EXAM 3                  November 30, 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  
	                                                           2
	  The moment of inertia of a cylinder about its axis:    MR /2
	
	                                                            2
	                        of a sphere about its diameter:  2MR /5
	
	1. (10 points)   Tell how to recognize that a problem is of type
	(a)  Equilibrium    (b)  Projectile motion  (c)  Elastic collision
	
	Tell how to recognize that a problem is likely to involve
	(d)  Energy conservation     (e)  Torques
	
	The remaining problems are worth 30 points each.
	
	2.  (From homework)  A uniform cylinder of mass  M  and radius  R 
	has a string wrapped around it.  The string is held fixed, and the
	cylinder falls vertically like a yo-yo.  Find the linear acceleration
	of the cylinder and the tension in the string.  
	
	3.  A small marble of mass  m  and 
	radius  r  rolls without slipping along
	the loop-the-loop shown in the diagram,
	having been released from rest somewhere
	on the straight section of track.  From
	what minimum height above the bottom of
	the track must the marble be released in
	order that it just stay on the track at
	the top of the loop?  Treat  r  as small
	compared to the radius of the loop,  R .
	
	4.  A heavy uniform bar of mass  M   
	rests on the top of two identical rollers  
	which are continuously turned rapidly in  
	opposite directions as shown in the diagram.    
	The centers of the rollers are a distance 
	 2L  apart.   The coefficient of friction  
	between the bar and the roller surfaces is  mu , a constant
	independent of the relative speed of the two surfaces.  Initially the
	bar is held at rest with its center at a distance of  x from the
	midpoint of the rollers.  At time  t=0  it is released. 
	
	(a).  Show all of the forces acting on the bar at t=0 and find their
	sizes and directions then, assuming M, L, x, and mu are known.   
	
	(b).  Will the bar accelerate?