1. Chapter 7 Lecture

2. Chapter 7 Newton’s Third Law
Chapter Goal: To use Newton’s third law to understand interacting objects.
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3. Chapter 7 Preview
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4. Chapter 7 Preview
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5. Chapter 7 Preview
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6. Chapter 7 Preview
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7. Chapter 7 Preview
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8. Chapter 7 Preview
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9. Chapter 7 Reading Quiz
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10. Two forces for which Newton’s Third Law applies are called
Reading Question 7.1
Two forces for which Newton’s Third Law applies are called
An action/reaction pair.
A couple.
An opposing pair.
A vector doublet.
Complementary components.
Answer: A
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11. Two forces for which Newton’s Third Law applies are called
Reading Question 7.1
Two forces for which Newton’s Third Law applies are called
An action/reaction pair.
A couple.
An opposing pair.
A vector doublet
Complementary components.
Answer: A
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12. What kind of diagram is this?
Reading Question 7.2
What kind of diagram is this?
Environment diagram.
Force diagram.
Free-body diagram.
Interaction diagram.
System diagram.
Answer: A
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13. What kind of diagram is this?
Reading Question 7.2
What kind of diagram is this?
Environment diagram.
Force diagram.
Free-body diagram.
Interaction diagram.
System diagram.
Answer: A
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14. The propulsion force on a car is due to
Reading Question 7.3
The propulsion force on a car is due to
Static friction.
Kinetic friction.
The car engine.
Elastic energy.
Answer: A
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15. The propulsion force on a car is due to
Reading Question 7.3
The propulsion force on a car is due to
Static friction.
Kinetic friction.
The car engine.
Elastic energy.
Answer: A
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16. Reading Question 7.4
Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1?
Greater than rope 2.
Less than rope 2.
Equal to rope 2.
Answer: C
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17. Reading Question 7.4
Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1?
Greater than rope 2.
Less than rope 2.
Equal to rope 2.
Answer: C
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18. An acceleration constraint says that in some circumstances
Reading Question 7.5
An acceleration constraint says that in some circumstances
The acceleration of an object has to be positive.
Two objects have to accelerate in the same direction.
The magnitude of the accelerations of two objects have to be equal.
An object is prevented from accelerating.
Acceleration constraints were not discussed in this chapter.
Answer: C
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19. An acceleration constraint says that in some circumstances
Reading Question 7.5
An acceleration constraint says that in some circumstances
The acceleration of an object has to be positive.
Two objects have to accelerate in the same direction.
The magnitude of the accelerations of two objects have to be equal.
An object is prevented from accelerating.
Acceleration constraints were not discussed in this chapter.
Answer: C
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20. Chapter 7 Content, Examples, and QuickCheck Questions
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21. Interacting Objects
When a hammer hits a nail, it exerts a forward force on the nail.
At the same time, the nail exerts a backward force on the hammer.
If you don’t believe it, imagine hitting the nail with a glass hammer.
It’s the force of the nail on the hammer that would cause the glass to shatter!
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22. Interacting Objects
When a bat hits a ball, the ball exerts a force on the bat.
When you pull someone with a rope in a tug-of- war, that person pulls back on you.
The bat and the ball are interacting with each other.
When your chair pushes up on you (the normal force), you push down on the chair.
All forces come in pairs, called action/reaction pairs.
These forces occur simultaneously, and we cannot say which is the “action” and which is the “reaction.”
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23. Interacting Objects
If object A exerts a force on object B, then object B exerts a force on object A.
The pair of forces, as shown, is called an action/reaction pair.
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24. Interacting Objects
Long-range forces, such as gravity, also come in pairs.
If you release a ball, it falls because the earth’s gravity exerts a downward force
At the same time, the ball pulls upward on the earth with a force
The ocean tides are an indication of the long-range gravitational interaction of the earth and moon.
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25. Objects, Systems, and the Environment
Chapters 5 and 6 considered forces acting on a single object, modeled as a particle.
The figure shows a diagram representing single-particle dynamics.
