natural

1. What class of motion, natural or violent, did Aristotle attribute to motion of the moon?

natural

2. What state of motion did Aristotle attribute to earth?

Earth circles the sun, and not the other way around.

3. What relationship between the sun and earth did Copernicus formulate?

That objects in fall pick up equal speeds whatever their weight.

4. What did Galileo discover in his legendary experiment on the Leaning Tower of Pisa?

That a moving object will continue in motion without the need of a force.

5. What did Galileo discover about moving bodies and force in his experiments?

Inertia is the name given to the property of matter that resist a change in motion.

6. Is inertia the reason for moving objects maintaining motion or the name given to this property?

Newton’s law is a restatement of Galileo’s concept of inertia.

7. How does Newton’s first law of motion relate to Galileo’s concept of inertia?

A straight line path.

8. What type of path does a moving object follow in the absence of a force?

The net force is 70 pounds to the right.

9. What is the net force on a cart that is pulled to the right with 100 pounds of force and to the left with 30 pounds of force?

A description of force involves magnitude and direction, and is therefore a vector quantity.

10. Why do we say that force is a vector quantity?

The resultant of the vector pair.

11. According to the parallelogram rule, what quantity is represented by the diagonal of a constructed parallelogram?

The resultant is √2 pounds.

12. What is the resultant of a pair of 1 pound forces at right angles to each other?

The tension in each rope would be half of Nellie’s weight.

13. Consider Nellie hanging at rest. If the ropes were vertical, with no angle involved, what would be the tension in each rope?

Yes, although science texts favor the newton.

14. Can force be expressed in units of pounds and also in units of newtons?

The net force is zero.

15. What is the net force on an object that is pulled with forces of 80 newton’s to the right and 80 newton’s to the left?

The net force is zero.

16. What is the net force on a bag pulled down by gravity with a force of 18 N and pulled upward by a rope with a force of 18 N?

All the forces on something in mechanical equilibrium add vectorally to zero.

17. What does it mean to say something is in mechanical equilibrium?

∑Ƒ=0

18. State the equilibrium rule for forces in symbolic notation.

The support force is 15 N. The net force on the book is zero.

19. Consider a book that weighs 15 N at rest on a flat table. How many N of support force does the table provide? What is the net force on the book in this case?

Weight and support force have equal magnitude.

20. When you stand at rest on a bathroom scale, how does your weight compare with the support force by the scale?

Yes, the ball moving at constant speed in a straight line path is in dynamic equillibrium.

21. A bowling ball at rest is in equilibrium. Is the ball in equilibrium when it moves at constant speed in a straight line path?

Zero net force on it.

22. What is the net force on an object in either static or dynamic equilibrium?

The force of friction is 100 N.

23. If you push on a crate with a force of 100 N and it slides at constant velocity, how great is the friction acting on the crate?

They had no understanding of the concept of inertia.

24. What concept was not understood in the 16th century when people couldn’t conceive of a moving earth?

The bird still moves at 30 km/s relative to the sun.

25. A bird sitting in a tree is traveling at 30 km/s relative to the faraway sun. When the bird drops to the ground below, does it still move at 30 km/s, or does this speed become zero?

Yes, like the bird, you maintain a speed of 30 km/s relative to the sun, In accord with the concept of inertia.

26. Stand next to a wall that travels at 30 km/s relative to the sun. With your feet on the ground, you also travel at the same 30 km/s. Do you maintain this speed when your feet leave the ground? What concept supports your answer?

Since each scale reads 350 N, Lucy’s weight is 700 N.

27. Lucy stands with one foot on one bathroom scale and the other on a second scale. Each scale reads 350 N. What is Lucy’s weight?

800 N on one scale, 400 N on the other. (2x + x = 1200N;

3x = 1200 N; x = 400 N)

3x = 1200 N; x = 400 N)

28. Henry weighs 1200 N and stands on a pair of scales so that one scale reads twice as much as the other. What are the scale readings?

From the equilibrium rule, ∑Ƒ=0, the upward forces are 800 N, and the downward forces are 500 N + the weight of the scaffold. So, the scaffold must weigh 300 N.

29. A painters scaffold is in mechanical equilibrium. The person in the middle weighs 500 N, and the tensions in each rope are 400 N. What is the weight of the scaffold?

From the equilibrium rule, ∑Ƒ=0, the upward forces are 800 N + tension in the right scale. This sum must equal the downward forces 500 N + 400 N + 400N. Arithmetic shows the reading on the right scale is 500 N.

30. A different scaffold that weighs 400 N supports two painters, one 500 N and the other 400 N. The reading in the left scale is 800 N. What is the reading in the right hand scale?

