## Kinetic Energy

7.2 Kinetic Energy

### Learning Objectives

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

- Calculate the kinetic energy of a particle given its mass and its velocity or momentum
- Evaluate the kinetic energy of a body, relative to different frames of reference

### Kinetic Energy

The kinetic energy of a particle is one-half the product of the particle’s mass *m* and the square of its speed *v*:

**Practice!**

Practice 7.2.1 |
---|

You observe two identical balls heading directly toward each other at equal speeds. What can you say about their total kinetic energy? |

(a) They have some total amount of kinetic energy, with a magnitude between zero and double the kinetic energy of either ball by itself. |

(b) They have zero total kinetic energy. |

(c) They have twice the kinetic energy of either ball by itself. |

(d) Nothing. The kinetic energy of separate objects cannot be combined. |

**Discuss!**

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

One particle has mass *m* and a second particle has mass 2*m*. The second particle is moving with speed *v* and the first with speed 2*v*. How do their kinetic energies compare?

A particle of *m* has a velocity of . Is its kinetic energy given by ? If not, what is the correct expression?