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Physics 10424 Weekly Assignment #1
Wednesday, January 18, 2011
Reading for the coming lectures:
Monday, January 23: Read Chapter 13. Go through the conceptual questions.
Make sure you complete the reading quiz on Concourse.
Wednesday, January 25: Read Chapter 14.1-14.5.
Homework Problems:
DUE Wednesday, January 25, IN LECTURE:
Chapter 13: 39, 42, 53, 56, 57, 63, 69
And these additional problems:
I. The figure shows a planetary object of uniform density ρ and radius R. (a) Show that the compressive stress S
(defined as the force per unit cross-sectional area) at the center of the planet is given by
!
! = !!"! ! ! !
m
(Hint: Construct a narrow column of cross-sectional area A extending from the center to
the surface. You should be able to show that the weight of the material in the column is
mgave, where m is the mass of the material in the column and gave is the value of g
A
midway between center and surface.) (b) In our solar system, objects (i.e., asteroids,
R
small satellites, etc.) with “diameters” less than 600km can be very irregular in shape,
whereas larger objects are more or less spherical. Only if the rocks have sufficient
ρ
strength to resist gravity can the objects maintain a non-spherical shape. Calculate the
maximum compressive stress that can be sustained by the rocks making up asteroids. Assume a
density of 4000 kg/m3. (c) What is the maximum size of a non-spherical self-gravitating satellite made of concrete?
Assume that concrete has a maximum compressive stress of 4.0×107 N/m2 and a density of 3000 kg/m3.
II. Write an expression for the force exerted by the Moon, mass M, on a particle of water, mass m on the earth’s
surface directly beneath the moon and lying on the line connecting the center of the earth with the center of the
Moon. Take the radius of the earth to be R, and the distance between the center of the earth and the center of the
Moon to be r. (b) Suppose that the particle of water was instead at the center of the earth. What force would the
Moon exert on it there? (c) Show that the difference in these forces is given by
2!"#$
!! = !!
And represents the tidal force, the force on water, relative to the earth, caused by the gravitational pull of the moon.
What is the direction of the tidal force? (d) Repeat for a particle on the far side of the earth, lying on the same line
connecting the earth-Moon centers. What the direction of this tidal force? (e) Explain why there are two tidal bulges
in the oceans (and in the earth’s crust), one pointing toward the Moon, and the other away from it.
III. In order to stage the Moon landings, the Apollo spacecraft had to fall into a circular orbit around the Moon after
their journey from Earth. Assume that the spaceship starts very far away from the Moon a distance D away from a
line parallel to its velocity passing through the Moon's center (see diagram), and that its initial velocity there is V.
The spaceship has mass m and the moon has mass M.
A. Calculate the initial angular momentum of the spaceship about the Moon's center.
B. For a circular orbit around the Moon of radius R (R > Rmoon!), what is the value of the gravitational potential
energy of the spaceship? Assume R is the total radius of the orbit.
Please put
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on EVERY assignment
C. What is its kinetic energy in this circular orbit?
D. The spaceship fires a thruster in a direction opposite its velocity when it reaches point C on the diagram. How
much must its linear momentum change to put it into the circular orbit?
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Suggested problems:
Chapter 13: 19, 23, 26, 29, 31, 43, 51, 52, 55, 59, 61, 62, 65