!

6. lf you drop a feather and a steel hammer at the same moment, they should hit the ground at the same instant. Why doesn't this work on Earth, and why does it work on the Moon?Will it work on Phobos,a moon of Mars?

7. What is the difference between mass and weight? 8. When a person says he gained weight, does he mean that he gained

ln mass, gravity, or both mass and gravity?9. An astronaut working in space near the International Space Station

says she feels weightless, What does she mean? Does the astronaut not have weight?

10. What is the difference between speed and velocity?11. A car is on a circular off ramp of an interstate and is traveling at

exactly 25 mph around the curve. Does the car have velocity? Doesthe car have acceleration? ls the car decelerating?

12. How many accelerators does a car have? What are they?13. You put your astronomy textbook and your No. 2 pencil on a

ceramic tile floor, and you blow on each. Which has more inertia­the pencil, the textbook, or neither? Why? Which has more momen­tum? Why?

14. An astronaut is in space with a baseball and a bowling ball. Theastronaut gives both objects an equal push in the same direction.Does the baseball have the same inertia as the bowling ball? Why?Does the baseball have the same acceleration as the bowling ballfrom the push? Why? If both balls are traveling at the same speed,does the baseball have the same momentum as the bowling ball?

15. You are at a red light in your car. The red light turns green, and youtake your foot off the brake and step on the gas pedal, withoutturning the steering wheel. The speedometer changes from Oto20 mph in" 3 seconds. In those 3 seconds, did the car change velocity? Is that an acceleration? Now, at a constant speed of 20 mph, you make a right turn. ls that an acceleration?

16. You weigh 100 pounds, your friend weighs 200 pounds, and you arein an arm wrestling contest with each other. Neither person iswinning, but each of you is struggling to push the other's forearmover to the tabletop. Which of Newton's laws applies to this scenarioand why? Now in one swift motion you plant your friend's forearmon the table, winning the contest. Which of Newton's laws applies tothis motion and why?

17. Why did Newton conclude that some force had to pull the Moontoward Earth?

18. Why did Newton conclude that gravity has to be mutual anduniversal?

19. You have the same mass as a person sitting next to you. Are yougravitationally attracted to them? If so, why don't you instantlyzoom over and stick to them? Is the attraction mutual? If not, whynot?

20. You are sitting next to a person who has twice as much weight. Areyou gravitationally attracted to them? If so, is it twice as much astheir attraction to you? If not, why not?

21. You are sitting next to a person who has twice as much weight. Youget up and move one seat over, doubling your distance from them.Did the gravitational force between you increase, decrease, or staythe same?

22. You are sitting next to a person who has twice as much weight as you do. A friend comes by and gives you a marshmallow, and youeat it. Did the gravitational force between you and your friendincrease, decrease, or stay the same? Why?

23. How does the concept of a field explain action at a distance? Name another kind of field also associated with action at a distance .

24. Why can't a spacecraft go "beyond Earth's gravity"? 25. Where is the center of mass of your body? 26. Balance a pencil lengthwise on the side of your finger. Where is the

center of mass? Balance a pencil widthwise (for example, on the

eraser side) on your finger. Where is the center of mass? Is the cent, of mass a plane, sphere, circle, point, or a line?

27. What is the center of mass of two bodies? Where is the center of mass of the Earth-Moon system?

28, Why can't you leave Earth's gravitational field when jumping vertically?

29. According to Kepler's first law, planets move in elliptical orbits. Whis that considered accelerated motion? According to Newton, wha1the force causing that acceleration?

30. How do planets orbiting the Sun and skaters doing a spin both conserve angular momentum?

31. If a planet were to slowly migrate inward toward the Sun while remaining in a stable orbit, would its orbital speed increase,decrease, or stay the same? Would its angular momentum changeiWhich of Kepler's laws or Newton's version of Kepler's laws does th scenario describe?

32. If you hold this textbook out at shoulder height and let go, at theinstant you let go, does the book have potential energy? Kineticenergy?

33. Today at the beach you see the highest of all high tides during thelast month. You see the Moon in the daytime sky. What is the mos1likely Moon phase? Why?

34. Why is the period of an open orbit undefined? 35. In what conditions do Newton's laws of motion and gravity need t,

be modified?

36. How does the first postulate of special relativity imply the secondpostulate?

37. When you ride a fast elevator upward, you fee! slightly heavier as t trip begins and slightly lighter as the trip ends. How is this phenonenon related to the equivalence principle?

