EXAM 2                  November 4, 1994            PHYS 207

If you need a constant not given here or do not understand a
problem, please ask me about it.  Remember to include diagrams
and explain your reasoning.  No notes, books, etc. may be
used during this exam.

               2             2
  g = 9.8 m/sec   = 32 ft/sec   

                                       -31
  The mass of the electron is 9.11 x 10    kg   

                                      6  
  The radius of the earth is 6.38 x 10  m  


        1. (10 points)    
           (a).  Find and justify the definition of the work unit Joules  J   
in terms of the fundamental units kg, m, and s.   
           (b).  Given that the change of momentum of a body subject

to an external force is  delta P = sum (F ) delta t, give a way of remembering
                                         i
the definition of momentum.

           (c).  Show how to remember the functional dependence of  
                          1     2                  
              K.E.  =    ---  mv   
                          2
on mass and velocity.   

        2. (30 points; from homework).  A rifle bullet of mass  
m = 9g  moves  d = 0.6 m  in a rifle barrel.  The speed of the
bullet as it leaves the barrel is  v = 1200 m/s .  Find the force
exerted on the bullet assuming it to be constant while the bullet is
in the barrel.  [If you work this problem symbolically, you need not
substitute to get a numerical answer].

        3. (30 points).  Two pendulums each of length  L  and each
of mass  m  are initially situated as shown in the diagram.  The
first pendulum is released and strikes the second in a perfectly
elastic collision.  What is the linear velocity of the second
pendulum immediately after the collision?  Prove any statements you
make about the effect of the collision.

        4. (30 points)  A massless ring hangs from a thread, and two
beads of mass  m  slide on it without friction (see diagram).  The
beads are released simultaneously from the top of the ring and slide
down opposite sides.  Show that the ring will start to rise when the
beads are at an angle of arccos (2/3) measured from the top of the ring.