Potential Energy

So, we've defined kinetic energy as the energy an object possesses due to its motion. However, where might that energy come from? The kinetic energy an object possesses often comes from the object's potential energy.

Potential energy is the energy an object stores due to its position, size, or configuration. For example, imagine

The work done by a conservative force on a system is equal to the potential energy changed to the system. If the work increases, then the potential energy decreases and if the work decreases, the potential energy increases.

If you've ever gone on a diving board in a pool, you've had to climb up a ladder to get to the diving board. Going up can be a struggle and make you tired, causing you to lose energy. Where is this energy going? It turns out that the chemical energy enabling you to function and move is being decreased because the force of gravity pulling you down is doing work on you.

Since gravity is conservative, the change in potential energy is:

When you compress a spring using another object(like a block of wood), you'll notice that the other object will eject from the spring. This means there must be some type of potential energy stored in the spring that is giving rise to the kinetic energy of an object compressed to the spring after releasing.

Most springs follow Hooke's Law, which states that the force exerted by a spring is proportional to the deformation of the spring, given in displacement of the spring.

where k is the spring constant, given in N/m. This is a constant characteristic of all springs that obey Hooke's Law. If the relation between displacement and force for a spring isn't linear, then the spring doesn't obey Hooke's Law. In other words, the spring isn't Hookean. The displacement is the distance that the spring compresses/stretches.

The equation above is the formula for the work done by a spring, also known as the potential energy stored in a spring. It is conservative, as you can differentiate the equation above with respect to x and notice that -1 times the result is Hooke's Law.