C,B,A

31. The weights of Burl, Paul, and the scaffold produce tensions in the supporting ropes. Rank the tensions in the left rope, from the most to the least, in the three situations.

C,A,B,D

32. Rank the net forces on the blocks from least to most in the four situations.

a) 10 N———-5 N

b) 7 N———-3 N

c) 12 N———-4 N

d) 3 N———-3 N

a) B,A,C,D

b) B,A,C,D

b) B,A,C,D

33. Different materials rest on a table.

a) rank how much they resist being set into motion, from greatest to least.

b) Rank the support (normal) forces the table exerts on them, from greatest to least.

a) 12kg sand

b) 15kg iron

c) 10kg water

d) 2kg pillow

a) A=B=C (no force)

b) C,B,A

b) C,B,A

34. Three pucks are shown sliding across ice at the noted speeds. Air and ice friction forces are negligible.

a) Rank the forces needed to keep them moving, from greatest to least.

b) Rank the forces needed to stop them in the same time interval, from greatest to least.

a) 2 m/s —->

b) 4 m/s —–>

c) 6 m/s —–>

B,A,C

35. As seen from above, a stubborn stump is pulled by a pair of ropes, each with a force of 200 N, but at different angles as shown. From greatest to least, rank the net forces on the stumps.

a)

b)

c)

(a)

36. Nellie hangs motionless by one hand from a clothesline. Which side of the line has the greatest tension?

Aristotle favored philosophical logic while Galileo favored experimentation.

37. Knowledge can be gained by philosophical logic and also by experimentation. Which of these did Aristotle favor and which did Galileo favor?

The tendency of a rolling ball is to continue rolling —–in the absence of a force. The fact that it slows down is likely due to the force of friction.

38. A ball rolling along a floor doesn’t continue rolling indefinitely. Is this because it is seeking a place of rest or because some force is acting upon it? If the latter, identify the force.

Copernicus and others of his day thought an enormous force would have to continuously push the earth to keep it in motion. He was unfamiliar with the concept of inertia, and didn’t realize that once a body is in motion, no force is needed to keep it moving (assuming no friction).

39. Copernicus postulated that earth moves around the sun ( rather than the other way around), but he was troubled about the idea. What concepts of mechanics was he missing that would have eased his doubt?

40. That the rate at which bodies fall is proportional to their weight.

40. What Aristotelian idea did Galileo discredit in his fabled Leaning Tower of Pisa?

A moving body requires a force to keep it moving. He showed that a force is needed to change motion, not to keep a body moving, so long as friction was negligible.

41. What Aristotelian idea did Galileo demolish with his experiments with inclined planes?

Galileo proposed the concept of inertia before Newton was born.

42. Was it Galileo or Newton who first proposed the concept of inertia?

Nothing keeps asteroids moving. The Sun’s force deflects their paths but is not needed to keep them moving.

43. Asteroids have been moving through space for billions of years. What keeps them moving?

44.Nothing keeps the probe moving. In the absence of a propelling or deflecting force it would continue moving in a straight line

44. A space probe may be carried by a rocket into space. What keeps the probe moving after the rocket no longer pushes it?

If you pull the cloth upward, even slightly, it will tend to lift the dishes, which will disrupt the demonstration to show the dishes remaining at rest. The cloth is best pulled horizontally for the dishes to remain at rest.

45. In doing the tablecloth pull demonstration of inertia, why is it important that you pull slightly downward when you attempt to whip the cloth from beneath the dishes? What occurs if you pull slightly upward?

46.The inertia of a whole roll resists the large acceleration of a sharp jerk and only a single piece tears. If a towel is pulled slowly, a small acceleration is demanded of the roll and it unwinds. This is similar to the hanging ball and string shown in Figure 2.5.

46. In tearing a paper towel or plastic bag from roll, why is a sharp jerk more effective than a slow pull?

Your body tends to remain at rest, in accord with Newton’s first law. The back of the seat pushes you forward. Without support at the back of your head, your head is not pushed forward with your body, which likely injures your neck. Hence, headrests are recommended.

47. If you’re in a car at rest that gets hit from behind, you can suffer a serious neck injury. What does whiplash have to do with Newton’s first law?

48.In a bus at rest your head tends to stay at rest. When the bus is rear-ended, the car lurches forward and you and your head also move forward. Without headrest your body tends to leave your head behind. Hence a neck injury.

48. In terms of Newton’s first law, how does a car headrest help to guard against whiplash?

49.The law of inertia applies in both cases. When the bus slows, you tend to keep moving at the previous speed and lurch forward. When the bus picks up speed, you tend to keep moving at the previous (lower) speed and you lurch backward.

