PROBLEMS FROM SERWAY AND ADDITIONS TO FISHBANE PROBLEMS
                               
                              JUNE 21 - JUNE 27
        
        FISHBANE - CHAPTER 12

        43. Misprint.  The correct equation numbers are 12-18 and 12-17.

        55. (c) Also give the new minimum ground speed for orbit.

        SERWAY - CHAPTER 11

        27.  A particle is located at the vector position
             r = (i + 3j) m, and the force acting on it is
             F = (3i + 2j) N.  (r,F,i, and j are vectors.)
             What is the torque about (a) the origin and (b)
             the point having coordinates (0,6) m.

        SERWAY - CHAPTER 12

        17.  A spaceship is fired from the Earth's surface with an
             initial speed of 20,000 m/s.  What will its speed be
             when it is very far from the Earth?  (Neglect friction.)
        
        19.  (a) Calculate the minimum energy required to send a
             3000 kg spacecraft from the Earth to a distant point
             in space where Earth's gravity is negligible.  
             (b) If the journey is to take three weeks, what average
             power will the engines have to supply?
        
        20.  A 1000 kg satellite orbits the Earth at an altitude of
             100 km.  It is desired to increase the altitude of the
             orbit to 200 km.  How much energy must be added to the
             system to effect this change in altitude?
        
        41.  Two hypothetical planets of masses m1 and m2 and radii 
             r1 and r2, respectively, are at rest when they are an
             infinite distance apart.  Because of their gravitational
             attraction, they head toward each other on a collision
             course.  (Hint:  Note that both energy and momentum are
             conserved.)
        
             (a)  When their center-to-center separation is d, find
             the speed of each planet and their RELATIVE speed.
        
             (b)  Find the kinetic energy of each planet just before
             they collide if m1 = 2 x 10^24 kg, m2 = 8 x 10^24 kg,
             r1 = 3 x 10^6 m, and r2 = 5 x 10^6 m.
        
        49.  (The picture for this problem is the same as for 
             Fishbane CH 8, problem 6.  You may use your result for
             that problem in solving this one.)  Two stars of masses
             M and m, separated by a distance of d, revolve in 
             circular orbits about their center of mass.  Show that
             each star has a period given by

                        T^2 = (4pi^2)d^3/G(M+m)
             
             (Hint: Write Newton's 2nd Law for each star, and use
              R+r = d)

        SERWAY - CHAPTER 21

        14.  A particle that hangs from an ideal spring has an omega 
             of 2.0 rad/s.  The spring is suspended from the ceiling
             of an elevator car and hangs motionless (relative to the
             elevator) as the car descends at a constant velocity of
             1.5 m/s.  The car then stops suddenly.  (a) With what
             amplitude does the particle oscillate?  (b) What is the 
             equation of motion for the particle?  (Choose the upward
             direction to be positive.)