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)?