PROBLEMS FROM SERWAY - CHAPTERS 7 AND 8
        
        
        CHAPTER 7
        
        22.  When a 4-kg mass is hung vertically on a certain light
             spring that obeys Hooke's law, the spring stretches
             2.5 cm.  If the 4-kg mass is removed, (a) how far will
             the spring stretch if a 1.5-kg mass is hung on it, and
             (b) how much work must an external agent do to stretch 
             the same spring 4.0 cm from its unstretched position?
        
        26.  If it takes 4 J of work to stretch a Hooke's-law spring
             10 cm beyond its unstressed length, determine the
             additional work required to stretch it another 10 cm.

        59.  A 200-g block is pressed against a spring of force 
             constant 1400 N/m until the block compresses the spring
             10 cm.  The spring rests at the bottom of a ramp 
             inclined at 60 degrees to the horizontal.  Determine
             how far up the incline the block moves before
             momentarily coming to rest, (a) if there is no friction 
             between the block and the ramp and (b) if the 
             coefficient of kinetic friction is 0.4.

        CHAPTER 8

        56.  A 10-g mass is attached to the end of an unstressed,
             light, vertical spring (k = 49 N/m) and then dropped.  
             Answer the following questions by considering the 
             potential energy due to the spring plus the potential
             energy due to gravity, i.e. measure distances from the
             equilibrium position of the spring with no mass 
             attached. (a)  What is the maximum speed of the falling 
             mass?  (b) How far does the mass drop before coming to 
             rest momentarily?

        56'. Repeat problem 56, but answer the questions by 
             considering the potential energy of the spring with
             the mass attached, i.e. measure distances from the
             equilibrium position of the spring with the mass
             attached.
        
        63.  A pinball machine launches a 100-g ball with a
             spring-driven plunger.  The game board is inclined
             at 8 degrees above the horizontal.  Find the force
             constant k of the spring that will give the ball a
             speed of 80 cm/s when the plunger is released from
             rest, with the spring compressed 5 cm from its
             relaxed position.  Assume that the plunger's mass
             and frictional effects are negligible.