49. Why do you seem to lurch forward in a bus that suddenly slows? Why do you seem to lurch backward when the bus picks up speed? What law applies here?

50.The maximum resultant occurs when the forces are parallel in the same direction—32 N. The minimum occurs when they oppose each other—8 N.

50. Consider a pair of forces, one having a magnitude of 20 N and the other 12 N. What is the strongest possible net force for these two forces? What is the weakest possible net force?

51. The vector sum of the forces equals zero. That means the net force must be zero.

51. When an object is in mechanical equilibrium, what can be correctly stated about all the forces that act on it? Must the net force necessarily be zero?

52.Vector quantities are force and acceleration. Age and temperature are scalars.

52. Which of the following are scalar quantities, which are vector quantities, and which are neither?

a) force

b) age

c) acceleration

d) temperature

53.You can correctly say the vectors are equal in magnitude and opposite in direction.

53. What can you correctly say about a pair of vectors that add together to equal zero?

54.A hammock stretched tightly has more tension in the supporting ropes than one that sags. The tightly stretched ropes are more likely to break.

54. Which is more likely to break: a hammock stretched tightly between a pair of trees or one that sags more when you sit on it?

55.The tension will be greater for a small sag. That’s because large vectors in each side of the rope supporting the bird are needed for a resultant that is equal and opposite to the bird’s weight.

55. A heavy bird sits on a clothesline. Will the tension in the clothesline be greater if the line sags a lot or if it sags a little?

56. By the parallelogram rule, the tension is less than 50 N.

56. The rope supports a lantern that weighs 50 N. Is the tension in the rope less than, equal to, or greater than 50 N? Use the parallelogram rule to defend your answer.

57. The upward force is the tension in the vine. The downward force is that due to gravity. Both are equal when the monkey hangs in equilibrium.

57. A monkey hangs stationary at the end of a vertical vine. What two forces act on the monkey? Which, if either, is greater?

58.By the parallelogram rule, the tension is greater than 50 N.

58. The rope of ex. 56 is repositioned as shown and still supports 50 N lantern. Is the tension in the rope less than, equal to, or greater than 50 N? Use the parallelogram rule to defend your answer.

59.No. If only a single nonzero force acts on an object, its motion will change and it will not be in mechanical equilibrium. There would have to be other forces to result in a zero net force for equilibrium.

59. Can an object be in mechanical equilibrium when only a single nonzero force acts on it? Explain.

60.At the top of its path (and everywhere else along its path) the force of gravity acts to change the ball’s motion. Even though it momentarily stops at the top, the net force on the ball is not zero and it therefore is not in equilibrium.

60. When a ball is tossed straight up, it momentarily comes to a stop at the top of its path. Is it in equilibrium during this brief moment? Why or why not.

61.Yes. If the puck moves in a straight line with unchanging speed, the forces of friction are negligible. Then the net force is practically zero, and the puck can be considered to be in dynamic equilibrium.

61. A hockey puck slides across the ice at a constant speed. Is it in equilibrium? Why/Why not.

62.You can say that no net force acts on your friend at rest, but there may be any number of forces that act—that produce a zero net force. When the net force is zero, your friend is in static equilibrium.

62. Your friend sits at rest on a chair. Can you say that no force acts on her? Or is it correct to say that no net force acts on her? Defend your answer.

63. The scale will read half her weight. In this way, the net force (upward pull of left rope + upward pull of right rope – weight) = 0.

63. Nellie hangs at rest from the ends of the rope. How does the reading on the scale compare with her weight?

64.In the left figure, Harry is supported by two strands of rope that share his weight (like the little girl in the previous exercise). So each strand supports only 250 N, below the breaking point. Total force up supplied by ropes equals weight acting downward, giving a net force of zero and no acceleration. In the right figure, Harry is now supported by one strand, which for Harry’s well-being requires that the tension be 500 N. Since this is above the breaking point of the rope, it breaks. The net force on Harry is then only his weight, giving him a downward acceleration of g. The sudden return to zero velocity changes his vacation plans.

64. Harry weighs 500 N and he hangs from a rope doubled that has a breaking point of 300 N. Why doesn’t the rope break when he is supported as shown on left? He hangs from the same rope but does not double it. What happened?

65.The upper limit he can lift is a load equal to his weight. Beyond that he leaves the ground!