We can use Newton’s second law, , to determine the particle’s acceleration.
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26. Objects, Systems, and the Environment
In this chapter we extend the particle model to include two or more objects that interact.
The figure shows three objects interacting via action/reaction pairs of forces.
The forces can be given labels, such as and
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27. Objects, Systems, and the Environment
For example, set:
Object A = the hammer
Object B = the nail
Object C = the earth
The earth interacts with both the hammer and the nail via gravity.
Practically, the earth remains at rest while the hammer and the nail move.
Define the system as those objects whose motion we want to analyze.
Define the environment as objects external to the system.
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28. Objects, Systems, and the Environment
The figure shows a new kind of diagram, an interaction diagram.
The objects of the system are in a box.
Interactions are represented by lines connecting the objects.
Interactions with objects in the environment are called external forces.
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29. Tactics: Analyzing Interacting Objects
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30. Tactics: Analyzing Interacting Objects
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31. Tactics: Analyzing Interacting Objects
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32. Example 7.1 Pushing a Crate
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33. Example 7.1 Pushing a Crate
VISUALIZE
1. The person and crate are obvious objects, with a pushing force connecting them.
2. There are normal and friction contact forces between the person and crate and the surface. Also there is the long-range force of gravity between the person and crate and the entire earth.
3. The person and crate are the System; these are the objects whose motion we wish to analyze.
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34. Example 7.1 Pushing a Crate
4. Below are the free-body diagrams of the person and the crate. For each, three forces are external forces. Subscripts label which object each force acts on. There is one internal interaction, labeled as an action/reaction pair.
ASSESS The completed free-body diagrams above could now be the basis for a quantitative analysis.
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35. Propulsion
If you try to walk across a frictionless floor, your foot slips and slides backward.
In order to walk, your foot must stick to the floor as you straighten your leg, moving your body forward.
The force that prevents slipping is static friction.
The static friction force points in the forward direction.
It is static friction that propels you forward!
What force causes this sprinter to accelerate?
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36. Examples of Propulsion
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37. “For every action there is an equal but opposite reaction.”
Newton’s Third Law
Every force occurs as one member of an action/reaction pair of forces.
The two members of an action/reaction pair act on two different objects.
The two members of an action/reaction pair are equal in magnitude, but opposite in direction:
A catchy phrase, which is less precise, is:
“For every action there is an equal but opposite reaction.”
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38. Reasoning with Newton’s Third Law
When you release a ball, it falls down.
The action/reaction forces of the ball and the earth are equal in magnitude.
The acceleration of the ball is
The acceleration of the earth is
If the ball has a mass of 1 kg, the earth accelerates upward at 2  10−24 m/s2.
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39. QuickCheck 7.1
A mosquito runs head-on into a truck. Splat! Which is true during the collision?
The mosquito exerts more force on the truck than the truck exerts on the mosquito.
The truck exerts more force on the mosquito than the mosquito exerts on the truck.
The mosquito exerts the same force on the truck as the truck exerts on the mosquito.
The truck exerts a force on the mosquito but the mosquito does not exert a force on the truck.
The mosquito exerts a force on the truck but the truck does not exert a force on the mosquito.
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40. QuickCheck 7.1
A mosquito runs head-on into a truck. Splat! Which is true during the collision?
The mosquito exerts more force on the truck than the truck exerts on the mosquito.
The truck exerts more force on the mosquito than the mosquito exerts on the truck.
The mosquito exerts the same force on the truck as the truck exerts on the mosquito.
The truck exerts a force on the mosquito but the mosquito does not exert a force on the truck.
The mosquito exerts a force on the truck but the truck does not exert a force on the mosquito.
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41. QuickCheck 7.2
A mosquito runs head-on into a truck. Which is true during the collision?
The magnitude of the mosquito’s acceleration is larger than that of the truck.
The magnitude of the truck’s acceleration is larger than that of the mosquito.
The magnitude of the mosquito’s acceleration is the same as that of the truck.
The truck accelerates but the mosquito does not.
