Chapter 4
Exercises
1. Recall acceleration is Force/mass, so a
large gravitational force acting on a large mass gives the same
acceleration as a small gravitational force acting on a small
mass.
4. The magnitude is 700 N and is directed
toward the center of the earth. What is his mass and weight in
pounds?
7. At 3m it will illuminate
9m2, at 5m it will illuminate 25 m2 .
10. Objects orbiting the earth, such as the
shuttle, are actually in a state of free fall. Their velocities are
great enough, however, to keep them in orbit. As the shuttles falls
toward earth, the earth moves out from under it, due to its
curvature. Since the shuttle is in free fall there is nothing to
support your weight, hence your feel weightless.
11. The earth's circumference is about
40,087 km (ref. page. 689). If we completed one revolution every 90
minutes = 5400 seconds we would be traveling at 7.4 km/s, at the
equator. Recall orbital speed is 8 km/s so one might have a difficult
time sticking to the ground at the equator. At the poles we would
sense no change in gravity while in the middle of the United States
we would feel something in-between.
14. Since we are in orbit around the sun we
are weightless relative to it. i.e. it does not affect our weight.
This is much like the weightlessness felt by astronauts orbiting the
earth.
22. About 2.25 m/s2.
24. As the ball falls toward the earth its
trajectory points, at least slightly, in the direction of the
gravitational force. The falling ball moves slightly in the direction
of the force, hence work is done, the work resulting in acceleration.
A ball in a circular orbit does not move at all in the direction of
the gravitational force, hence no work and no acceleration.
28. To take advantage of earth's rotational
velocity.
30. In an elliptical orbit the satellite's
distance from earth changes, which means at times it moves somewhat
in the direction, or opposite direction, of the gravitational force.
When this happens a change in velocity results, that is work is
done.
32. The nearer one overtakes the further
one. The further out you go, the less the orbital velocity
becomes.
33. The wrench "dropped" by the astronaut
has the same velocity as the orbiting space station, thus the wrench
would continue to orbit the earth.
36. The best solution would be to launch the
rocket in the opposite direction of earth's orbit around the sun with
a velocity of 30 km/s.
39. Point A gives the greatest gravitational
force, greatest speed, greatest velocity, greatest momentum, greatest
kinetic energy, and greatest acceleration. The total energy and
angular momentum is the same everywhere in the orbit. Point C gives
the greatest potential energy.
Problems
2. F = Gx(mM)/d2. G = 6.67 x 10-11, m = 1 kg, M = 7.4 x 1022, d = 3.8 x 108.
So, F = 3.42 x 10-5 N.
3. Note formula on bottom of page 100. G = 6.67 x 10-11, M = 6 x 1024, d = 3.8 x 108 .
So, v = 1026 m/s.
6. First we need to know the force the sun exerts on the earth.
G = 6.67 x 10-11, m (earth) = 6 x 1024, M (sun) = 1.98 x 1030, d = 1.496 x 1011.
So, F = 3.54 x 1022 N.
Determine what times 2 x 1011 N/m2 (strength of steel) = 3.54 x 1022 N?
Answer is 1.77 x 1011 m2 . This is a circular area (cross section).
Determine diameter, D, from area = ¹(D2/4). Where ¹ = 3.14159
We find D = 474766 m = 474.766 km = 297
miles thick.