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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 did gravity do on the red sphere when it was moved from equilibrium to its release point (as displayed above).
    1. mgh
    2. -mgh
    3. ½ mgh
    4. cannot be determined 
    A B C D       not sure?

  2. What was the speed of the red sphere just before its collision?
    1. (2gh)½
    2. (gh)½
    3. g(L2-h2)½
    4. ½ gh2 
    A B C D       not sure?

  3. What was the speed of the red sphere just after its collision?
    1. (1/2) its speed before the collision
    2. (1/5) its speed before the collision
    3. (2/5) its speed before the collision
    4. (1/6) its speed before the collision 
    A B C D       not sure?

  4. If the collision was elastic rather than inelastic how would the post-elastic-collision speeds compare to the post-inelastic-collision speed?
    1. The red sphere would be moving faster, the blue slower.
    2. The red sphere would be moving slower, the blue faster.
    3. Both red and blue would be moving faster than the post-inelastic-collision speed.
    4. Neither red and blue would be moving faster than the post-inelastic-collision speed. 
    A B C D       not sure?

  5. 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       not sure?

  6. In this problem:
    1. momentum and energy are always conserved.
    2. potential energy is converted into kinetic energy, but their total is conserved.
    3. angular momentum is conserved since the string exerts no torque.
    4. momentum is conserved only during the collision and mechanical energy is conserved at all times except during the collision. 
    A B C D       not sure?

  7. The maximum height reached by the combined spheres is:
    1. (1/5) h
    2. (1/6) h
    3. (1/10) h
    4. (1/36) h 
    A B C D       not sure?

  8. The maximum height reached by the combined spheres would be most increased by:
    1. doubling the initial height (h)
    2. halving the mass of the blue ball (to 2.5m)
    3. doubling the mass of the red ball (to 2m)
    4. either B or C 
    A B C D       not sure?

  9. Which graph best represents the horizontal velocity of the red sphere as a function of time?

    A       B  

    C       D   

    A B C D       not sure?

  10. Aside from the moment of the collision, the acceleration of the red sphere is largest:
    1. at the time of release
    2. just before the collision
    3. just after the collision
    4. when the combined spheres reach their maximum height 
    A B C D       not sure?