65. For the pulley system, what is the upper limit of weight the strong man can lift?

66.800 N; The pulley simply changes the direction of the applied force.

66. If the strong man exerts downward force of 800 N on the rope, how much upward force is exerted on the block?

67. The force that prevents downward acceleration is the support (normal) force—the table pushing up on the book.

67. A force of gravity pulls downward on a book on a table. What force prevents the book from accelerating downward?

68.Two significant forces act on the book: the force due to gravity and the support force (normal force) of the table.

68. How many significant forces act on a book at rest on a table? Identify the forces.

69.If the upward force were the only force acting, the book indeed would rise. But another force, that due to gravity, results in the net force being zero.

69. Place a heavy book on a table and the table pushes up on the book. Why doesn’t this upward push cause the book to rise from the table?

70.When standing on a floor, the floor pushes upward against your feet with a force equal to that of gravity, your weight. This upward force (normal force) and your weight are oppositely directed, and since they both act on the same body, you, they cancel to produce a net force on you of zero—hence, you are not accelerated.

70. As you stand on a floor, does the floor exert an upward force against your feet? How much force doesn’t it exert? Why aren’t you moved upward by this force?

71.Only when you are in equilibrium will the support force on you correctly show your weight. Then it is equal to the force of gravity on you.

71. Suppose that you jounce up and down while weighing yourself. Which varies: the upward support force or the force of gravity on you? Why is your weight reading best shown when you stand still?

72.Without water, the support force is W. With water, the support force is W + w.

72. An empty jug of weight W rests on a table. What is the support force exerted on the jug by the table? What is the support force when water of weight w is poured into the jug?

73.The friction on the crate has to be 200 N, opposite to your 200-N pull.

73. If you pull horizontally on a crate with a force of 200 N, it slides across the floor in dynamic equilibrium. How much friction is acting on the crate?

74.The friction force is 600 N for constant speed. Only then will

∑ƒ = 0.

∑ƒ = 0.

74. In order to slide a heavy cabinet across the floor at constant speed, you exert a horizontal force of 600 N. Is the force of friction between the cabinet and the floor greater than, less than, or equal to 600 N? Defend your answer.

75.The support force on the crate decreases as the load against the floor decreases. When the crate is entirely lifted from the floor, the support force by the floor is zero. The support force on the workmen’s feet correspondingly increases as the load transfers from the floor to them. When the crate is off the floor and at rest, its weight is transferred to the men, whose normal force is then increased.

75. Consider a crate at rest. As a pair of workmen begin lifting it, does the support force on the crate provided by the floor increase, decrease, or remain unchanged? What happens to the support force on the workmen’s feet?

76. The net force on the rope is zero. The force exerted by the rope on each person is 300 N (in opposite directions).

76. Two people each pull with a force of 300 N on a rope. What is the net force on the rope? How much force is exerted on each person by the rope?

77.Two forces must be equal and opposite so that the net force = 0. Then the parachutist is in dynamical equilibrium.

77. Two forces act on a parachutist falling in air: the force of gravity and air resistance. If the fall is steady, with no gain or loss of speed, then the parachutist is in dynamic equilibrium. How do the magnitudes of gravitational force and air resistance compare?

78.We aren’t swept off because we are traveling just as fast as the Earth, just as in a fast-moving vehicle you move along with the vehicle. Also, there is no atmosphere through which the Earth moves, which would do more than blow our hats off!

78. A child learns that earth is traveling faster than 100,00 kilometers per hour around the sun and in a frightened tone, asks why we aren’t swept off. What is your explanation.

79. Your friend should learn that inertia is not some kind of force that keeps things like the Earth moving, but is the name given to the property of things to keep on doing what they are doing in the absence of a force. So your friend should say that nothing is necessary to keep the Earth moving. Interestingly, the Sun keeps it from following the straight-line path it would take if no forces acted, but it doesn’t keep it moving. Nothing does. That’s the concept of inertia.

79. What keeps earth moving around the sun?

80.You should disagree with your friend. In the absence of external forces, a body at rest tends to remain at rest; if moving, it tends to remain moving. Inertia is a property of matter to behave this way, not some kind of force.

80. Your friend says that inertia is a force that keeps things in their place, either at rest or in motion. Do you and your discussion partners agree? Why/Why not?

81.The tendency of the ball is to remain at rest. From a point of view outside the wagon, the ball stays in place as the back of the wagon moves toward it. (Because of friction, the ball may roll along the cart surface—without friction the surface would slide beneath the ball.)

81. Consider a ball at rest in the middle of a toy wagon. When the wagon is pulled forward, the ball rolls against the back of the wagon. Discuss and interpret this observation in terms of Newton’s 1st law.

