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. 4.1 Aristotle on Motion
Natural motion on Earth was thought to be either straight up or straight down.
Objects seek their natural resting places: boulders on the ground and smoke high in the air like the clouds.
Heavy things fall and very light things rise.
Circular motion was natural for the heavens.
These motions were considered natural–not caused by forces.

4. 4.1 Aristotle on Motion
Violent motion, on the other hand, was imposed motion.
It was the result of forces that pushed or pulled.
The important thing about defining violent motion was that it had an external cause.
Violent motion was imparted to objects.
Objects in their natural resting places could not move by themselves.

5. 4.1 Aristotle on Motion
Boulders do not move without cause.

6. 4.1 Aristotle on Motion
It was commonly thought for nearly 2000 years that a force was responsible for an object moving “against its nature.”
The state of objects was one of rest unless they were being pushed or pulled or moving toward their natural resting place.
Most thinkers before the 1500s considered it obvious that Earth must be in its natural resting place.
A force large enough to move it was unthinkable.
Earth did not move.

7. 4.1 Aristotle on Motion
According to Aristotle, what were the two types of motion?

8. 4.1 Aristotle on Motion
Aristotle, the foremost Greek scientist, studied motion and divided it into two types: natural motion and violent motion.

9. 4.2 Copernicus and the Moving Earth
The astronomer Nicolaus Copernicus (1473–1543) formulated a theory of the moving Earth.
This idea was extremely controversial at the time. People preferred to believe that Earth was at the center of the universe.
Copernicus worked on his ideas in secret. The first copy of his work, De Revolutionibus, reached him on the day of his death, May 24, 1543.

10. 4.2 Copernicus and the Moving Earth
Nicolaus Copernicus proposed that Earth moved around the sun.

11. 4.2 Copernicus and the Moving Earth
What did Copernicus state about Earth’s motion?

12. 4.2 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.

13. 4.3 Galileo on Motion
Galileo, the foremost scientist of late-Renaissance Italy, was outspoken in his support of Copernicus.
One of Galileo’s great contributions to physics was demolishing the notion that a force is necessary to keep an object moving.

14. 4.3 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 whatever to remain in motion.

15. 4.3 Galileo on Motion
Galileo tested his idea by rolling balls along plane surfaces tilted at different angles.
A ball rolling down an inclined plane speeds up.
A ball rolling up an inclined plane—in a direction opposed by gravity—slows down.
A ball rolling on a smooth horizontal plane has almost constant velocity.

16. 4.3 Galileo on Motion
Downward, the ball moves with Earth’s gravity.

17. 4.3 Galileo on Motion Downward, the ball moves with Earth’s gravity.
Upward, the ball moves against gravity.

18. 4.3 Galileo on Motion Downward, the ball moves with Earth’s gravity.
Upward, the ball moves against gravity.
On a level plane, it does not move with or against gravity.

19. 4.3 Galileo on Motion
Galileo stated that if friction were entirely absent, a ball moving horizontally would move forever.
No push or pull would be required to keep it moving once it is set in motion.

20. 4.3 Galileo on Motion
Galileo’s conclusion was supported by another line of reasoning.
He described two inclined planes facing each other.
A ball released to roll down one plane would roll up the other to reach nearly the same height.
The ball tended to attain the same height, even when the second plane was longer and inclined at a smaller angle than the first plane.

21. 4.3 Galileo on Motion
The ball rolling down the incline rolls up the opposite incline and reaches its initial height.

22. 4.3 Galileo on Motion
The ball rolling down the incline rolls up the opposite incline and reaches its initial height.
The ball rolls a greater distance to reach its initial height.

23. 4.3 Galileo on Motion
The ball rolling down the incline rolls up the opposite incline and reaches its initial height.
The ball rolls a greater distance to reach its initial height.
If there is no friction, the ball will never stop.

24. 4.3 Galileo on Motion
If the angle of incline of the second plane were reduced to zero so that the plane was perfectly horizontal, only friction would keep it from rolling forever.
It was not the nature of the ball to come to rest as Aristotle had claimed.

