EXAM 2                 November 2, 1995                PHYS 207H
                                                                               
      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                                    -31
g = 9.8 m/sec  = 32 ft/sec .   Mass of the electron = 9.11 x 10   kg

                                                 6             
                  Radius of the earth = 6.38 x 10  m           

  1.  (10 points)
         (a).  The MKS unit of force in the Newton (N).  Find its
definition in terms of the units kg, m, and s.  Justify your answer.

         (b).  Show how to remember the functional dependence of the
spring potential energy
 
                        1            2
                   U  = - K (delta x)   
                    sp  2                                    

on  delta x, where  F  = - K delta x  .
                     sp

         (c)  Under what circumstances do you apply the principle
of conservation of energy?  


The remaining problems count 30 points each.  A diagram is required
for each problem.

   2.  A uniform rope of weight
W   hangs between two trees.  The
ends of the rope are at the same 
height, and they each make an angle
theta with the trees.  Find the 
tension at either end of the rope
and at the middle of the rope.

   3.  A 5 kg block is held against a spring of force constant 2000
N/m, compressing it 0.03 m.  The block is released and the spring
extends, pushing the block along a rough horizontal surface.  The
coefficient of friction between the surface and the block is 0.2 . 
What is the speed of the block when the spring returns to its
equilibrium position?  You may wish to evaluate the work done on the
block during the return by the spring and by friction.

   4.  A good but foolhardy skier wishes to shuss down the back of
Halfdome, a large mountain in Yosemite Park which has the form of a
half-sphere of radius  R .  He starts at the top of the mountain. It
is very icy and the skier makes no attempt to stop or slow down. 
How far does he get before leaving the ground?