EXAM 1                  March 10, 1986                  PS 207

     If you need a constant not given here or do not understand a
problem, please ask me about it.  No notes, books, etc. may be
used during this exam.  Please answer each question on a separate
sheet of paper.

                  2
    g = 9.8 m/sec

     Remember to include diagrams, units, directions, etc.
Points will be assigned for each of these.

1.  A sound wave is transmitted down a metal rod of cross
sectional area  A .  The wave is generated by varying a force  F
applied to the end of the rod.  The elongation  delta-L  of the rod
will be given by  delta-L = L delta-F/(YA) , where  Y  is a constant
called Young's modulus.  Derive from dimensional analysis (units)
a formula for the speed of sound inside the metal in terms of  Y
                                                        3
and the density rho  of the metal (rho has units of kg/m  ).

(If your answer takes more than 2-3 minutes to write down, you 
are not using dimensional analysis).

2.   Find the centripetal acceleration of a car travelling 30 mph
around a curve whose radius is 100 ft. 

3. (From homework)  Show that the maximum height reached by a

                                      2
projectile is y     = (v  sin theta-0)  /(2g) .
               max      0
 
4. A person is leaning over the edge of a (large) basket being
lifted by a balloon which is ascending with a speed of 3 m/s.  He
throws a flower pot upward with a speed of 5 m/s relative to the
basket when he is 12m above the ground.  How long does it take
the pot to hit the ground, and how fast is it moving just before
it hits?