EXAM 3                  December 5, 1990            PS 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)  Write down the equations or general principles

generally used to solve problems involving  

  (a).  collisions.  

  (b).  equilibrium.   


  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 particle is projected horizontally along

the interior of a smooth hemispherical bowl of radius r which is

kept at rest.  Find the initial speed v  required
                                       0           
for the particle to just reach the top of the bowl, given an

initial angle theta  measured from the bottom of the bowl.
                   0

  4.  Two smooth balls of steel of mass  m  and radius  R  are

sitting inside a tube of radius 1.5R.  The balls are in contact with

the bottom of the tube and with the wall (at two points as shown in

the diagram).  Find the contact force at the bottom and at the two

points on the wall.