Directions: Select the best possible answer from the choices A-D.
Guessing will not (on average) reduce your score, but if you have no idea
how to work a problem, leave it blank and I'll give you the expected ¼
point.

This is a timed test. Your start time is:
12:34

Your Name:

Ballistic Pendulum

A red sphere (of mass m) and a blue sphere (of mass
5m) are attached to the ceiling by massless strings of identical length
forming twin pendulums of length L. The red sphere is drawn to the
left so that its center of mass has been raised a distance h and is
then released. As the red sphere moves back through equilibrium it hits and adheres
to the blue sphere. The combined system swings to the right, eventually reaching
some maximum height before returning to equilibrium.

If the post-collision speed of the combined spheres is initially v, what maximum height
will be achieved?

v^{2}/(2gL)^{½}

mgh

v^{2}/g

v^{2}/(2g)

A B C D

Compare the time required for the red sphere to move from its release point
to the collision point (t_{red}) to the time for the combined spheres to move from the
collision point to the point of maximum height (t_{both}).

t_{red} < t_{both}; the time differential
gets larger as h gets bigger.

t_{red} > t_{both}; the time differential
gets smaller as h gets bigger.

t_{red} and t_{both} are quite similar as long as
h<<L

t_{red} and t_{both} are both proportional
to h^{½}