25. 4.3 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.

26. 4.3 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?

27. 4.3 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!

28. 4.3 Galileo on Motion
According to Galileo, when is a force needed to keep an object moving?

29. 4.3 Galileo on Motion
Galileo argued that only when friction is present—as it usually is—is a force needed to keep an object moving.

30. 4.4 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.

31. 4.4 Newton’s Law of Inertia
Objects at Rest
Simply put, things tend to keep on doing what they’re already doing.
Objects in a state of rest tend to remain at rest.
Only a force will change that state.

32. 4.4 Newton’s Law of Inertia
Objects at rest tend to remain at rest.

33. 4.4 Newton’s Law of Inertia
Objects in Motion
Now consider an object in motion.
In the absence of forces, a moving object tends to move in a straight line indefinitely.
Toss an object from a space station located in the vacuum of outer space, and the object will move forever due to inertia.

34. 4.4 Newton’s Law of Inertia
Blasts of air from many tiny holes provide a nearly friction-free surface on the air table. If you slide a hockey puck along the surface of a city street, the puck soon comes to rest. If you slide it along an air table where friction is practically absent, it slides with no apparent loss in speed.

35. 4.4 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.

36. 4.4 Newton’s Law of Inertia

37. 4.4 Newton’s Law of Inertia

38. 4.4 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?

39. 4.4 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.

40. 4.4 Newton’s Law of Inertia
think!
Is it correct to say that the reason an object resists change and persists in its state of motion is that it has inertia?

41. 4.4 Newton’s Law of Inertia
think!
Is it correct to say that the reason an object resists change and persists in its state of motion is that it has inertia?
Answer: We don’t know the reason why objects persist in their motion when nothing acts on them, but we know that they do, and we call this property inertia.

42. 4.4 Newton’s Law of Inertia
What is Newton’s first law of motion?

43. 4.4 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 a nonzero net force.

44. 4.5 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.

45. 4.5 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.

46. 4.5 Mass—A Measure of Inertia
Mass Is Not Volume
Do not confuse mass and volume.
Volume is a measure of space and is measured in units such as cubic centimeters, cubic meters, and liters.
Mass is measured in the fundamental unit of kilograms.

47. 4.5 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.

48. 4.5 Mass—A Measure of Inertia
The pillow has a larger size (volume) but a smaller mass than the battery.

49. 4.5 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. Weight, on the other hand, is a measure of the gravitational force acting on the object.

50. 4.5 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 on Earth and on the moon, and still different in outer space.

51. 4.5 Mass—A Measure of Inertia
The stone’s inertia, or mass, is a property of the stone and not its location.
The same force would be required to shake the stone with the same rhythm whether the stone was on Earth, on the moon, or in a force-free region of outer space.

52. 4.5 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.

53. 4.5 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.

54. 4.5 Mass—A Measure of Inertia
Mass and weight are proportional to each other in a given place:
In the same location, twice the mass weighs twice as much.
Mass and weight are proportional to each other, but they are not equal to each other.

55. 4.5 Mass—A Measure of Inertia
One Kilogram Weighs 10 Newtons
It is common to describe the amount of matter in an object by its gravitational pull to Earth, that is, by its weight.
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.

56. 4.5 Mass—A Measure of Inertia
The SI unit of force is the newton. The SI symbol for the newton is N.
One newton is equal to slightly less than a quarter pound.
If you know the mass of something in kilograms and want its weight in newtons at Earth’s surface, multiply the number of kilograms by 10.

57. 4.5 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.

58. 4.5 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?

59. 4.5 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: Two kilograms of anything has twice the inertia and twice the mass of one kilogram of anything else. In the same location, where mass and weight are proportional, two kilograms of anything will weigh twice as much as one kilogram of anything. 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.

60. 4.5 Mass—A Measure of Inertia
What is the relationship between mass and inertia?

61. 4.5 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.

