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: 10:23

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.

  1. How much work had to be done to move the red sphere from equilibrium to its release point (as displayed above).
    1. mgh
    2. -mgh
    3. ½ mgh
    4. cannot be determined 
    A B C D

  2. Compare the time required for the red sphere to move from its release point to the collision point (tred) to the time for the combined spheres to move from the collision point to the point of maximum height (tboth).
    1. tred < tboth; the time differential gets larger as h gets bigger.
    2. tred > tboth; the time differential gets smaller as h gets bigger.
    3. tred and tboth are quite similar as long as h<<L
    4. tred and tboth are both proportional to h½ 
    A B C D
    The next random number would have been: .98022