Physics 7A, Spring 2012, Sections 2 and 3, Instructor: Professor Adrian Lee
2nd Midterm Examination, Tuesday, April 3, 2012
Please do work in your greenbooks. Show your reasoning carefully so that we can be sure that you derived the
answer rather than guessing it or relying on memory; in addition, this enables us to give partial credit. You may
use one double-sided 3.5 x 5 index cards of notes. Test duration is 110 minutes. Calculators are not allowed.
1 Rifle Demo [25 pts. total]
Consider the rifle demo from class. A rifle with mass mRand a block of wood with
mass mWare suspended so that they can both swing freely. Initially, both the
wood block and rifle are stationary. Then, the rifle fires a bullet with mass mBand
velocity vBinto the wood block.
a) What is the velocity of the wood immediately after the bullet hits it? [5 pts.]
b) At the peak of its swing what is the maximum change in height of the wood
block? [10 pts.]
c) What is the ratio of the maximum change in height of the wood block to that of
the rifle? [5 pts.]
d) Is any energy lost when the bullet hits the block? If yes, how much? [5 pts.]
2 Collisions [25 pts. total]
Consider three spheres lined up in a row along the x-axis with masses m1=M,
m2=M/2, and m3=M. The sphere with m=m1has an initial velocity V0in
the +xdirection, while the other two spheres are initially at rest. The sphere with
m=m1has an elastic collision with m2and then m2collides and sticks to m3.
a) Determine the velocities of m1and m2after the first collision. [10 pts.]
b) Determine the velocities of m2and m3after the second collision. [5 pts.]
c) After the second collision will m1collide with the m2, m3combination? If they
do not collide, for what values of m3would this collision occur? [10 pts.]
3 Twin Planets [25 pts. total]
Consider a planetary system with two planets identical to earth with mass Mand
radius Rwhich are separated with their centers a distance of 4Rapart.
a) Show that potential energy due to one planet and a mass mcan be described by
−GMm/r for r > R. Consider a person at point A that wishes to fire a projectile
from the far surface of one planet to reach very far away from the system. What is
the minimum speed that she must fire the projectile? [10 pts.]
b) Consider a similar situation at point B, on the near side of one of the planets.
What is the minimum firing speed for a projectile to escape the planets? [5 pts.]
c) Now consider if the person at point B only wants to fire her projectile from point
B to point C on the next planet. What is the minimum firing speed required for
this projectile? Draw a potential energy diagram for this path. [10 pts.]
4 Block Launcher [25 pts. total]
Consider a block launched from a wedge of height Hand angle θby a spring with
spring constant k. The spring is compressed from its equilibrium by a distance d.
A block with mass mis placed on the compressed spring half way on the incline of
the wedge with a height H/2
a) What is the velocity of the block as it leaves the hill? Include the effect of friction
with coefficient of kinetic friction µ. Assume the spring is strong enough to launch
the block from the wedge. [10 pts.]
b) What is the velocity of the block when it falls back to a height H/2? [5 pts.]
c) If at that point in part (b) the block breaks into two pieces with mass 1/3 mand
2/3 msuch that the 1/3 mpiece falls straight down with the same vertical velocity
as before, how far apart will the two pieces be when they land? For the answer to
this section, you do not have to plug in your values from parts (a) and (b). [10 pts.]
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