The mosquito accelerates but the truck does not.
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42. QuickCheck 7.2
A mosquito runs head-on into a truck. Which is true during the collision?
The magnitude of the mosquito’s acceleration is larger than that of the truck.
The magnitude of the truck’s acceleration is larger than that of the mosquito.
The magnitude of the mosquito’s acceleration is the same as that of the truck.
The truck accelerates but the mosquito does not.
The mosquito accelerates but the truck does not.
Newton’s second law:
Don’t confuse cause and effect! The same force can have very different effects.
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43. Example 7.3 The Forces on Accelerating Boxes
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44. Example 7.3 The Forces on Accelerating Boxes
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45. Example 7.3 The Forces on Accelerating Boxes
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46. Acceleration Constraints
If two objects A and B move together, their accelerations are constrained to be equal: aA = aB.
This equation is called an acceleration constraint.
Consider a car being towed by a truck.
In this case, the acceleration constraint is aCx = aTx = ax .
Because the accelerations of both objects are equal, we can drop the subscripts C and T and call both of them ax .
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47. Acceleration Constraints
Sometimes the acceleration of A and B may have different signs.
Consider the blocks A and B in the figure.
The string constrains the two objects to accelerate together.
But, as A moves to the right in the +x direction, B moves down in the −y direction.
In this case, the acceleration constraint is aAx = −aBy .
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48. Problem-Solving Strategy: Interacting-Objects Problems
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49. Problem-Solving Strategy: Interacting-Objects Problems
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50. QuickCheck 7.3
What, if anything, is wrong with these free-body diagrams for a truck towing a car at steady speed? The truck is heavier than the car and the rope is massless.
STT1.2
Nothing is wrong.
One or more forces have the wrong length.
One of more forces have the wrong direction.
One or more action/reaction pairs are wrong.
Both B and D.
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51. QuickCheck 7.3
What, if anything, is wrong with these free-body diagrams for a truck towing a car at steady speed? The truck is heavier than the car and the rope is massless.
STT1.2
Nothing is wrong.
One or more forces have the wrong length.
One of more forces have the wrong direction.
One or more action/reaction pairs are wrong.
Both B and D.
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52. QuickCheck 7.4
A car is parked at rest on a horizontal road. The upward force of the road on the car (the normal force) is the same size as the downward pull of gravity
Because they are an action/reaction pair.
Because of Newton’s first law.
Both A and B.
Neither A nor B. Some other reason.
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53. QuickCheck 7.4
A car is parked at rest on a horizontal road. The upward force of the road on the car (the normal force) is the same size as the downward pull of gravity
Because they are an action/reaction pair.
Because of Newton’s first law.
Both A and B.
Neither A nor B. Some other reason.
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54. Tension Revisited Figure (a) shows a heavy safe hanging from a rope.
The combined pulling force of billions of stretched molecular springs is called tension.
Tension pulls equally in both directions.
Figure (b) is a very thin cross section through the rope.
This small piece is in equilibrium, so it must be pulled equally from both sides.
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55. Example 7.5 Pulling a Rope
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56. Example 7.5 Pulling a Rope
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57. Example 7.5 Pulling a Rope
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58. The rope’s tension is the same in both situations.
Example 7.5 Pulling a Rope
The rope’s tension is the same in both situations.
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59. The Massless String Approximation
Often in problems the mass of the string or rope is much less than the masses of the objects that it connects.
In such cases, we can adopt the following massless string approximation:
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60. The Massless String Approximation
Two blocks are connected by a massless string, as block B is pulled to the right.
Forces and act as if they are an action/reaction pair:
All a massless string does is transmit a force from A to B without changing the magnitude of that force.
For problems in this book, you can assume that any strings or ropes are massless unless it explicitly states otherwise.
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61. QuickCheck 7.5
Boxes A and B are being pulled to the right on a frictionless surface. Box A has a larger mass than B. How do the two tension forces compare?
T1 > T2
T1 = T2
T1 < T2
Not enough information to tell.
