## (15) Energy## Potential and KineticAn interesting thing about the final speed of an object descending (with no friction) from some given height Reducing the slope of the surface reduces the acceleration a, but it also lengthens the time of descent, and these two variations cancel, leaving the final speed unchanged. The same speed is also obtained if the object falls vertically from that height h = g t Multiply both sides by gh = g Then since the final velocity is v = gt one gets gh = v By the last equation, as the object loses elevation--assuming nothing interferes with its motion-- This exchange between up an incline loses v in direct proportion to the elevation ^{2}h it gains. A marble rolling down the inside of a smooth bowl gathers speed as it approaches the bottom, then as it shoots up the other side it loses all of it again. If no friction existed, it would rise again to the same height as the one from which it had started. A simple pendulum, or a child on a swing, also trades height for something with which we could purchase speed, and which later, if the occasion demanded, could be converted back to height. That "something" is called This back and forth trading suggests that perhaps the sum gh + v has a constant value: if one part decreases, the other part must get bigger. Is that sum the energy? Not quite. The effort of getting heavy load up a height If energy is to measure the effort in lifting a load, it should also be proportional to its mass Energy = E = mgh + mv A well-known fact--already hinted at--is that in a system which does not interact with its surroundings, the total energy (denoted here by the letter mgh drops, until at the bottom of the swing the first term is at its smallest and the second reaches maximum. On the upswing the process reverses, and the sequence is repeated for every swing. Both terms in the equation above have names: kinetic energy, the energy of motion. The exact number representing ## Other kinds of energyTextbooks define energy as "the ability to do work" and they define work as "overcoming resistance over a distance". For instance, if W = mgh Dragging that brick a distance W = Fx For the record, work is measured in |

Devices or processes that convert energy from one form (column) to another (row) | ||||||
---|---|---|---|---|---|---|

- | Kinetic | Potential | Heat | Light | Chemical | Electric |

Kinetic | ***** | Pendulum | Rocket Nozzle | Solar sail | Muscles | Electric motor |

Potential | Pendulum | ***** | Steam boiler | x | x | x |

Heat | Friction | x | ***** | Solar heater | Fire | Electric stove |

Light | x | x | Lightbulb, Sun | ***** | Firefly light | Light emitting diode |

Chemical | x | x | Quicklime kiln | Green plants | ***** | Car battery |

Electric | Windmill power | Hydroelectric power | Thermocouple | Solar Cell | Flashlight battery | ***** |

. | Bar | 100 gr. |

Energy Kj | 885 | 2300 |

..........Kcal | 210 | 550 |

Protein | 2.7 gr | 7.1 |

Carbohyd. | 20.8 | 53.9 |

Fat | 13.2 | 34.2 |

**Next Stop: #16 Newton and his Laws**

Author and curator: David P. Stern, u5dps@lepvax.gsfc.nasa.gov

Last updated 24 August 1998