62. An object in mechanical equilibrium is stable, without changes in motion.

63. Things that are in balance with one another illustrate equilibrium.
Things in mechanical equilibrium are stable, without changes of motion.
The rocks are in mechanical equilibrium.
An unbalanced external force would be needed to change their resting state.

64. 4.6 Net Force Net Force A force is a push or a pull.
A force of some kind is always required to change the state of motion of an object.
The combination of all forces acting on an object is called the net force. The net force on an object changes its motion.
The scientific unit of force is the newton, abbreviated N.

65. 4.6 Net Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

66. 4.6 Net Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

67. 4.6 Net Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

68. 4.6 Net Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

69. 4.6 Net Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

70. 4.6 Net Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

71. 4.6 Net Force
Net Force
When the girl holds the rock with as much force upward as gravity pulls downward, the net force on the rock is zero.

72. 4.6 Net Force Tension and Weight
A stretched spring is under a “stretching force” called tension.
Pounds and newtons are units of weight, which are units of force.

73. 4.6 Net Force Tension and Weight
The upward tension in the string has the same magnitude as the weight of the bag, so the net force on the bag is zero.
The bag of sugar is attracted to Earth with a gravitational force of 2 pounds or 9 newtons.

74. 4.6 Net Force Tension and Weight
The upward tension in the string has the same magnitude as the weight of the bag, so the net force on the bag is zero.
The bag of sugar is attracted to Earth with a gravitational force of 2 pounds or 9 newtons.

75. 4.6 Net Force Tension and Weight
There are two forces acting on the bag of sugar:
tension force acting upward
weight acting downward
The two forces on the bag are equal and opposite. The net force on the bag is zero, so it remains at rest.

76. 4.6 Net Force Force Vectors
A vector is an arrow that represents the magnitude and direction of a quantity.
A vector quantity needs both magnitude and direction for a complete description. Force is an example of a vector quantity.
A scalar quantity can be described by magnitude only and has no direction. Time, area, and volume are scalar quantities.

77. 4.6 Net Force Force Vectors
This vector represents a force of 60 N to the right.

78. 4.6 Net Force
Force Vectors

79. 4.6 Net Force
How can you change an object’s state of motion?

80. 4.6 Net Force
A force is needed to change an object’s state of motion.

81. 4.7 Equilibrium – When Net Force Equals Zero
What forces act on a book lying at rest on a table?
One is the force due to gravity—the weight of the book.
There must be another force acting on it to produce a net force of zero—an upward force opposite to the force of gravity.
The upward force that balances the weight of an object on a surface is called the support force.
A support force is often called the normal force.

82. 4.7 Equilibrium – When Net Force Equals Zero
The table pushes up on the book with as much force as the downward weight of the book.

83. 4.7 Equilibrium – When Net Force Equals Zero
The table supports the book with a support force—the upward force that balances the weight of an object on a surface.
A support force is often called the normal force.

84. 4.7 Equilibrium – When Net Force Equals Zero
The upward support force is positive and the downward weight is negative.
The two forces add mathematically to zero.
Another way to say the net force on the book is zero is F = 0.
The book lying on the table compresses atoms in the table and they squeeze upward on the book. The compressed atoms produce the support force.

85. 4.7 Equilibrium – When Net Force Equals Zero
The upward support force is as much as the downward pull of gravity.

86. 4.7 Equilibrium – When Net Force Equals Zero
The upward support force is as much as the downward pull of gravity.

87. 4.7 Equilibrium – When Net Force Equals Zero
think!
What is the net force on a bathroom scale when a 110-pound person stands on it?

88. 4.7 Equilibrium – When Net Force Equals Zero
think!
What is the net force on a bathroom scale when a 110-pound person stands on it?
Answer: Zero–the scale is at rest. The scale reads the support force, not the net force.

89. 4.7 Equilibrium – When Net Force Equals Zero
think!
Suppose you stand on two bathroom scales with your weight evenly distributed between the two scales. What is the reading on each of the scales? What happens when you stand with more of your weight on one foot than the other?

