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.

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.

How much work did gravity do on the red sphere when it was
moved from equilibrium to its release point (as displayed above).

mgh

-mgh

½ mgh

cannot be determined

A B C D

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

What was the speed of the red sphere just after its collision?

(1/2) its speed before the collision

(1/5) its speed before the collision

(2/5) its speed before the collision

(1/6) its speed before the collision

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}

A B C D

In this problem:

momentum and energy are always conserved.

potential energy is converted into kinetic energy, but their total is conserved.

angular momentum is conserved since the string exerts no torque.

momentum is conserved only during the collision and mechanical energy is conserved at all
times except during the collision.