E = mc²

"E" stands for energy measured in Joules. "Joules" are abbreviated with a capital "J" -because it is named after James Prescott Joules. "m" is the mass measured in kilograms. "c" is the speed of light measured in m/s. The speed of light is 3.0 x 10⁸ m/s. (This about 186,000 miles/second.) This formula defines the amount of energy stored in any body with mass. In other words, if you annihilated a 1 kilogram body, then it will release (3.0 x 10⁸)² Joules of energy. ("Annihilation" means nothing is left behind.) This is 90,000,000,000,000,000 Joules of energy. This is a huge amount of energy.(A chocolate candy bar is about 1000 J.) So why don't we all explode when we burn a log. When a log is burned it is not annihilated. Evidence of this is because after the log burns, it leaves behind ashes and smoke. Also, when it burns, it does burn in one instant in time. E = mc² represents the energies associated with the forces that hold molecules and atoms together. It does not represent a form of mechanical energy, so it will not be an energy of importance in this chapter. But you should know about it because it is the most famous energy formula.

EXAMPLE

There is only one form of kinetic energy, but there are many forms of potential energy. For example there is a potential energy stored in the gravitational field. If you lift a body up, then you are putting energy in the body. Anytime a body is lifted higher than it was earlier then is has potential energy. Physicists refer to gravitational potential as energy of position or energy of height. A body has zero potential when it is as the lowest height of its motion. It has the most at the highest point of its motion. Where the potential energy equal to "zero" is a relative thing. What is the same about each of the potential energies in the two animations?

Potential energy due to gravity is determined by the folowing math expression:

Example

Question Solution In a pinewood derby contest, a contestant's vehicle starts at the top of a ramp that is 4.0 meers long and placed at a 30 degree angle with the floor. If an entry has a mass of 0.140 kg , then what is the car's potential energy compared to the floor's height?   In a pinewood derby contest, a contestant's vehicle starts at the top of a ramp that is 4.0 meers long and placed at a 30 degree angle with the floor. If an entry has a mass of 0.140 kg , then what is the car's potential energy compared to the floor's height? Notice that the potential energy is zero at the lowest height.