90. 4.7 Equilibrium – When Net Force Equals Zero
think!
Suppose you stand on two bathroom scales with your weight evenly distributed between the two scales. What is the reading on each of the scales? What happens when you stand with more of your weight on one foot than the other?
Answer: In the first case, the reading on each scale is half your weight. In the second case, if you lean more on one scale than the other, more than half your weight will be read on that scale but less than half on the other. The total support force adds up to your weight.

91. 4.7 Equilibrium – When Net Force Equals Zero
For an object at rest on a horizontal surface, what is the support force equal to?

92. 4.7 Equilibrium – When Net Force Equals Zero
For an object at rest on a horizontal surface, the support force must equal the object’s weight.

93. 4.7 Equilibrium – When Net Force Equals Zero
Mechanical equilibrium is a state wherein no physical changes occur.
Whenever the net force on an object is zero, the object is in mechanical equilibrium—this is known as the equilibrium rule.

94. 4.7 Equilibrium – When Net Force Equals Zero
The  symbol stands for “the sum of.”
F stands for “forces.”
For a suspended object at rest, the forces acting upward on the object must be balanced by other forces acting downward.
The vector sum equals zero.

95. 4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

96. 4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

97. 4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

98. 4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

99. 4.7 Equilibrium – When Net Force Equals Zero
think!
If the gymnast hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Suppose she hangs with slightly more of her weight supported by the left ring. How would a scale on the right read?

100. 4.7 Equilibrium – When Net Force Equals Zero
think!
If the gymnast hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Suppose she hangs with slightly more of her weight supported by the left ring. How would a scale on the right read?
Answer: In the first case, the reading on each scale will be half her weight. In the second case, when more of her weight is supported by the left ring, the reading on the right reduces to less than half her weight. The sum of the scale readings always equals her weight.

101. 4.7 Equilibrium – When Net Force Equals Zero
How can you express the equilibrium rule mathematically?

102. 4.7 Equilibrium – When Net Force Equals Zero
You can express the equilibrium rule mathematically as F = 0.

103. 4.7 Equilibrium – When Net Force Equals Zero
The state of rest is only one form of equilibrium.
An object moving at constant speed in a straight-line path is also in a state of equilibrium. Once in motion, if there is no net force to change the state of motion, it is in equilibrium.

104. 4.7 Equilibrium – When Net Force Equals Zero
An object under the influence of only one force cannot be in equilibrium.
Only when there is no force at all, or when two or more forces combine to zero, can an object be in equilibrium.

105. 4.7 Equilibrium – When Net Force Equals Zero
When the push on the desk is the same as the force of friction between the desk and the floor, the net force is zero and the desk slides at an unchanging speed.

106. 4.7 Equilibrium – When Net Force Equals Zero
If the desk moves steadily at constant speed, without change in its motion, it is in equilibrium.
Friction is a contact force between objects that slide or tend to slide against each other.
In this case, F = 0 means that the force of friction is equal in magnitude and opposite in direction to the pushing force.

107. 4.7 Equilibrium – When Net Force Equals Zero
think!
An airplane flies horizontally at constant speed in a straight-line direction. Its state of motion is unchanging. In other words, it is in equilibrium. Two horizontal forces act on the plane. One is the thrust of the propeller that pulls it forward. The other is the force of air resistance (air friction) that acts in the opposite direction. Which force is greater?

108. 4.7 Equilibrium – When Net Force Equals Zero
think!
An airplane flies horizontally at constant speed in a straight-line direction. Its state of motion is unchanging. In other words, it is in equilibrium. Two horizontal forces act on the plane. One is the thrust of the propeller that pulls it forward. The other is the force of air resistance (air friction) that acts in the opposite direction. Which force is greater?
Answer: Neither, for both forces have the same strength. Call the thrust positive. Then the air resistance is negative. Since the plane is in equilibrium, the two forces combine to equal zero.

