EXAM 3                  May 14, 1986               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          

     

   1.  (Modified from homework)  A block of mass m  extends a  
                                                  1
   spring a distance  x  from its unstretched position.  The block  

   is removed and a body of mass  m  is hung from the same  
                                   2               
   spring.  If the spring is then stretched and released, what is  

   its period of oscillation?  

     

   2.  The original Ferris wheel, built by George Ferris, had a  

   radius  R  and a mass  M .  Assume that almost all the mass was  

   uniformly distributed along the rim of the wheel.  If the wheel  

   was initially rotating at an angular frequency of theta , what  
                                                          0
   constant torque had to be applied to bring it to a full stop in a  

   time  t ?  What force exerted on the rim would have given such a  

   torque?   

     

   3.  A wooden box, filled with a material of uniform density,  

   stands on a concrete floor.  The box has a mass  M,  width and  

   length  L , and height 3L.  The coefficient of friction between  

   the box and the floor is  mu .  If you exert a sufficiently  
                               s         
   strong horizontal push against the side of the box, it will  

   either topple over or start sliding without toppling over,  

   depending on how high above the level of the floor you push.  

   What is the maximum height at which you can push if you want the  

   box to slide?  What is the magnitude of the force you must exert  

   to start the sliding?  (Assume that mu  is large enough that  
                                         s
   if you push at the top of the side the box topples.)  

     

   4.  The wheels of an automobile are separated by a  

   transverse distance of  L .  The center of mass of this  

   automobile is a distance  h  above the ground and midway between  

   the wheels.  If the automobile is driven around an unbanked curve  

   of radius  R  with an excessive speed, it will topple over  

   sideways.  What is the speed  v  at which it will begin to  

   topple?  Assume that the wheels do not skid.  Since the  

   automobile is not in an inertial reference frame, torques can be  

   taken only around axes through the center of mass.