82.The car has no tendency to resume to its original twice-as-fast speed. Instead, in accord with Newton’s first law, it tends to continue at half speed, decreasing in speed over time due to air resistance and road friction.

82. Suppose you are in a moving car and the motor stops. You step on the brakes and slow the car to half speed. If you release your foot from the brakes, will the car speed up a bit, or will it continue at half speed and slow due to friction? Defend

83.No. If there were no friction acting on the cart, it would continue in motion when you stop pushing. But friction does act, and the cart slows. This doesn’t violate the law of inertia because an external force indeed acts.

83. When you push a cart it moves. When you stop pushing it, it comes to rest. Does this violate Newton’s law of inertia? Discuss.

84.An object in motion tends to stay in motion, hence the discs tend to compress upon each other just as the hammer head is compressed onto the handle in Figure 2.5. This compression results in people being slightly shorter at the end of the day than in the morning. The discs tend to separate while sleeping in a prone position, so you regain your full height by morning. This is easily noticed if you find a point you can almost reach up to in the evening, and then find it is easily reached in the morning. Try it and see!

84. Each bone in the skeletal chain forming your spine is separated by disk of elastic tissue. What happens when you jump heavily onto your feet from an elevated position? Are you a little taller in the morning than at night?

85.No. If there were no force acting on the ball, it would continue in motion without slowing. But air drag does act, along with slight friction with the lane, and the ball slows. This doesn’t violate the law of inertia because external forces indeed act.

85. Start a ball rolling down a bowling alley and you’ll find that it moves slightly slower with time. Does this violate Newton’s law of inertia? Discuss.

86.Normal force is greatest when the table surface is horizontal, and progressively decreases as the angle of tilt increases. As the angle of tilt approaches 90°, the normal force approaches zero. When the table surface is vertical, it no longer presses on the book, then freely falls.

86. Consider the normal force on a book at rest on a tabletop. If the table is tilted so that the surface forms an inclined plane, will the magnitude of the normal force change? If so, how.

87.No. The normal force would be the same whether the book was on slippery ice or sandpaper. Friction plays no role unless the book slides or tends to slide along the table surface.

87. When you push downward on a book at rest on a table, you feel an upward force. Does this force depend on friction? Discuss/Defend.

88.A stone will fall vertically if released from rest. If the stone is dropped from the top of the mast of a moving ship, the horizontal motion is not changed when the stone is dropped—providing air resistance on the stone is negligible and the ship’s motion is steady and straight. From the frame of reference of the moving ship, the stone falls in a vertical straight-line path, landing at the base of the mast.

88. Before the time of Galileo and Newton, some learned scholars thought that a stone dropped from the top of a tall mast of a moving ship would fall vertically and hit the deck behind the mast by a distance equal to how far the ship had moved forward while the stone was falling. In light of your understanding of Newton’s first law, what do you think about this?

89.A body in motion tends to remain in motion, so you move with the moving Earth whether or not your feet are in contact with it. When you jump, your horizontal motion matches that of the Earth and you travel with it. Hence the wall does not slam into you.

89. Because earth rotates once every 24 hours, the west wall in your room moves in a direction toward you at a linear speed that is probably more than 1000 kilometers per hour. When you stand facing the wall, you are carried along at the same speed, so you don’t notice it. But when you jump upward, with your feet no longer in contact with the floor, why doesn’t the high speed wall slam into you?

90.The coin is moving along with you when you toss it. While in the air it maintains this forward motion, so the coin lands in your hand. If the train slows while the coin is in the air, it will land in front of you.

90. If you toss a coin straight upward while riding in a train, where does the coin land when the motion of the train is uniform along a straight line track. When the train slows while the coin is in the air?

92.This is similar to Question 88. If the ball is shot while the train is moving at constant velocity (constant speed in a straight line), its horizontal motion before, during, and after being fired is the same as that of the train; so the ball falls back into the smokestack as it would have if the train were at rest. If the train increases its speed, the ball will hit the train behind the smokestack because the ball’s horizontal speed continues unchanged after it is fired, but the speeding-up train pulls ahead of the ball. Similarly, on a circular track the ball will also miss the smokestack because the ball will move along a tangent to the track while the train turns away from this tangent. So the ball returns to the smokestack in the first case, and misses in the second and third cases because of the change in motion.

92. The smokestack of a stationary train consist of a vertical spring gun that shoots a steel ball a meter or so straight into the air, so straight that the ball always falls back into the smokestack. Suppose the train moves at constant speed along the straight track. Do you think the ball will still return to the smokestack if shot from the moving train? What if the train gains speed along the straight track? What if it moves at a constant speed on a circular track?