109. 4.7 Equilibrium – When Net Force Equals Zero
How are static and dynamic equilibrium different?

110. 4.7 Equilibrium – When Net Force Equals Zero
Objects at rest are said to be in static equilibrium; objects moving at constant speed in a straight-line path are said to be in dynamic equilibrium.

111. 4.8 Vector Addition of Forces
The sum of two or more vectors is called their resultant.
Combining vectors is quite simple when they are parallel:
If they are in the same direction, they add.
If they are in opposite directions, they subtract.

112. 4.8 Vector Addition of Forces
The tension in the rope is 300 N, equal to Nellie’s weight.

113. 4.8 Vector Addition of Forces
The tension in the rope is 300 N, equal to Nellie’s weight.
The tension in each rope is now 150 N, half of Nellie’s weight. In each case, F = 0.

114. 4.8 Vector Addition of Forces
The Parallelogram Rule
To find the resultant of nonparallel vectors, we use the parallelogram rule.
Consider two vectors at right angles to each other, as shown below. The constructed parallelogram in this special case is a rectangle. The diagonal is the resultant R.

115. 4.8 Vector Addition of Forces
The Parallelogram Rule
In the special case of two perpendicular vectors that are equal in magnitude, the parallelogram is a square.
The resultant is times one of the vectors.
For example, the resultant of two equal vectors of magnitude 100 acting at a right angle to each other is

116. 4.8 Vector Addition of Forces
Applying the Parallelogram Rule
When Nellie is suspended at rest from the two non-vertical ropes, is the rope tension greater or less than the tension in two vertical ropes?
You need to use the parallelogram rule to determine the tension.

117. 4.8 Vector Addition of Forces
Applying the Parallelogram Rule
Notice how the tension vectors form a parallelogram in which the resultant R is vertical.

118. 4.8 Vector Addition of Forces
Applying the Parallelogram Rule
Nellie’s weight is shown by the downward vertical vector.
An equal and opposite vector is needed for equilibrium, shown by the dashed vector. Note that the dashed vector is the diagonal of the parallelogram defined by the dotted lines.
Using the parallelogram rule, we find that the tension in each rope is more than half her weight.

119. 4.8 Vector Addition of Forces
Applying the Parallelogram Rule
As the angle between the ropes increases, tension increases so that the resultant (dashed-line vector) remains at 300 N upward, which is required to support 300-N Nellie.

120. 4.8 Vector Addition of Forces
Applying the Parallelogram Rule
When the ropes supporting Nellie are at different angles to the vertical, the tensions in the two ropes are unequal.
By the parallelogram rule, we see that the right rope bears most of the load and has the greater tension.

121. 4.8 Vector Addition of Forces
Applying the Parallelogram Rule
You can safely hang from a clothesline hanging vertically, but you will break the clothesline if it is strung horizontally.

122. 4.8 Vector Addition of Forces
think!
Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?

123. 4.8 Vector Addition of Forces
think!
Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?
Answer: The tension is greater in the ropes hanging at an angle. The angled ropes are more likely to break than the vertical ropes.

124. 4.8 Vector Addition of Forces
think!
Consider what would happen if you suspended a 10-N object midway along a very tight, horizontally stretched guitar string. Is it possible for the string to remain horizontal without a slight sag at the point of suspension?

125. 4.8 Vector Addition of Forces
think!
Consider what would happen if you suspended a 10-N object midway along a very tight, horizontally stretched guitar string. Is it possible for the string to remain horizontal without a slight sag at the point of suspension?
Answer: No way! If the 10-N load is to hang in equilibrium, there must be a supporting 10-N upward resultant. The tension in each half of the guitar string must form a parallelogram with a vertically upward 10-N resultant.

126. 4.8 Vector Addition of Forces
How can you find the resultant of two vectors?

127. 4.8 Vector Addition of Forces
To find the resultant of two vectors, construct a parallelogram wherein the two vectors are adjacent sides. The diagonal of the parallelogram shows the resultant.