38. From your knowledge of general relativity, would you expect radic waves from distant galaxies to be deflected as they pass near the Sun? Why or why not?

39. How is gravity related to acceleration? Are all accelerations the res of gravity?

40. Near a massive planet, is gravitational acceleration large or small? space strongly curved, or not? What about near a small marble?

41. How Do We Know? Why would science be impossible if some natural events happened without causes?

42. How Do We Know? Why is it important that a theory make testabpredictions?

ACTIVE INQUIRY QUESTIONS -------

1. Give an example from everyday life to illustrate each of Newton's laws.

2, People who lived before Newton may not have believed in cause and effect as strongly as you do. How do you suppose that affecte how they saw their daily lives?

3. If Newton modified Kepler's laws and Einstein modified Newton'slaws, is it possible Einstein's laws (postulates) might be modified?

PROBLEMS

1. An astronomy textbook is to be dropped from a tall building on Earth. One second aher dropped, what are the textbook 's speed,velocity, and acceleration? After 2 seconds? After 3 seconds? The book hits the ground; what are the book's speed, velocity, and acceleration?

Chapter 5 Gravity

Review questions

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2. Compared to the strength of Earth's gravity at its surfacer= RE

where RE is the radius of Earth, how much weaker is gravity at a distance of r = 10 RE? At r = 20 RE?

3. Compare the force of gravity on a 1 kg mass on the Moon's surfacewith the force that mass on Earth's surface. Which force is greater,why, and by how much?

4. A satellite is in orbit at a distance r from the center of Earth. If theorbit radius is halved so that the satellite is orbiting closer to Earth'ssurface, will the field strength increase, decrease, or stay the same?Jf it changes, by how much?

5. The International Space Station is in orbit around Earth at a distance rfrom the center of Earth. A recent addition increased the Station's mass by a factor of 3. Did Earth's gravitational force on the Station increase, decrease, or stay the same? If it changes, by how much?

6. If a small lead ball falls from a high tower on Earth, what will be itsvelocity after 2 seconds? After 4 seconds?

7. What is the circular velocity of an Earth satellite 1000 km above Earth's surface? (Note: Earth's average radius is 6370 km.Hint: Convert all quantities to m, kg, s.)

8, What is the circular velocity of an Earth satellite 36,000 km above Earth's surface? What is its orbital period? (Note: Earth's average radius is 6370 km. Hint: Convert all quantities tom, kg, s.)

9. What is the orbital speed at Earth's surface? Ignore atmosphericfriction. (Note: Earth's average radius is 6370 km. Hint: Convert allquantities to m, kg, s.)

1 O. Describe the shape of the orbit followed by the slowest cannonball in Figure 3 of the Concept Art, pretending that the cannonball could pass freely through Earth. (Newton got thls problem wrong the first time he tried to solve it.)

11, If you visited a spherical asteroid 30 km in radius with a mass of 4.0 X 1017 kg, what would be the circular velocity at its surface? A major league fastball travels about 90 mph. Could a good pitcher throw a baseball into orbit around the asteroid? (Note: 90 mph is 40 m/s.)

12. What is the orbital period of a satellite orbiting just above thesurface of the asteroid in Problem 11?

13. What would be the escape velocity at the surface of the asteroid inProblem 11? Could a major league pitcher throw a baseball off theasteroid so that it never came back?

14. Pretend you are an asteroid. What is the escape velocity from you,assuming your mass is 60 kg and your radius is 0.8 meters? Estimatehow fast a fly flies. Would a fly be able to reach your escape velocity?

15. A moon of Jupiter takes 1.8 days to orbit at a distance of4.2 X 105 km from the center of the planet. What is the total massof Jupiter plus this moon? (Note; One day is 86,400 seconds.)

SENSE OF PROPORTION

1. Arrange the followlng motions in order of increasing velocity: orbit of Earth around the Sun; an orbit around Earth near Earth's surface; an object just barely escaping Earth; orbit of the Moon around Earth; orbit of a geosynchronous satellite

2. Arrange the following motions in order of increasing acceleration: adragster car; an object dropped off a cliff near the top of Mt. Everest; an object dropped by an astronaut standing on the Moon; an object dropped from the top of a New York Cit y skyscraper

100 PART 1 Exploring the Sky

LEARNING TO LOOK

1. Why can the object shown here be bolted in place and used 24 hours a day without adjustment?

2. What is the flux at position 2 compared to position 1 in Figure 5-5?How does the distance from the center to position 2 compare with the distance to position 1?

3, Why ls it a little bit misleading to say that this astronaut is weightless?