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Physics 103 – Fall 2010
Midterm Examination
Thursday, October 28, 2010
90 minutes
Instructions: When you are told to begin, check that this examination booklet contains
all the numbered pages from 2 through 10.
Do not be discouraged if you cannot do all three problems, or all parts of a given
problem. If a part of a problem depends on a previous answer you have not obtained,
assume an answer and proceed. Keep moving and finish as much as you can!
Read each problem carefully. You must show your work—the grade you get depends on
how well we can understand your solution even when you write down the correct answer.
Always write down analytic answers first and only then calculate numerical values.
Include correct units where appropriate. For the purposes of this exam g = 9.8m/s2.
Please Box Your Answers.
THE ONLY MATERIALS ALLOWED DURING THE EXAM ARE
THE EXAMINATION BOOKLET, PEN OR PENCIL, AND YOUR
CALCULATOR. DO ALL THE WORK YOU WANT TO HAVE
GRADED IN THIS EXAMINATION BOOKLET! YOU MAY USE
THE BACK OF EACH SHEET, BUT YOU WILL NOT BE
ALLOWED TO HAND IN ANYTHING ELSE.
If you need to use the restroom briefly you may do so, but your exam booklet cannot leave
the room. This is a timed examination. You will have 50 minutes to complete this exam.
Two preceptors will be outside the room to answer questions during the exam.
_________________________________________________
_________________________________________________
REWRITE IN FULL AND SIGN THE PLEDGE IN THE SPACE ABOVE
“I pledge my honor that I have not violated the Honor Code during this examination.
SIGNATURE
PHY103 – Exam 1
Problem 1, Page 2
Problem 1. Pulley and Blocks (30 pts)
Two blocks, one with mass m and the other with mass 5m , are
connected by a massless string wound over a massless, frictionless
pulley. Both blocks start at rest, with the lighter block resting on a
horizontal surface, and the heavier block hanging a distance h above
the surface. When released, the heavier block begins to fall, while
the lighter block begins to rise. You can assume that the string does
not stretch, so that the speed of the heavier block is always equal to
the speed of the lighter block.
5m
h
a) (8 pts) What is the final speed of each mass just before the heavier
one hits the surface?
m
b) (7 pts) What is the net work done by gravity on the system consisting of both blocks?
PHY103 – Exam 1
Problem 1, Page 3
Problem 1 (cont)
The lighter mass is now attached to a massless spring with force
constant k that is anchored to the surface and is initially
unstretched. When released, the heavier block begins to fall
while the lighter block begins to rise, stretching the spring
beyond its equilibrium length. At some point, both blocks come
to rest and the spring is maximally stretched. You can assume
this happens before the heavier block hits the surface.
5m
c) (8 pts) What is the maximum elongation of the spring?
m
k
d) (7 pts) The blocks start and end at rest, therefore, there must be an intermediate moment
at which the speed is maximum. What is the length by which the spring has stretched when
the speed of the blocks is at its maximum value?
PHY103 – Exam 1
Problem 2, Page 4
Problem 2. Collision-O-Rama (20 pts)
In this problem we will consider the interaction between two blocks sliding across a
horizontal, frictionless surface. The mass of one block is m , while the mass of the
second block is 2m . In each part below we will consider a different situation, so pay
close attention to what is happening in each case.
Note that the speeds given in each part represent the magnitudes of the velocity vectors of
the corresponding blocks, so they are positive quantities. As always, you must define a
coordinate system and keep track of plus and minus signs multiplying the speeds.
a) (6 pts) Assume that the block of mass m is moving with an initial speed 3v0 to the
right when it collides with the second block of mass 2m , which is moving with a speed

2v0 to the right. The two blocks stick together. What is their final velocity v
(magnitude and direction) in terms of v0 ?
m
3v0
2m
2v0
PHY103 – Exam 1
Problem 2, Page 5
Problem 2 (cont)
b) (4 pts) Now the lighter block is moving to the right with an initial speed 3v0 when it
strikes the heavier block moving with a speed 2v0 to the left. The blocks collide

elastically. What is the center-of-mass velocity VCM (magnitude and direction) of the
system consisting of both blocks?
m
3v0


c) (10 pts) What are the final velocities v m and v 2 m of the blocks of mass m and 2m ,
respectively? Remember to give magnitude (in terms of v0 ) and direction for both.
2v0
2m
PHY103 – Exam 1
Problem 3, Page 6
Problem 3. Conical Pendulum. (25 pts)
In lecture (and on the homework) you saw a conical pendulum
consisting of a mass m on a massless string executing uniform
circular motion in the horizontal plane with a radius r . The string
makes an angle of  with respect to the vertical. All of your answers
should include at most the given quantities and g , no other symbols
should appear.

a) (4 pts) Draw a free-body diagram for the mass.
r
b) (5 pts) What is the tension in the string?
c) (8 pts) What is the angular velocity of the mass around the center of the circle?
m
PHY103 – Exam 1
Problem 3, Page 7
Problem 3 (cont)
Now consider a conical pendulum with the string replaced by a spring
with force constant k . All other parameters are the same as before.
d) (8 pts) As a function of m , g , r , k , and  only, what is the ratio
U K of the potential energy in the spring to the kinetic energy of m ?

spring
r
m
PHY103 – Exam 1
Problem 4, Page 8
Problem 4. Beads on a Circular Wire (25 pts)
Two beads are constrained to move without friction along a
circular wire of radius R oriented rigidly in a vertical plane.
One bead has a mass of m and is at rest at the bottom of the ring
(    ). The second bead has a mass of 3m and is released
from rest at an angle  as measured clockwise from the vertical
(see diagram;   0 at the top). It then slides down the ring and
collides elastically with the lighter bead at the bottom.
The wire passes through the center of each bead, so both beads
always remain on the wire (they cannot fall off). You can
assume that the beads are very small, so that you can neglect
their actual size (the beads collide exactly at the bottom).
3m

m
a) (5 pts) What is the speed of the heavier bead just before it collides with the lighter
bead at the bottom of the ring? If you cannot get this part, use the symbol v for this
speed in the remainder of the problem.
R
PHY103 – Exam 1
Problem 4, Page 9
Problem 4 (cont)
m
After the collision, both masses are moving clockwise around
the circular ring, as shown in the diagram.

b) (15 pts) For which starting angle  of the bead of mass 3m
will the bead of mass m just barely make it over the top of
the circular wire?
3m
R
PHY103 – Exam 1
Problem 4, Page 10
Problem 4 (cont)
m
c) (5 pts) Assuming the bead of mass m just barely makes it
over the top of the circular wire, to what maximum vertical
height h above the bottom of the loop will the bead of mass
3m reach?

3m
h
R