128. 4.9 The Moving Earth Again
Copernicus announced the idea of a moving Earth in the sixteenth century. One of the arguments against a moving Earth was:
Consider a bird sitting at rest in the top of a tall tree.
The bird sees a worm, drops down vertically, and catches it.
It was argued that this would not be possible if Earth moved as Copernicus suggested.
The fact that birds do catch worms from high tree branches seemed to be clear evidence that Earth must be at rest.

129. Objects Move With Earth
4.9 The Moving Earth Again
Objects Move With Earth
You can refute this argument using the idea of inertia.
Earth moves at 30 km/s, but so do the tree, the worm below, and even the air in between.
Objects on Earth move with Earth as Earth moves around the sun.

130. 4.9 The Moving Earth Again
Earth does not need to be at rest for the bird to catch the worm.

131. Objects Move With Vehicles
4.9 The Moving Earth Again
Objects Move With Vehicles
If we flip a coin in a high-speed car, bus, or plane, we can catch the vertically moving coin as we would if the vehicle were at rest.
We see evidence for the law of inertia when the horizontal motion of the coin before, during, and after the catch is the same.
The vertical force of gravity affects only the vertical motion of the coin.

132. 4.9 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!

133. 4.9 The Moving Earth Again

134. 4.9 The Moving Earth Again
How does the law of inertia apply to objects in motion?

135. 4.9 Mass—A Measure of Inertia
The law of inertia states that objects in motion remain in motion if no unbalanced forces act on them.

136. 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.

137. 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

138. 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.

139. 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

140. 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.

141. 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

142. 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.

143. 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

144. 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.

145. 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

146. Assessment Questions
When you hold a rock in your hand at rest, the forces on the rock
are mainly due to gravity.
are mainly due to the upward push of your hand.
cancel to zero.
don’t act unless the rock is dropped.

147. Assessment Questions
When you hold a rock in your hand at rest, the forces on the rock
are mainly due to gravity.
are mainly due to the upward push of your hand.
cancel to zero.
don’t act unless the rock is dropped.
Answer: C

148. Assessment Questions
Burl and Paul have combined weights of 1300 N. The tensions in the supporting ropes that support the scaffold they stand on add to 1700 N. The weight of the scaffold itself must be
400 N.
500 N.
600 N.
3000 N.

149. Assessment Questions
Burl and Paul have combined weights of 1300 N. The tensions in the supporting ropes that support the scaffold they stand on add to 1700 N. The weight of the scaffold itself must be
400 N.
500 N.
600 N.
3000 N.
Answer: A

150. Assessment Questions
Harry gives his little sister a piggyback ride. Harry weighs 400 N and his little sister weighs 200 N. The support force supplied by the floor must be
200 N.
400 N.
600 N.
more than 600 N.

151. Assessment Questions
Harry gives his little sister a piggyback ride. Harry weighs 400 N and his little sister weighs 200 N. The support force supplied by the floor must be
200 N.
400 N.
600 N.
more than 600 N.
Answer: C

152. Assessment Questions
When a desk is horizontally pushed across a floor at a steady speed in a straight-line direction, the amount of friction acting on the desk is
less than the pushing force.
equal to the pushing force.
greater than the pushing force.
dependent on the speed of the sliding crate.

153. Assessment Questions
When a desk is horizontally pushed across a floor at a steady speed in a straight-line direction, the amount of friction acting on the desk is
less than the pushing force.
equal to the pushing force.
greater than the pushing force.
dependent on the speed of the sliding crate.
Answer: B

154. Assessment Questions
When Nellie hangs at rest by a pair of ropes, the tensions in the ropes
always equal her weight.
always equal half her weight.
depend on the angle of the ropes to the vertical.
are twice her weight.

155. Assessment Questions
When Nellie hangs at rest by a pair of ropes, the tensions in the ropes
always equal her weight.
always equal half her weight.
depend on the angle of the ropes to the vertical.
are twice her weight.
Answer: C

156. 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.

157. 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