PHY 3221: Mechanics I
Fall Term 2010
Final Exam, December 14, 2010
•
This is a closed book exam lasting 90 minutes.
•
Since calculators are not allowed on this test, if the problem asks for a numerical answer,
answering 2 + 2 is as good as 4, and
√
2 is as good as 1
.
4142
...
.
•
There are six equally weighted problems worth a total of 30 points. The problems appear
on the second and third page of this test. Begin each problem on a fresh sheet of paper.
Use only one side of the paper. Avoid microscopic handwriting.
•
Put your name, the problem number and the page number in the upper righthand corner
of each sheet.
•
To receive partial credit you must explain what you are doing. Carefully labelled figures
are important! Randomly scrawled equations are not helpful.
•
Draw a box around important results (or at least results which you think might be im
portant).
•
Good luck!
1
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Problem 1.
[5 pts] You use a rope to pull a crate across a level floor.
The maximum
tension that the rope can have without breaking is
T
max
, and the coefficient of kinetic friction
is
μ
k
. Suppose that you tug on the rope so that it makes an angle
θ
with the horizontal (refer
to Fig. 1). Find the maximum possible mass
M
max
of the crate that you can pull at constant
speed without breaking the rope, and the optimal angle
θ
opt
that will allow you to do that.
Hint: make sure to draw a force diagram and clearly label all forces.
M
θ
vectorg
μ
k
Figure 1: An illustration for the crate pulling problem.
Problem 2.
[5 pts.] Obtain the Fourier expansion of the periodic function
F
(
t
) =
+1
,
if
−
π/ω < t <
0
,
−
1
,
if 0
< ω <
+
π/ω.
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 Spring '08
 CHAN
 mechanics, pi˜ ata

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