EXAM 2                    April 23, 1993                 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.   

               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  
    
  1.  (10 points)
     (a).  Find and justify the definition of the work unit Joules  J   

in terms of the fundamental units kg, m, and s.   

     (b).  Show how to remember the functional dependence of  

                          1     2                  
              K.E.  =    ---  mv   
                          2
on mass and velocity.   

     (c).  Show how to remember that the potential energy of a spring  

which exerts a force  F   = -kx .   
                       x
    
       The remaining problems count 30 points each.  A diagram is  
required for each problem.

  2.  A trunk of mass  m = 32 kg  is pushed a distance  d = 12 m  at a  
                                                               o
constant speed of  2 m/sec  up an incline of angle  theta  = 10    by a   

horizontal force of 7 N. The coefficient of sliding friction between  

the trunk and the incline is 0.5.  Calculate the work done by  (a)  the  

applied force,  (b)  the frictional force, and  (c)  the gravitational  

force.  
    
  3.  Material is blown into cart A from cart B at a rate of  b  kilograms  

per second.  The material leaves the chute downward and has the same  

horizontal velocity   u   as cart B.  At the moment of interest, cart A  

has mass  M  and velocity  v .  Find   dv/dt , the instantaneous acceleration 

of A.  
    
  4.  In a concrete mixer, cement, gravel, and water are mixed by  
tumbling action in a slowly rotating drum.  If the drum spins too fast  
the ingredients stick to the drum wall instead of mixing.  Assume that  
the drum of a mixer has radius  R  and that it is mounted with its axle  
horizontal.  What is the fastest the drum can rotate without the  
ingredients sticking to the wall all the time?