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PHYS 113 University of Rochester P113 12 Exam 3 SolutionssExam

Course Code
PHY 113
Study Guide

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P113 University of Rochester NAME _________________________________________
S. Manly Fall 2012
Exam 3 (December 4, 2012)
Please read the problems carefully and answer them in the space provided. Write on
the back of the page, if necessary. Show all your work. Partial credit will be given
unless specified otherwise.
Problem 1 (10 pts ):
a) Consider three identical wheel rims with the three configurations of spokes sketched
below. For each wheel, the spokes have a uniform mass density and the same mass. The
only difference is that the spokes are different in shape (as shown). If the three wheels
roll simultaneously without slipping down an inclined plane from the same height, in
what order will they reach the bottom of the inclined plane. Provide a sentence or two
justifying your answer.
i. A first, then B, then C
ii. A first, then C, then B
iii. C first, then B, then A
iv. C first, then A, then B
v. B first, then A, then C
vi. B first, then C, then A
vii. All three reach the bottom at the same time
b) Consider the same physical situation where the inclined plane has a Teflon surface which
removes all friction between the wheels and the plane. In this case , in what order will
they reach the bottom of the inclined plane (choose from above). Provide a sentence
justifying your answer.
Problem 2 (15 pts, show work ):
Determine the position of the center of mass of the
arrangement of the uniform identical cubes shown in the
figure. Assume the cubes have sides of 1 meter. Note that one
cube sits with a corner at (x,y,z)=(0,0,0) and is obscured by the
other five cubes.

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P113 University of Rochester NAME _________________________________________
S. Manly Fall 2012
Problem 3 (14 pts, show your work ):
One day you take your date out for a fine meal at Al’s
Steakhouse and Explosive Ordinance Testing Ground.
While enjoying your meal by the romantic light of
mortar explosions, your mind wanders to physics, as it
is prone to do. In particular, you see one explosion
that gets you to thinking. Fortunately, you know the
owner of the establishment and quickly manage to get
the data on that explosion delivered to you so that you
can do a calculation.
In the explosion of interest to you, a 6 kg mortar shell
explodes into four fragments moving in the horizontal
plane, as shown in the sketch. After the explosion, a 1
kg fragment moves in the east direction at 30 m/s, a 1
kg fragment moves north at 30 m/s and a 2 kg
fragment moves west at 20 m/s. Unfortunately the proving ground technicians failed to record
the direction and speed of the fourth fragment, though they were able to determine its mass as 2
kg. To satisfy your curiosity and to exercise your amazing dexterity in physics, you determine
the direction and speed of the fourth fragment … (please do/repeat that calculation below). You
might find it useful to know the trig identitity (sin
)2 + (cos
)2 = 1.
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