When an object falls, its gravitational potential energy is changed to kinetic energy. You can use this relationship to calculate the speed of the object’s descent. Gravitational potential energy for a mass m at height h near the surface of the Earth is mgh more than the potential energy would be at height 0. (It’s up to you where you choose height 0.)

For example, say that you lift a 40-kilogram cannonball onto a shelf 3.0 meters from the floor, and the ball rolls and slips off, headed toward your toes. If you know the potential energy involved, you can figure out how fast the ball will be going when it reaches the tips of your shoes. Resting on the shelf, the cannonball has this much potential energy with respect to the floor:


The cannonball has 1,200 joules of potential energy stored by virtue of its position in a gravitational field. What happens when it drops, just before it touches your toes? That potential energy is converted into kinetic energy. So how fast will the cannonball be going at toe impact? Because its potential energy is converted into kinetic energy, you can write the problem as the following:


Plugging in the numbers and putting velocity on one side, you get the speed:


The velocity of 7.7 meters/second converts to about 25 feet/second. You have a 40-kilogram cannonball — or about 88 pounds — dropping onto your toes at 25 feet/second. You play around with the numbers and decide you don’t like the results. Prudently, you turn off your calculator and move your feet out of the way.