1. Forces cause changes in motion.

2. A ball at rest in the middle of a flat field is in equilibrium
A ball at rest in the middle of a flat field is in equilibrium. No net force acts on it.
If you saw it begin to move across the ground, you’d look for forces that don’t balance to zero.
We don’t believe that changes in motion occur without cause.

3. 3.1 Aristotle on Motion
Aristotle, the foremost Greek scientist, studied motion and divided it into two types: natural motion and violent motion.

4. 3.2 Copernicus and the Moving Earth
Copernicus reasoned that the simplest way to interpret astronomical observations was to assume that Earth and the other planets move around the sun.

5. 3.3 Galileo on Motion
Galileo argued that only when friction is present—as it usually is—is a force needed to keep an object moving.

6. 3.3 Galileo on Motion
Friction is the name given to the force that acts between materials that touch as they move past each other.
Friction is caused by the irregularities in the surfaces of objects that are touching.
Even very smooth surfaces have microscopic irregularities that obstruct motion.
If friction were absent, a moving object would need no force to remain in motion.

7. 3.3 Galileo on Motion
Galileo stated that this tendency of a moving body to keep moving is natural and that every material object resists changes to its state of motion.
The property of a body to resist changes to its state of motion is called inertia.

8. 3.3 Galileo on Motion think!
A ball is rolled across a counter top and rolls slowly to a stop. How would Aristotle interpret this behavior? How would Galileo interpret it? How would you interpret it?
Answer: Aristotle would probably say that the ball stops because it seeks its natural state of rest. Galileo would probably say that the friction between the ball and the table overcomes the ball’s natural tendency to continue rolling—overcomes the ball’s inertia—and brings it to a stop. Only you can answer the last question!

9. 3.3 Galileo on Motion
According to Galileo, when is a force needed to keep an object moving?

10. 3.4 Newton’s Law of Inertia
Newton’s first law states that every object continues in a state of rest, or of uniform speed in a straight line, unless acted on by an unbalanced force.

11. 3.4 Newton’s Law of Inertia
Newton’s first law, usually called the law of inertia, is a restatement of Galileo’s idea that a force is not needed to keep an object moving.

12. 3.4 Newton’s Law of Inertia
Objects at rest tend to remain at rest.

13. 3.4 Newton’s Law of Inertia
The law of inertia provides a completely different way of viewing motion from the ancients.
Objects continue to move by themselves.
Forces are needed to overcome any friction that may be present and to set objects in motion initially.
Once the object is moving in a force-free environment, it will move in a straight line indefinitely.

14. 3.4 Newton’s Law of Inertia

15. 3.4 Newton’s Law of Inertia

16. 3.4 Newton’s Law of Inertia
think!
A force of gravity between the sun and its planets holds the planets in orbit around the sun. If that force of gravity suddenly disappeared, in what kind of path would the planets move?
Answer: Each planet would move in a straight line at constant speed.

17. 3.4 Newton’s Law of Inertia
What is Newton’s first law of motion?

18. 3.5 Mass—A Measure of Inertia
The more mass an object has, the greater its inertia and the more force it takes to change its state of motion.

19. 3.5 Mass—A Measure of Inertia
The amount of inertia an object has depends on its mass—which is roughly the amount of material present in the object.
Mass is a measure of the inertia of an object.

20. 3.5 Mass—A Measure of Inertia
You can tell how much matter is in a can when you kick it. Kick an empty can and it moves. Kick a can filled with sand and it doesn’t move as much.

21. 3.5 Mass—A Measure of Inertia
Which has more mass, a feather pillow or a common automobile battery?
Clearly an automobile battery is more difficult to set into motion. This is evidence of the battery’s greater inertia and hence its greater mass.

22. 3.5 Mass—A Measure of Inertia
Mass Is Not Weight
Mass is often confused with weight.
We often determine the amount of matter in an object by measuring its gravitational attraction to Earth. However, mass is more fundamental than weight.
Mass is a measure of the amount of material in an object.

23. 3.5 Mass—A Measure of Inertia
We can define mass and weight as follows:
Mass is the quantity of matter in an object. More specifically, mass is a measure of the inertia, or “laziness,” that an object exhibits in response to any effort made to start it, stop it, or otherwise change its state of motion.
Weight is the force of gravity on an object.

24. 3.5 Mass—A Measure of Inertia
Mass Is Inertia
The amount of material in a particular stone is the same whether the stone is located on Earth, on the moon, or in outer space.
The mass of the stone is the same in all of these locations.
The weight of the stone would be very different.

