Energy is the capacity to do work. An object that can do work is said to possess energy, and the more work it can do, the more energy it has. Because energy is measured by the work it can perform, it has the same SI unit as work, the joule (J). Energy comes in many forms — mechanical, heat, light, sound, chemical, electrical and nuclear. In this chapter we focus on mechanical energy, which is the sum of two kinds: kinetic energy and potential energy.
Kinetic energy is the energy an object possesses because of its motion. A moving cricket ball can knock down stumps, flowing water can turn a turbine, and wind can drive a windmill — all because moving objects carry kinetic energy. The kinetic energy of an object of mass $m$ moving with speed $v$ is:
$E_k=\frac{1}{2}mv^2$
Notice that kinetic energy depends on the square of the speed. If the speed doubles, the kinetic energy becomes four times as large; if it triples, the energy becomes nine times as large. This is why high-speed collisions are so much more dangerous than slow ones.
The work–energy theorem connects work and kinetic energy: the work done by the net force on an object equals the change in its kinetic energy. In symbols, $W=\Delta E_k=\frac{1}{2}mv^2-\frac{1}{2}mu^2$, where $u$ is the initial speed and $v$ the final speed. If you do positive work on a body it speeds up; if friction does negative work it slows down.
Potential energy is the energy stored in an object because of its position or configuration. A stone held high above the ground, a stretched rubber band, and a wound-up spring all store potential energy that can later be released to do work. The most common type at this level is gravitational potential energy — the energy a body has due to its height above the ground.
When an object of mass $m$ is raised to a height $h$ above a reference level, the work done against gravity is stored as gravitational potential energy:
$E_p=mgh$
where $g$ is the acceleration due to gravity (about $9.8\,\text{m/s}^2$, often taken as $10\,\text{m/s}^2$). The potential energy depends on the height measured from a chosen reference level — usually the ground. Lifting a heavier object, or raising it higher, stores more potential energy, which is why water stored high in a dam can generate so much electricity.