EXAM 3                  May 14, 1993         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
   g = 9.8 m/sec   
                                        -31
   The mass of the electron is 9.11 x 10    kg. 



   1. (10 points)  Show how to use the equations for motion in one  

dimension with constant acceleration to construct the equations for  

angular motion with constant angular acceleration and the formulas for  

the kinetic energy and angular momentum of a rigid body. 


   The remaining problems are worth 30 points each:  

  2.  On July 27, 1956, the ships Andrea Doria (mass m ) and  
                                                      A
Stockholm (mass m ) collided in the fog south of Nantucket Island and  
                 S   
remained locked together for a short time.  Immediately before the  

collision the velocity of the Andrea Doria was  v  at an angle of  theta   
                                                 A
east of south and that of the Stockholm was  v  at an angle of  phi  east  
                                              S
of south.  Calculate the magnitude and direction of the velocity of the  

combined wreck immediately after the collision and the amount of kinetic  

energy converted into other forms of energy by the collision.  



   3.  (From homework)  A heavy, homogeneous cylinder has a mass  m  and  

a radius  R .  It is accelerated by a force  T , which is applied  
                                                            
through a rope wound around a light drum of radius  r  that is  

attached to the cylinder.  The coefficient of static friction is  

sufficient for the cylinder to roll without slipping.  Find the  

acceleration and angular acceleration of the cylinder.  The moment of  
                                                  1    2  
inertia of a cylinder about its symmetry axis is  - M R  . 
                                                  2


   4.  A ring of mass  M   hangs from a thread, and two beads of mass  m   
                        R           
slide on it without friction (see figure).  The beads are released  

simultaneously from the top of the ring and slide down opposite sides.   

Show that the ring will start to rise if  m > 3M  / 2  , and find the  
                                                R
angle at which this occurs.