25. 3.5 Mass—A Measure of Inertia
It’s just as difficult to shake a stone in its weightless state in space as it is in its weighted state on Earth.

26. 3.5 Mass—A Measure of Inertia
One Kilogram Weighs 10 Newtons
In the United States, the traditional unit of weight is the pound.
In most parts of the world, however, the measure of matter is commonly expressed in units of mass, the kilogram (kg).
At Earth’s surface, 1 kilogram has a weight of 2.2 pounds.

27. 3.5 Mass—A Measure of Inertia
One kilogram of nails weighs 10 newtons, which is equal to 2.2 pounds. Away from Earth’s surface, where the force of gravity is less, the bag of nails weighs less.

28. 3.5 Mass—A Measure of Inertia
think!
Does a 2-kilogram bunch of bananas have twice as much inertia as a 1-kilogram loaf of bread? Twice as much mass? Twice as much volume? Twice as much weight, when weighed in the same location?
Answer: Except for volume, the answer to all the questions is yes. Bananas are much more dense than bread, so two kilograms of bananas must occupy less volume than one kilogram of bread.

29. 3.5 Mass—A Measure of Inertia
What is the relationship between mass and inertia?

30. 3.6 The Moving Earth Again
Flip a coin in an airplane, and it behaves as if the plane were at rest. The coin keeps up with you—inertia in action!

31. 3.6 The Moving Earth Again

32. 3.6 The Moving Earth Again
How does the law of inertia apply to objects in motion?

33. An object accelerates when a net force acts on it.

34. Recall the definition of acceleration:
The cause of acceleration is force.

35. 6.1 Force Causes Acceleration
Unbalanced forces acting on an object cause the object to accelerate.

36. 6.1 Force Causes Acceleration
When a hockey puck is at rest, the net force on it (gravity and the support force) is balanced, so the puck is in equilibrium.
Hit the puck (that is, apply an unbalanced force to it) and the puck experiences a change in motion—it accelerates.
Apply another force by striking the puck again, and the puck’s motion changes again.

37. 6.1 Force Causes Acceleration
What causes an object to accelerate?

38. 6.2 Mass Resists Acceleration
For a constant force, an increase in the mass will result in a decrease in the acceleration.

39. 6.2 Mass Resists Acceleration
The acceleration produced depends on the mass that is pushed.

40. 6.2 Mass Resists Acceleration
How does an increase in mass affect acceleration?

41. 6.3 Newton’s Second Law
Newton’s second law states that the acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.

42. 6.3 Newton’s Second Law
Newton’s second law describes the relationship among an object's mass, an object's acceleration, and the net force on an object.

43. 6.3 Newton’s Second Law
By using consistent units, such as newtons (N) for force, kilograms (kg) for mass, and meters per second squared (m/s2) for acceleration, we get the exact equation: or

44. 6.3 Newton’s Second Law
The acceleration is equal to the net force divided by the mass.
If the net force acting on an object doubles, its acceleration is doubled.
If the mass is doubled, then acceleration will be halved.
If both the net force and the mass are doubled, the acceleration will be unchanged.

45. 6.3 Newton’s Second Law think!
If a car can accelerate at 2 m/s2, what acceleration can it attain if it is towing another car of equal mass?
Answer: The same force on twice the mass produces half the acceleration, or 1 m/s2.

46. 6.3 Newton’s Second Law do the math!
A car has a mass of 1000 kg. What is the acceleration produced by a force of 2000 N?

47. 6.3 Newton’s Second Law do the math!
If the force is 4000 N, what is the acceleration?
Doubling the force on the same mass simply doubles the acceleration.

48. 6.3 Newton’s Second Law do the math!
How much force, or thrust, must a 30,000-kg jet plane develop to achieve an acceleration of 1.5 m/s2?
Arrange Newton’s second law to read:
force = mass × acceleration
F = ma
= (30,000 kg)(1.5 m/s2)
= 45,000 kg•m/s2
= 45,000 N

49. 6.4 Friction
The force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together.

50. 6.4 Friction
Rubber against concrete produces more friction than steel against steel, so concrete road dividers have replaced steel rails.
The friction produced by a tire rubbing against the concrete is more effective in slowing the car than the friction produced by a steel car body sliding against a steel rail.

51. 6.4 Friction
The direction of the force of friction always opposes the direction of motion.
a. Push the crate to the right and friction acts toward the left.
b. The sack falls downward and air friction acts upward.

