4.5 Newton's Third Law of Motion

Imagine you are in a football game. You line up facing your opponent, the ball is snapped, and the two of you crash together. No doubt, you feel a force. But think about your opponent. He too feels something, for while he is applying a force to you, you are applying a force to him. In other words, there isn't just one force on the line of scrimmage; there is a pair of forces. Newton was the first to realize that all forces occur in pairs and there is no such thing as an isolated force, existing all by itself. His third law of motion deals with this fundamental characteristic of forces.
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These two red foxes are fighting over territory. In the process, they exert action and reaction forces on each other.

Newton's Third Law of Motion

Whenever one object exerts a force on a second object, the second object exerts an oppositely directed force of equal magnitude on the first object.

The third law is often called the “action-reaction” law, because it is sometimes quoted as follows: “For every action (force) there is an equal, but opposite, reaction.”

Figure 4.7 illustrates how the third law applies to an astronaut who is drifting just outside a spacecraft and who pushes on the spacecraft with a force ModifyingAbove Bold Upper P With right-arrow. According to the third law, the spacecraft pushes back on the astronaut with a force negative ModifyingAbove Bold Upper P With right-arrow that is equal in magnitude but opposite in direction. In Example 4, we examine the accelerations produced by each of these forces.

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Figure 4.7   The astronaut pushes on the spacecraft with a force plus ModifyingAbove Bold Upper P With right-arrow. According to Newton's third law, the spacecraft simultaneously pushes back on the astronaut with a force negative ModifyingAbove Bold Upper P With right-arrow.

EXAMPLE 4The Accelerations Produced by Action and Reaction Forces

Suppose that the mass of the spacecraft in Figure 4.7 is m Subscript Upper S Baseline equals 11000  kg and that the mass of the astronaut is m Subscript Upper A Baseline equals 92  kg. In addition, assume that the astronaut pushes with a force of ModifyingAbove Bold Upper P With right-arrow equals plus 36  Upper N on the spacecraft. Find the accelerations of the spacecraft and the astronaut.

Reasoning

Consistent with Newton's third law, when the astronaut applies the force ModifyingAbove Bold Upper P With right-arrow equals plus 36  Upper N to the spacecraft, the spacecraft applies a reaction force negative ModifyingAbove Bold Upper P With right-arrow equals negative 36  Upper N to the astronaut. As a result, the spacecraft and the astronaut accelerate in opposite directions. Although the action and reaction forces have the same magnitude, they do not create accelerations of the same magnitude, because the spacecraft and the astronaut have different masses. According to Newton's second law, the astronaut, having a much smaller mass, will experience a much larger acceleration. In applying the second law, we note that the net force acting on the spacecraft is sigma-summation ModifyingAbove Bold Upper F With right-arrow equals ModifyingAbove Bold Upper P With right-arrow, while the net force acting on the astronaut is sigma-summation ModifyingAbove Bold Upper F With right-arrow equals negative ModifyingAbove Bold Upper P With right-arrow.

Solution

Using the second law, we find that the acceleration of the spacecraft is

ModifyingAbove Bold a With right-arrow Subscript Upper S Baseline equals StartFraction ModifyingAbove Bold Upper P With right-arrow Over m Subscript Upper S EndFraction equals StartFraction plus 36  Upper N Over 11000  kg EndFraction StartLayout equals1st Row 1st Column plus 0.0033  m divided by s squared EndLayout

The acceleration of the astronaut is

ModifyingAbove Bold a With right-arrow Subscript Upper A Baseline equals StartFraction negative ModifyingAbove Bold Upper P With right-arrow Over m Subscript Upper A EndFraction equals StartFraction negative 36  Upper N Over 92  kg EndFraction StartLayout equals1st Row 1st Column negative 0.39  m divided by s squared EndLayout

Problem-Solving Insight 

Even though the magnitudes of the action and reaction forces are always equal, these forces do not necessarily produce accelerations that have equal magnitudes, since each force acts on a different object that may have a different mass.

The physics of automatic trailer brakes. There is a clever application of Newton's third law in some rental trailers. As Figure 4.8 illustrates, the tow bar connecting the trailer to the rear bumper of a car contains a mechanism that can automatically actuate brakes on the trailer wheels. This mechanism works without the need for electrical connections between the car and the trailer. When the driver applies the car brakes, the car slows down. Because of inertia, however, the trailer continues to roll forward and begins pushing against the bumper. In reaction, the bumper pushes back on the tow bar. The reaction force is used by the mechanism in the tow bar to “push a brake pedal” for the trailer.

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Figure 4.8   Some rental trailers include an automatic brake-actuating mechanism.

Check Your Understanding 

6.  

A father and his seven-year-old daughter are facing each other on ice skates. With their hands, they push off against one another. Which one or more of the following statements is (are) true?

  • (a)Each experiences an acceleration that has a different magnitude.
  • (b)Each experiences an acceleration of the same magnitude.
  • (c)Each experiences a pushing force that has a different magnitude.
  • (d)Each experiences a pushing force that has the same magnitude.