EXAM 3                  December 4, 1991            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.    

                                        -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.  (From homework)  Two vehicles A and B  are traveling west and  

south, respectively, toward the same intersection where they collide  

and lock together.  Before the collision  A  (which has mass M ) is  
                                                              A
travelling at a speed v  and  B (which has mass M )  is travelling at a  
                       A                         B
speed v  .   Find the (vector) velocity of the interlocked vehicles  
       B
immediately after the collision.   


   3.  A marble of mass  M  and radius  R  is rolled up a plane of angle theta.
                    
If the initial velocity of the marble is v  , what is the distance  L  
                                          0        
that it travels up the plane before beginning to roll back down?   

[The moment of inertia of a sphere around any axis through its center  
      2
is 2MR /5.   


   4.  Two playing cards stand on a table leaning against each other so  

as to form an "A-frame" roof.  The frictional coefficient between the  

bottom of each card and the table is mu .  What is the maximum angle  
                                       s                     
that the cards can make with the vertical without slipping?