52. 6.4 Friction
think!
Two forces act on a book resting on a table: its weight and the support force from the table. Does a force of friction act as well?
Answer: No, not unless the book tends to slide or does slide across the table. Friction forces occur only when an object tends to slide or is sliding.

53. 6.4 Friction
What factors affect the force of friction between surfaces?

54. 6.6 Free Fall Explained
F stands for the force (weight) acting on the cannonball, and m stands for the correspondingly large mass of the cannonball. The small F and m stand for the weight and mass of the stone.
The ratio of weight to mass is the same for these or any objects.
All freely falling objects undergo the same acceleration at the same place on Earth.

55. 6.6 Free Fall Explained
The ratio of weight (F) to mass (m) is the same for the 10-kg cannonball and the 1-kg stone.

56. 6.6 Free Fall Explained
Why do all freely falling objects fall with the same acceleration?

57. For every force, there is an equal and opposite force.

58. 7.1 Forces and Interactions
A force is always part of a mutual action that involves another force.

59. 7.1 Forces and Interactions
In the simplest sense, a force is a push or a pull.
A mutual action is an interaction between one thing and another.

60. 7.1 Forces and Interactions
When you push on the wall, the wall pushes on you.

61. 7.1 Forces and Interactions
The interaction that drives the nail is the same as the one that halts the hammer.

62. 7.1 Forces and Interactions
think!
Does a stick of dynamite contain force? Explain.
Answer: No. Force is not something an object has, like mass. Force is an interaction between one object and another. An object may possess the capability of exerting a force on another object, but it cannot possess force as a thing in itself. Later we will see that something like a stick of dynamite possesses energy.

63. 7.1 Forces and Interactions
Why do forces always occur in pairs?

64. 7.2 Newton’s Third Law
Newton’s third law states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

65. 7.2 Newton’s Third Law
Newton’s third law describes the relationship between two forces in an interaction.
One force is called the action force.
The other force is called the reaction force.
Neither force exists without the other.
They are equal in strength and opposite in direction.
They occur at the same time (simultaneously).
Newton’s third law is often stated: “To every action there is always an equal opposing reaction.”

66. 7.2 Newton’s Third Law The interactions depend on friction.
A person trying to walk on ice, where friction is minimal, may not be able to exert an action force against the ice.
Without the action force there cannot be a reaction force, and thus there is no resulting forward motion.

67. 7.2 Newton’s Third Law
When the girl jumps to shore, the boat moves backward.

68. 7.2 Newton’s Third Law
The dog wags the tail and the tail wags the dog.

69. 7.3 Identifying Action and Reaction
Sometimes the identity of the pair of action and reaction forces in an interaction is not immediately obvious.
For example, what are the action and reaction forces in the case of a falling boulder?
If we call the action Earth exerting a force on the boulder, then the reaction is the boulder simultaneously exerting a force on Earth.

70. 7.3 Identifying Action and Reaction
When action is A exerts force on B, the reaction is simply B exerts force on A.

71. 7.3 Identifying Action and Reaction
When action is A exerts force on B, the reaction is simply B exerts force on A.

72. 7.3 Identifying Action and Reaction
think!
We know that Earth pulls on the moon. Does the moon also pull on Earth? If so, which pull is stronger?
Answer: Asking which pull is stronger is like asking which distance is greater—between New York and San Francisco, or between San Francisco and New York. The distances either way are the same. It is the same with force pairs. Both Earth and moon pull on each other with equal and opposite forces.

73. 7.4 Action and Reaction on Different Masses
A given force exerted on a small mass produces a greater acceleration than the same force exerted on a large mass.

74. 7.4 Action and Reaction on Different Masses
The cannonball undergoes more acceleration than the cannon because its mass is much smaller.

75. 7.4 Action and Reaction on Different Masses
F represents both the action and reaction forces; m (large), the mass of the cannon; and m (small), the mass of the cannonball.
Do you see why the change in the velocity of the cannonball is greater compared with the change in velocity of the cannon?

76. 7.4 Action and Reaction on Different Masses
The balloon recoils from the escaping air and climbs upward.

77. 7.4 Action and Reaction on Different Masses
The rocket recoils from the “molecular cannonballs” it fires and climbs upward.

78. 7.4 Action and Reaction on Different Masses
Why do objects that experience the same amount of force accelerate at different rates?

