EXAM 2                  November 6, 1991            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     

        1. (10 points)    
           (a).  Given that the change of momentum of a body subject to  

an external force is  delta P  = integral (F dt), give a way of remembering the  

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

           (c)  Under what circumstances do you apply the principle of  
conservation of energy?  Conservation of momentum?   
      
   The remaining problems are worth 30 points each.    

        2.  (From homework)  A 2.0-kg block is placed against a  
                                                     O
compressed spring on a frictionless board inclined 30  above the  

horizontal.  The spring, whose force constant is 1960 N/m, is  
compressed 20 cm, after which the block is released.  How far up the  
incline will it go before coming to rest?  Assume that the spring has  
negligible mass, that the spring and block are not attached to each  
other, and that the spring is stationary at its equilibrium length  
when it loses contact with the block.  Measure the final position of  
the block with respect to its position when the spring is fully  
compressed, just before the block is released.    
      
        3.  A mass  m  is suspended from a string and swung in a circle of  
radius  R  as shown in the figure.  If this pendulum makes one circuit  
in  T  seconds, what angle must the string make with the vertical?   

        4.  An instrument-carrying projectile accidentally explodes at  
the top of its trajectory.   The horizontal distance between the  
launch point and the point of explosion is  L .  The projectile breaks  
into two pieces which fly apart horizontally.  The larger piece has  
three times the mass of the smaller piece.  To the surprise of the  
scientist in charge, the smaller piece returns to earth at the  
launching station.  How far away does the larger piece land?  Neglect  
air resistance and effects due to the earth's curvature.