upon.
1. A 2.0 kg block slides along a frictionless surface at
5.0!m/s toward an identical block that is sitting at
rest attached to a 72 N/m spring as shown at right.
The first block strikes and sticks to the second and
the combination oscillates thereafter.
a) [8 pts] How long a time does it take to complete one oscillation?
b) [8 pts] What is the maximum amount that the spring is ever compressed? [Hint: Momentum is conserved.]
c) [4 pts] How does the energy of the oscillating spring and combined block system compare to the kinetic energy of the
first block before the collision? Explain!
2. Consider a system of three stars, two of which have mass 2M and orbit about a motionless
third star of mass M along the same circular path of radius R as shown at right.
a) [8 pts] Find the magnitude of the net force on either of the two orbiting stars (in terms, of
course, of the givens—M and R.)
b) [12 pts] Therefore, find the orbital period of either orbiting star (in terms of M and R.)
3. Water in a large vertical cylinder of diameter D is open to the air above and is
draining out through a narrower pipe that has a diameter D/10 as shown in the
figure. The surface of the water in the large vertical pipe is descending at a
speed of 12.0 cm/s. [Note: The outlet is not shown in the figure and may be
higher or lower than the horizontal section of pipe.]
a) [10 pts] What is the flow speed of the water in the narrower pipe?
[Big hint: It has to speed up when the cross sectional area gets smaller.]
b) [10 pts] What is the gauge pressure in the horizontal pipe, 4.0 m below the surface of the water in the vertical pipe?
[Hints: Apply Bernoulli’s principle between two clearly indicated points. Recall that gauge pressure is simply the
actual pressure minus atmospheric pressure. The density of water is
1.00 ×103 kg/m3
.]
EXTRA CREDIT [5 pts] The narrow pipe continues on to an open air outlet (not shown in the figure) without changing its
diameter. Is the open air outlet at a higher or lower elevation than the horizontal section of pipe in the figure?
(over)
4.0 m
(to the outlet)
2
M
2
M
M
m
= 2.0 kg
k
= 72 N/m
v = 5.0 m/s
m