79. 7.7 Action Equals Reaction
For every interaction between things, there is always a pair of oppositely directed forces that are equal in strength.

80. 7.7 Action Equals Reaction
If you hit the wall, it will hit you equally hard.

81. 7.7 Action Equals Reaction
If a sheet of paper is held in midair, the heavyweight champion of the world could not strike the paper with a force of 200 N (45 pounds).
The paper is not capable of exerting a reaction force of 200 N, and you cannot have an action force without a reaction force.
If the paper is against the wall, then the wall will easily assist the paper in providing 200 N of reaction force, and more if needed!

82. 7.7 Action Equals Reaction
What must occur in every interaction between things?

83. Assessment Questions
Two thousand years ago, people thought that Earth did not move. One major reason for thinking this was that
no force was large enough to move the Earth.
Earth’s motion would be unnatural.
Earth was near the center of the universe.
Earth moved in a perfect circle.
Answer: A

84. Assessment Questions
According to Aristotle and his followers over centuries, Earth was at the center of the universe. The first European to effectively challenge that notion was
Copernicus.
Galileo.
Newton.
Einstein.
Answer: A

85. Assessment Questions
Galileo’s conclusions about motion helped advance science because they were based on
experiments rather than philosophical discussions.
philosophical discussions rather than experiments.
nonmathematical thinking.
Aristotle’s theories of motion.
Answer: A

86. Assessment Questions
If gravity between the sun and Earth suddenly vanished, Earth would continue moving in a(n)
curved path.
straight-line path.
outward spiral path.
inward spiral path.
Answer: B

87. Assessment Questions
To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter
will weigh 10 N everywhere.
has ten times less volume than 10 kg of matter.
has ten times more inertia than 10 kg of matter.
is attracted to Earth with 10 N of force.
Answer: D

88. Assessment Questions
The Earth moves about 30 km/s relative to the sun. But when you jump upward in front of a wall, the wall doesn’t slam into you at 30 km/s. A good explanation for why it doesn’t is that
the sun’s influence on you is negligible.
the air in the room is also moving.
both you and the wall are moving at the same speed, before, during, and after your jump.
the inertia of you and the wall is negligible compared with that of the sun.
Answer: C

89. Assessment Questions An object will accelerate when SF = 0.
it is unbalanced.
it is pushed or pulled with a net force.
its mass increases.
Answer: C

90. Assessment Questions
When a net force acts on an object, its acceleration depends on the object’s
initial speed.
mass.
volume.
weight.
Answer: B

91. Assessment Questions
A cart is pushed and undergoes a certain acceleration. Consider how the acceleration would compare if it were pushed with twice the net force while its mass increased by four. Then its acceleration would be
one quarter.
half.
twice.
the same.
Answer: B

92. Assessment Questions
Friction is a force like any other force and affects motion. Friction occurs in
solids sliding over one another.
fluids.
air.
all of these
Answer: D

93. Assessment Questions
The reason a 20-kg rock falls no faster than a 10-kg rock in free fall is that
air resistance is negligible.
the force of gravity on both is the same.
their speeds are the same.
the force/mass ratio is the same.
Answer: D

94. Assessment Questions A force interaction requires at least a(n)
single force.
pair of forces.
action force.
reaction force.
Answer: B

95. Assessment Questions
Whenever one object exerts a force on a second object, the second object exerts a force on the first that is
opposite in direction and equal in magnitude at the same time.
in the same direction and equal in magnitude a moment later.
opposite in direction and greater in magnitude at the same time.
in the same direction and weaker in magnitude a moment later.
Answer: A

96. Assessment Questions
The force that directly propels a motor scooter along a highway is that provided by the
engine.
fuel.
tires.
road.
Answer: D

97. Assessment Questions
When you jump vertically upward, strictly speaking, you cause Earth to
move downward.
also move upward with you.
remain stationary.
move sideways a bit.
Answer: A

98. Assessment Questions
A system undergoes acceleration only when acted on by a(n)
net force.
pair of forces.
action and reaction forces.
internal interactions.
Answer: A

99. Assessment Questions
If a net force acts on a horse while it is pulling a wagon, the horse
accelerates.
is restrained.
is pulled backward by an equal and opposite net force.
cannot move.
Answer: A

100. Assessment Questions
At a pizza shop, the cook throws the pizza dough in the air. The amount of force the cook exerts on the dough depends on the
mass of the dough.
strength of the cook.
weight of the dough.
height of the cook.
Answer: A