Chapter 4 answers
Review questions:
1. The motion of both is governed by a single force: gravity.
2. The moon is in free fall around the earth just like any other earth satellite, or like the cannonball fired from Newton's cannon.
5. This was done by Henry Cavendish in the late 1700's. He created an ingenious device to directly measure the gravitational force between two pairs of lead balls. Since he knew the masses of the balls in his experiment, he could easily find G. Phillip Von Jolly's method was much simpler: he just hung a bottle of mercury (same stuff in thermometers) on a one end of a really sensitive balance scale and then rolled a big 6 ton ball of lead underneath the bottle o' mercury (see figure 4.2 on page 78). It worked. Three cheers for the brute force approach.
7. Easy: F = ma = (1kg)x(10 m/s2) = 10 N
9. The apple has to be twice the distance from the earth's center for the inverse square law to predict this result, not twice the distance from earth's surface (see figure 4.4 or your notes).
10. No! Gravity fills the universe. Every particle of matter attracts every other through any distance just by virtue of being matter according to Newton's famous formula. According to Newton's universal law of gravity, your body is being attracted to every atom in the universe! Therefore you can never travel far enough away from earth (or any other body) such that the attraction from that body drops to zero. Spacecraft and their occupants are only weightless because they are in free fall-- not because they have escaped the influence of gravity.
18. Newton's 1st law explains why this is true. An object in motion continues in motion unless a net force acts upon it. A baseball curves toward the ground under the influence of an outside force (in this case, gravity). However, this force (except for insignificant variations) always acts down near the surface of the earth. Since it therefore does not act horizontally at all, it can't speed up the ball or slow it down in the horizontal direction. Thus the ball keeps moving at the same velocity horizontally even while it accelerates toward the ground.
20. They are the same. Read pages 86 & 87. Pay close attention to figures 4.16 & 4.17.
21. 45 degrees.
25. 5 meters
28. One way to understand it is this: The path of the projectile is curved. As we keep increasing the initial speed of the projectile, this curved path begins to ever more closely match the earth's curvature until the path becomes a closed loop or 'orbit'. See Newton's cannon again for practice with this idea.
34. This topic won't be covered on your test (Spring 2000 PHS 111). The answers are:
greatest speed: closest to the planet or body that it orbits.
least speed: furthest from the planet/body that it orbits.
Exercises:
3. They weigh the same.
4. Those which are closer. (won't be on Sp '2000 PHS 111 exam II)
5. 700 N straight down.
7. same: Newton's 3rd law says so!
12. Passengers on a jet liner are not in free fall (we hope not!): the plane moves experiences significant air resistance which prevents free fall during a normal flight while the shuttle does not (it is above most of the atmosphere and is in free fall about the earth). Now it is true that airplanes can achieve free fall for short periods of time, sometimes as long as 30 seconds. This technique was (and still is) used by NASA to train astronauts for weightlessness. Follow the link and Read about the Vomit Comet.
29. The satellite in a circular orbit keeps a constant speed at right angles (90 degrees) to the direction of earth's center. This is called 'moving tangentially' to a circular path. Because of this, the satellite's speed can't be changed by gravity since, again, gravity only acts toward earth's center, not in the 'tangential' direction. See #18 review question above
32. You may have seen the space shuttle do this. The reason is clear if you understand #18 above. The satellite must act like Newton's cannonball (see #28 above & follow the link & interact with the applet again). The cannonball, remember, is fired at a 90 degree angle to the direction of the earth's center. The rocket must do three things. It must go up to leave earth's atmosphere (reach the top of the 'mountain'). It must also be accelerating to orbital velocity (above 17,000 m.p.h. for low earth orbit!). Finally, it must gradually bend its path from a vertical to a 'tangential' path so that it can enter a nearly circular orbit (like the cannonball).
Problems:
1. one 16th as much or about .6 m/s2
2. Using these values, you should have gotten 9.2 m/s2
7. It works out to about 67,000 m.p.h. (hint: the distance to the sun is about 93 million miles. Using this figure, the circumference of earth's orbit is about 584 million miles. Then just divide this distance by time. One year equals 8760 hours).