EXAM 2                  November 7, 1990            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             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).  Given that the change of momentum of a body subject
                                ->   ->
to an external force is   delta P =  F  delta t  , give a way of remembering

the definition of momentum.

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

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

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

spring obeying   F  = -kx .
                  x


 The remaining problems are worth 30 points each.

 2.  (From homework)  A student wants to determine the

coefficients of static friction and kinetic friction between a box

and a plank.  He places the box on the plank and gradually raises

the plank.  When the angle of inclination with the horizontal
          o
reaches 30  , the box starts to slip and slides 4.0 m down the

plank in 4.0 s.  What are the coefficients of friction?


 3.  A passenger in a ship travelling in a quiet sea hangs a
ball from the ceiling of his cabin by means of a long thread.
Whenever the ship accelerates, he notes the pendulum ball lags
behind the point of suspension and so the pendulum no longer hangs
vertically.  If the ship goes from rest to a speed  v  in a distance
d , what will be the angle  theta  of the pendulum from the vertical?


 4.  A circus acrobat of mass  M  leaps straight up with

initial velocity  v   from a trampoline.  As he rises up, he takes
                   0
a trained monkey of mass  m  off a perch at a height  h  above the

trampoline.  What is the maximum height above the trampoline

attained by the pair?