# Conservation of Energy

## Practice

### practice problem 1

- Find the speed of the bus at point B.
- An extortionist has planted a bomb on the bus. If the speed of the bus falls below 22.35 m/s (50 mph) the bomb will explode. Will the speed of the bus fall below this value and explode? If you feel the bus will explode, identify the interval in which this occurs.
- Derive an equation to determine the speed of the bus at any altitude.

#### solution

- Answer it.
- Answer it.
- Answer it.

### practice problem 2

#### solution

The situation starts with the boulder's gravitational potential energy (measured relative to the surface of the blob). The boulder falls and it's potential energy is transformed into kinetic energy. That kinetic energy gets transfered to the stick figure. Up goes the stick person. Kinetic energy is now transformed into potential energy. The energies at these four prominant times are all equal. Assuming energy was not lost, the initial potential energy of the boulder is equal to the final potential energy of the stick figure.

U_{s} |
= | U_{b} |

m_{s}gh_{s} |
= | m_{b}gh_{b} |

m_{s}h_{s} |
= | m_{b}h_{b} |

(64 kg)h_{s} |
= | (256 kg)(7.0 m) |

h_{s} |
= | 28 m |

Another way to look at this problem is as a proportion. Potential energy is partly the product of mass and height. (It's also the product of gravity with mass and height, but since gravity doesn't change appreciably during a blob jump we can treat it as constant.) When the product of two numbers is contant, they are inversely proportional. The boulder has 4 times the mass of the stick figure. Therefore, the stick figure should have 4 times the height of the boulder.

m_{s}h_{s} |
= | m_{b}h_{b} |

m4_{s}h_{b} |
= | 4m_{s}h_{b} |

h_{s} |
= | 4h = 4(7.0 m)_{b} |

h_{s} |
= | 28 m |

### practice problem 3

#### solution

Answer it.

### practice problem 4

#### solution

Answer it.