Kinetic energy is the energy of mass in motion. The kinetic energy of an object is the energy it has because of its motion.

In Newtonian (classical) mechanics, which describes macroscopic objects moving at a small fraction of the speed of light, the kinetic energy (*E*) of a massive body in motion can be calculated as half its mass (*m*) times the square of its velocity (*v*): *E = ½mv**2*. Note that energy is a *scalar* quantity, i.e., it does not depend on direction, and it is always positive. When we double the mass, we double the energy; however, when we double the velocity, energy increases by a factor of four.

## Get to work

Perhaps the most important property of kinetic energy is its ability to do *work*. Work is defined as force acting on an object in the direction of motion. Work and energy are so closely related as to be interchangeable. While energy of motion is usually expressed as *E* = ½*mv*^{2}, work (*W*) is more often thought of as force (*F*) times distance (*d*): *W* = *Fd*. If we want to change the kinetic energy of a massive object, we must do work on it.

For example, in order to lift a heavy object, we must do work to overcome the force due to gravity and move the object upward. If the object is twice as heavy, it takes twice as much work to lift it the same distance. It also takes twice as much work to lift the same object twice as far. Similarly, to slide a heavy object across a floor, we must overcome the force of friction between the object and the floor. The work required is proportional to the weight of the object and the distance it is moved. (Note that if you are carrying a piano on your back down a hallway, you are not actually doing any real work.)

## Potential energy

Kinetic energy can be stored. For example, it takes work to lift a weight and place it on a shelf or to compress a spring. What happens to the energy then? We know that energy is conserved, i.e., it cannot be created or destroyed; it can only be converted from one form to another. In these two cases, the kinetic energy is converted to *potential* energy because while it is not actually doing work, it has the potential to do work. If we drop the object from the shelf or release the spring, that potential energy is converted back into kinetic energy.

Kinetic energy can also be transferred from one body to another in a collision, which can be *elastic* or *inelastic*. One example of an elastic collision would be one billiard ball striking another. Ignoring the friction between the balls and the table or any spin imparted to the cue ball, ideally the total kinetic energy of the two balls after the collision is equal to the kinetic energy of the cue ball before the collision.

An example of an inelastic collision might be a moving train car bumping into a similar stationary car and coupling to it. The total energy would remain the same, but the mass of the new system would be doubled. The result would be the two cars continuing in the same direction at a lower speed such that *mv*_{2}^{2} = ½*mv*_{1}^{2}, where *m* is the mass of one car, *v*_{1} is the velocity of the first car, and *v*_{2} is the velocity of the coupled cars after the collision. Dividing by *m* and taking the square root of both sides we get *v*_{2} = √2/2∙*v*_{1}. (Note that *v*_{2} ≠ ½*v*_{1}.)

Additionally, kinetic energy can be converted into other forms of energy and vice versa. For example, kinetic energy can be converted into electrical energy by a generator or into thermal energy by the brakes on a car. Conversely, electrical energy can be converted back to kinetic energy by an electric motor, thermal energy can be converted to kinetic energy by a steam turbine, and chemical energy can be converted to kinetic energy by an internal combustion engine.

*Jim Lucas is a freelance writer and editor specializing in physics, astronomy and engineering. He is general manager of **Lucas Technologies**. *