# Height from What?

There is a certain ambiguity in the gravitational potential energy expression $E_G=mgh$: where should we measure the height *from*?

Measuring from... | ...the table | ...the | ...the |

$0.6\u{m} \text{ to } 0\u{m}$ | $\BLUE{1.6\u{m}\text{ to } 1\u{m}}$ | $\RED{-0.4\u{m}\text{ to }-1.0\u{m}}$ | |

Initial $E_G$ | $=(5\u{kg})(9.8\u{N/kg}) \mathbf{(0.6m)}$$29\u{J}$ | $=(5\u{kg})(9.8\u{N/kg}) \mathbf{\BLUE{(1.6m)}}$ | $=(5\u{kg})(9.8\u{N/kg}) \mathbf{\RED{(-0.4m)}}$ |

Final $E_G$ | $=(5\u{kg})(9.8\u{N/kg}) \mathbf{(0m)}$0\u{J}$ | $=(5\u{kg})(9.8\u{N/kg}) \mathbf{\BLUE{(1m)}}$ | $=(5\u{kg})(9.8\u{N/kg}) \mathbf{\RED{(-1m)}}$ |

Change in $E_G$ | $0\u{J}-29\u{J}$$-29\u{J}$ | $49\u{J}-78\u{J}$ | $-49\u{J}-(-20\u{J})$ |

In fact all of them *could* be correct. The actual gravitational potential energy of the box is physically irrelevant; it is only changes in potential energy that are important, because those changes are what cause work to be done on objects.

and so long as you are consistent throughout the problem, the physical behavior of the system will remain the same. You might compare this with the choice of the positive *x* and *y* directions when solving a kinematics problem: another person might make a different choice, but you will both describe the same physical phenomenon. One consequence of this fact is that the fact that an object has "zero" gravitational potential energy has no significance whatsoever: that only means that the object is currently located at the height you've chosen as your reference height.