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62. QuickCheck 7.5
Boxes A and B are being pulled to the right on a frictionless surface. Box A has a larger mass than B. How do the two tension forces compare?
T1 > T2
T1 = T2
T1 < T2
Not enough information to tell.
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63. Example 7.6 Comparing Two Tensions
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64. Example 7.6 Comparing Two Tensions
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65. Example 7.6 Comparing Two Tensions
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66. Example 7.6 Comparing Two Tensions
T1 > T2
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67. QuickCheck 7.6
Boxes A and B are sliding to the right on a frictionless surface. Hand H is slowing them. Box A has a larger mass than B. Considering only the horizontal forces:
FB on H = FH on B = FA on B = FB on A
FB on H = FH on B > FA on B = FB on A
FB on H = FH on B < FA on B = FB on A
FH on B = FH on A > FA on B
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68. QuickCheck 7.6
Boxes A and B are sliding to the right on a frictionless surface. Hand H is slowing them. Box A has a larger mass than B. Considering only the horizontal forces:
FB on H = FH on B = FA on B = FB on A
FB on H = FH on B > FA on B = FB on A
FB on H = FH on B < FA on B = FB on A
FH on B = FH on A > FA on B
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69. Pulleys Block B drags block A across a frictionless table as it falls.
The string and the pulley are both massless.
There is no friction where the pulley turns on its axle.
Therefore, TA on S = TB on S.
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70. Pulleys
Since TA on B = TB on A, we can draw the simplified free-body diagram on the right, below.
Forces and act as if they are in an action/reaction pair, even though they are not opposite in direction because the tension force gets “turned” by the pulley.
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71. QuickCheck 7.7
All three 50-kg blocks are at rest. The tension in rope 2 is
greater than the tension in rope 1.
equal to the tension in rope 1.
less than the tension in rope 1.
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72. QuickCheck 7.7
All three 50-kg blocks are at rest. The tension in rope 2 is
greater than the tension in rope 1.
equal to the tension in rope 1.
less than the tension in rope 1.
Each block is in static equilibrium, with
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73. QuickCheck 7.8
The two masses are at rest. The pulleys are frictionless. The scale is in kg. The scale reads
0 kg.
5 kg.
10 kg.
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74. QuickCheck 7.8
The two masses are at rest. The pulleys are frictionless. The scale is in kg. The scale reads
0 kg.
5 kg.
10 kg.
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75. QuickCheck 7.9 The acceleration constraint here is aAy = aBy.
C. aAy = –aBy.
D. aBy = –aAy.
E. Either C or D.
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76. QuickCheck 7.9 The acceleration constraint here is aAy = aBy.
C. aAy = –aBy.
D. aBy = –aAy.
E. Either C or D.
Either says that the acceleration vectors point in opposite directions.
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77. Tactics: Working With Ropes and Pulleys
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78. QuickCheck 7.10
The top block is accelerated across a frictionless table by the falling mass m. The string is massless, and the pulley is both massless and frictionless. The tension in the string is
T < mg.
T = mg.
T > mg.
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79. QuickCheck 7.10
The top block is accelerated across a frictionless table by the falling mass m. The string is massless, and the pulley is both massless and frictionless. The tension in the string is
T < mg.
T = mg.
T > mg
Tension has to be less than mg for the block to have a downward acceleration.
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80. QuickCheck 7.11
Block A is accelerated across a frictionless table. The string is massless, and the pulley is both massless and frictionless.
Which is true?
Block A accelerates faster in case a than in case b.
Block A has the same acceleration in case a and case b.
Block A accelerates slower in case a than in case b.
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81. QuickCheck 7.11
Block A is accelerated across a frictionless table. The string is massless, and the pulley is both massless and frictionless.
Which is true?
Block A accelerates faster in case a than in case b.
Block A has the same acceleration in case a and case b.
Block A accelerates slower in case a than in case b.
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82. Chapter 7 Summary Slides

83. General Principles
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84. General Principles
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85. Important Concepts
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86. Important Concepts
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