## Types of Collisions

9.4 Types of Collisions

### Learning Objectives

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

- Identify the type of collision
- Correctly label a collision as elastic or inelastic
- Use kinetic energy along with momentum and impulse to analyze a collision

### Collisions and Explosions

Although momentum is conserved in all interactions, not all interactions (collisions or explosions) are the same. The possibilities include:

- A single object can explode into multiple objects (explosions).
- Multiple objects can collide and bounce off each other, called an elastic collision, resulting in the same kinetic energy of the system before and after the collision.
- Multiple objects can collide and the system loses kinetic energy, called an inelastic collision. One such case is where the two objects stick together, forming a single object.

It’s useful, therefore, to categorize different types of interactions, according to how the interacting objects move before and after the interaction.

**Practice!**

Practice 9.4.1 |
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A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision? |

(a) v |

(b) v/2 |

(c) v/3 |

(d) 2v |

(e) None of those answers is correct. |

Practice 9.4.2 |
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A 2.0-kg object moving 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision. |

(a) 20 J |

(b) 15 J |

(c) 30 J |

(d) 25 J |

(e) 5.0 J |

**Discuss!**

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

A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position?

### Elastic Collisions

Practice 9.4.3 |
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A 3.0-kg object moving in the positive x direction has a one-dimensional elastic collision with a 5.0-kg object initially at rest. After the collision the 5.0-kg object has a velocity of 6.0 m/s in the positive x direction. What was the initial speed of the 3.0 kg object? |

(a) 6.0 m/s |

(b) 7.0 m/s |

(c) 4.5 m/s |

(d) 8.0 m/s |

(e) 5.5 m/s |

**Discuss!**

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

A steel ball of mass 0.600 kg is fastened to a cord that is 80.0 cm long and fixed at the far end. The ball is then released when the cord is horizontal. At the bottom of its path, the ball strikes a 3.00 kg steel block initially at rest on a frictionless surface. The collision is elastic.

(a) Find the speed of the ball just after collision.

(b) Find the speed of the block just after collision.