## Conservation of Linear Momentum

9.3 Conservation of Linear Momentum

### Learning Objectives

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

- Explain the meaning of “conservation of momentum”
- Correctly identify if a system is, or is not, closed
- Define a system whose momentum is conserved
- Mathematically express conservation of momentum for a given system
- Calculate an unknown quantity using conservation of momentum

Practice 9.3.1 |
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A 3.00-kg rifle fires a 0.00500-kg bullet at a speed of 300 m/s. Which force is greater in magnitude: the force that the rifle exerts on the bullet or the force that the bullet exerts on the rifle? |

(a) The force that the rifle exerts on the bullet is greater. |

(b) The force that the bullet exerts on the rifle is greater. |

(c) Both forces have the same magnitude. |

(d) The answer depends on how the rifle is held. |

(e) The answer depends on how the rifle is held and on the inner workings of the rifle. |

### Conservation of Linear Momentum

Pause & Predict 9.3.1 |
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A 2-kg block, moving in the positive x-direction at 4 m/s, collides with a 3-kg block moving at 7 m/s in the negative x-direction. If the 2-kg block rebounds at 3 m/s after the collision, what is the final velocity of the 3-kg block? |

(a) -2.3 m/s |

(b) 2.3 m/s |

(c) 12 m/s |

(d) 6.3 m/s |

(e) -6.3 m/s |

Pause & Predict 9.3.2 |
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A 2-kg block and a 3-kg block are held at rest with a compressed light spring between them. When released, the 3-kg block moves in the positive x-direction at 5 m/s. What is the velocity of the 2-kg block after release? |

(a) 0 m/s |

(b) 3.3 m/s |

(c) -3.3 m/s |

(d) 7.5 m/s |

(e) -7.5 m/s |

**Discuss!**

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

The red ball in the diagram is chasing after the blue ball; they have the same mass. The speed of the red ball is 3 m/s and the speed of the blue ball is 2 m/s. After the collision the red ball rebounds at 2 m/s and the blue ball speeds away at 3 m/s.

(a) What was the change in velocity experienced by the red ball during the collision?

(b) What was the change in velocity experienced by the blue ball during the collision?

(c) Normally, momentum is conserved during a collision. However if a huge external force acts during the collision, it may not be. Was momentum conserved during this collision or not?

**Practice!**

Practice 9.3.2 |
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Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. At one moment, when Max is skating away from the shore at 8.2 m/s and Maya is skating towards the shore at 4.6 m/s, they collide and bounce off each other without falling. If Maya rebounds at 3.4 m/s, what is Max’s velocity after their collision? |

(a) 1.8 m/s towards the shore |

(b) 1.8 m/s away from the shore |

(c) 9.2 m/s towards the shore |

(d) 9.2 m/s away from the shore |

(e) 7.2 m/s towards the shore |

(f) 7.2 m/s away from the shore |

Momentum is conserved in this collision since the contact force between Max and Maya during the collision is internal to the system of colliding objects.

Practice 9.3.3 |
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Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. When Max is standing on the shore, he throws a 1.5-kg snowball at Maya, who is standing at the center of the pond. Maya catches the snowball and she and the snowball move away from the shore at 2.0 m/s. How fast was the snowball moving right before Maya caught it? |

(a) 22 m/s |

(b) 3.6 m/s |

(c) 2.3 m/s |

(d) 18 m/s |

Momentum is conserved in this collision since the contact force between the snowball and Maya during the collision is internal to the system of colliding objects.

Practice 9.3.4 |
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Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. While standing at the center of the pond, Maya throws a 1.5-kg snowball at Max and, as a result, recoils away from Max at 2.5 m/s. With what speed did Maya throw the snowball at Max? |

(a) 25 m/s |

(b) 2.5 m/s |

(c) 20 m/s |

(d) 30 m/s |

(e) 0.31 m/s |

Momentum is conserved in this explosion since the contact force between the snowball and Maya during the explosion is internal to the system of objects.