EXAM 2                  November 2, 1988            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 
                                             -31
        The mass of the electron is 9.11 x 10    kg
(Read #4 first but work it last.)

 

     1. (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).  Find and justify the definition of the work unit
Joules (J) in terms of the units kg, m, and s.
 

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

                  1   2
           K.E. = - mv   on mass and velocity and of the spring potential
                  2
 
                        1            2
           energy  U  = - K (delta x)   on  delta x, where  F  = - K delta x .
                    sp  2                                    sp

     2.  Using work and energy concepts only, prove that under the
                                2     2               
action of a constant force,   v   = v   + 2 a s  , where  s  is the
                               f     0                
distance travelled between the points where the velocity of the

particle is  v   and  v  .
              0        f

     3.  (From homework)  A ball of mass  m   is attached to a rigid 

vertical rod by  means of two massless strings each of length  L  .  

The strings are attached to the rod at points a distance  L  apart.     

The tension in the upper string,  T  , is known.  Find the 
                                   1
ension,  T  ,  in the lower string and the velocity  v  of the ball.
          2

     
4.  A block is placed against a massless
 

     spring of spring constant K ,, compressed
 

     by  delta x =  250 cm.  The equilibrium point
 

     of the spring is at the edge of a cliff        [Diagram not available in 
                                                     this format]

     of height  h = 1.23 m , and the
 

     coefficient of kinetic friction between
 

     the block and the ground is  mu   = 0.5 .  If the block lands a
                                    k
distance  R = 3.00 m from the foot of the cliff, what is the

value of  K ?  Neglect air resistance and the size of the block.