PROBLEMS FROM OTHER TEXTS and other ADDITIONAL PROBLEMS
                               
                              JUNE 26 - JULY 2
        
        FISHBANE - CHAPTER 8
         6. (The figure for this problem is Fig. 14-16 on page 309 of HRW.)  
            Two objects, of masses m1 and m2 (m2 > m1), respectively, move 
            in circular orbits that have the same center.  If the force that 
            gives rise to this motion is a force of attraction between the 
            two objects acting along a line joining them, using momentum 
            conservation and Newton's second law, (a) show that they move 
            with the same angular speed, and (b) calculate the ratio of
            the radii of the two circular orbits.

        FISHBANE - CHAPTER 9
        50. A child of mass 25 kg stands at the edge of a rotating platform 
            of mass 150 kg and radius 4.0 m.  The platform with the child on 
            it rotates with an angular speed of 6.2 rad/s.  The child jumps 
            off in a radial direction.  (a) What happens to the angular speed 
            of the platform? (b) What happens to the platform if, a little 
            later, the child, starting at rest, jumps back onto the platform?  
            (Treat the platform as a uniform disk.)
        
        FISHBANE - CHAPTER 12
        35. A small package is fired off Earth's surface with a speed v at a 
            45 degree angle with the local horizontal.  It reaches a maximum 
            height h above the surface at h = 6370 km, a value equal to Earth's 
            radius itself.  What is its speed when it reaches this height?  
            Ignore any effects that might come from Earth's rotation or from 
            air resistance.  (Hint: You will need to use two conservation 
            equations and solve two equations in two unknowns.)

        55. The Little Prince ( a character in a book by Antoine de Saint-
            Exupery) lives on the spherically symmetric asteroid B-612.  The 
            density of B-612 is 5200 kg/cubic meter.  Assume that the asteroid 
            does not rotate.  The Little Prince noticed that he felt lighter 
            whenever he walked quickly around the asteroid.  In fact, he found 
            that he became weightless and started to orbit the asteroid like a 
            satellite whenever he speeded up to 2 m/s.  (a) Estimate the radius 
            of the asteroid from these data.  (b) What is the escape speed for 
            the asteroid?  (c) Suppose that B-612 does rotate about an axis 
            such that the length of the day there is 12 h.  Can the Little 
            Prince take advantage of this rotation when he wants to orbit the 
            asteroid?  What is his minimum ground speed for orbit in this case?

        SERWAY - CHAPTER 12 
        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 m1 and m2, 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(m1+m2)
             
             (Hint: Write Newton's 2nd Law for each star, and use r2+r1 = d)

        PROBLEM G1
             You weigh 530 N at sidewalk level outside the Petronas Towers in 
             Kuala Lumpur, Malaysia.  Supose that you ride from this level to 
             the top of one of its 420 m towers.  Ignoring Earth's rotation, 
             how much less would you weigh there (because you are slightly 
             farther from the center of Earth)?