EXAM 2                  November 1, 1989            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).  Given that the change of momentum of a body subject

to an external force is  delta P = sum (F ) delta t, give a way of remembering
                                         i
the definition of momentum.
 

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

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

     2.  (From homework)  The last stage of a rocket is traveling
                       3
at a speed of 8.00 x 10   m/s .  This last stage is split by a spring

into two parts travelling at a relative speed of 900 m/s.  The

faster part has a mass of 150 kg and the slower a mass of 250 kg.

What are the speeds of the two parts?  Will the total kinetic

energy after separation be greater or less than that before

(justify your answer)?
 

     3.  A small block of mass  m
 

     starts from rest and slides  along
 

     a frictionless loop-the-loop of               [Diagram not available in 
                                                     this format]
 
     radius  r  as shown to the right.
 

     What is the speed of the block at
 

     the top of the loop, if it was released at a height  h  and
remains in contact with the track?  How large must  h  be for the
block to remain in contact with the track at the top of the loop?
 

     4.  (Borrowed)  The "Eureka Hovercraft Corporation" wanted to
hold hovercraft races as an advertising stunt.  The hovercraft
supports itself by blowing air downward, and has a big fixed
propeller on the top deck for forward propulsion.  Unfortunately,
it has no steering equipment, so that the pilots found that making
high speed turns was very difficult.  The company decided to
overcome this problem by designing a bowl-shaped track in which
the hovercraft, once up to speed, would coast along in a circular
path with no need to steer.  They hired an engineer to design and
build the track, and when he finished, he hastily left the
country.  When the company held their first race, they found to
their dismay that the craft took exactly the same time  T  to
circle the track, no matter what its speed.  Find the angle of
inclination of each part of the track as a function of the
distance from that point to the center of the track.