Kinetic and Potential Energy: What's the Difference

The energy of movement

A body in motion holds kinetic energy, and it holds it because it is moving. HyperPhysics, the teaching collection of Georgia State University, calls it the energy associated with movement, and adds that making a body acquire it means doing work on it: applying a force that sets it going or speeds it up. Physics textbooks call that link between work and energy gained the work-energy theorem, or the work-energy principle. It runs in both directions, since a moving object can in turn do work on whatever it strikes, shoving it or denting it. The formula taught at school, reported by OpenStax, is KE = ½ m v², where m is the mass and v the speed, and it holds while the speed stays far below the speed of light, the territory of classical mechanics. Double the speed, then, and the kinetic energy becomes four times as large.

Practical example: a car travelling at twice the speed carries four times the kinetic energy with it. That is one of the reasons high-speed crashes do so much more damage, because all of that energy has to be dissipated in the impact.

Energy that depends on position

Potential energy is measured on position instead. The University of Oregon, in the glossary of its Earth Sciences department, describes it as energy stored in the arrangement of a system’s parts: a squeezed or stretched spring holds more of it than one left alone, and a steel ball lifted off the floor holds more than once it has landed. That is why the word system keeps coming up, and why the quantity is not pinned on one isolated body. The form studied most at school is gravitational potential energy, which OpenStax presents as the energy stored in the object-Earth system when the object is carried up to a certain height, and which depends on the distance between the two bodies that gravity pulls towards each other. The formula is PE = m g h, with m the mass, g the acceleration of gravity and h the height, and the change in potential energy grows in proportion to each of the three.

The potential energy of a system follows only from the starting arrangement and the finishing one, never from the journey travelled in between. Gravity is a conservative force, and this is one of their traits.

The two energies side by side

The sum of the two has a name of its own. HyperPhysics calls it total mechanical energy, meaning kinetic energy plus potential energy, and OpenStax adds the condition that makes the quantity useful when solving problems: if only conservative forces act, as gravity does when friction is negligible, that total stays the same over time. This is why the two energies are studied as a couple, and the Recap on work, energy and the conservation of mechanical energy follows that balance step by step. The forces that enter these balances, for that matter, are the same ones described by Newton’s three laws of motion.

Practical examples

Every textbook starts from a descent. When a body comes down and friction is negligible, OpenStax writes, the fall in its potential energy matches the rise in its kinetic energy exactly: on a roller coaster the energy gained while climbing to the top shows up as speed at the bottom, and the same thing happens to a swing on its way back down.

Practical example: anyone who jumps from a height reaches the ground with a kinetic energy equal to the potential energy they held at the start. This is why bending the knees on landing changes things, since that energy has to end up somewhere and the legs absorb it over a longer distance.

Even small amounts of potential energy come out as real numbers. OpenStax works out almost 5 joules for a half-kilo weight raised by one metre, like the weights of a cuckoo clock, which hand that energy back as they descend.

From the dam to the power grid

The large-scale example is the water behind a dam, and the University of Oregon traces the chain: water held high up has potential energy, coming down through the turbines that energy becomes kinetic, and the turbines convert it into electrical energy, with part of the amount escaping as heat. The electrical energy is then the same energy that reaches homes in the form of electric current. The same accounting between position and movement comes back in the study of the orbits of the solar system.