## Newton’s Third Law

5.5 Newton’s Third Law

### Learning Objectives

By the end of this section, you will be able to:

- State Newton’s third law of motion
- Identify the action and reaction forces in different situations
- Apply Newton’s third law to define systems and solve problems of motion

### Newton’s Third Law

Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.

“Every action has an equal and opposite reaction.”

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

Identify the action and reaction forces in the following situations:

- Earth attracts the Moon
- a person kicks a football
- a rocket accelerates upward
- a car accelerates forward
- a high jumper leaps
- a bullet is shot from a gun

**Practice!**

Practice 5.5.1 |
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An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. The upward force exerted on the elevator by the cable is |

(a) greater than the downward force of gravity. |

(b) equal to the force of gravity. |

(c) less than the force of gravity. |

(d) any of the above, depending on the speed of the elevator. |

(e) any of the above, depending on the acceleration of the elevator. |

Practice 5.5.2 |
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An elevator is being lowered at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. The upward force exerted on the elevator by the cable is |

(a) greater than the downward force of gravity. |

(b) equal to the force of gravity. |

(c) less than the force of gravity. |

(d) any of the above, depending on the speed of the elevator. |

(e) any of the above, depending on the acceleration of the elevator. |

Practice 5.5.3 |
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An elevator is being lowered with an increasing speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. The upward force exerted on the elevator by the cable is |

(a) greater than the downward force of gravity. |

(b) equal to the force of gravity. |

(c) less than the force of gravity. |

(d) any of the above, depending on the speed of the elevator. |

(e) any of the above, depending on the acceleration of the elevator. |

Practice 5.5.4 |
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An elevator is being by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. The upward force exerted on the elevator by the cable is lowered with a decreasing speed |

(a) greater than the downward force of gravity. |

(b) equal to the force of gravity. |

(c) less than the force of gravity. |

(d) any of the above, depending on the speed of the elevator. |

(e) any of the above, depending on the acceleration of the elevator. |

Practice 5.5.5 |
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An elevator is being lowered at constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. Why does the upward force exerted on the elevator by the cable have the same magnitude as the downward force of gravity on the elevator? |

(a) Because of Newton’s first law |

(b) Because of Newton’s third law |

(c) Both (a) and (b) |

Practice 5.5.6 |
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A ball sits at rest on a horizontal tabletop. The weight of the ball is equal to the magnitude of the upward force that the tabletop exerts on the ball. Why? |

(a) This is a consequence of Newton’s first law. |

(b) This is a consequence of Newton’s third law. |

(c) We assume that the table top is perfectly rigid. |

(d) Two of the above three statements are correct. |

(e) All of the first three statements are correct. |

Practice 5.5.7 |
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A ball sits at rest on a horizontal tabletop. According to Newton’s third law, F _{A on B} = -F_{B on A}, the weight of the ball has the same magnitude as |

(a) the downward force of the ball on the table. |

(b) the upward force of the table on the ball. |

(c) the upward force that the ball exerts on planet earth. |

(d) two of (a), (b), and (c). |

(e) all of (a), (b), and (c). |

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

A passenger is riding in an elevator. The passenger weighs 650 N and the floor of the elevator exerts a force of 620 N on the passenger.

(a) What are the reaction forces to these two forces?

(b) Is the passenger accelerating?

(c) If so, what are the magnitude and direction of the acceleration?