Kinetic energy
The adjective kinetic has its roots in the Greek word kinesis, meaning motion. This linguistic origin traces back to Aristotle's concepts of actuality and potentiality. The dichotomy between kinetic energy and potential energy can be traced directly to these ancient philosophical ideas. Gottfried Leibniz and Johann Bernoulli developed the principle that energy is proportional to mass times velocity squared. They described this concept as living force or vis viva. Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship in 1722. He dropped weights from different heights into a block of clay. Gravesande determined that their penetration depth was proportional to the square of the impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation. Her work connected the physical observations to mathematical theory.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v equals one half mv squared. The SI unit of energy is the joule, while the English unit of energy is the foot-pound. Mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. One would calculate the kinetic energy of an 80 kg mass traveling at 18 metres per second as 13 kilojoules. When a person throws a ball, the person does work on it to give it speed as it leaves the hand. The moving ball can then hit something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work required to bring it from rest to that speed. Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force.
If a body's speed relative to an inertial frame is a significant fraction of the speed of light, it is necessary to use relativistic mechanics. In relativistic mechanics, energy combines with momentum in a way analogous to the combination of time and space into spacetime. The total energy equals the sum of rest energy plus kinetic energy. At low speeds, the square root can be expanded and the rest energy drops out, giving the Newtonian kinetic energy. If the object is on the atomic or sub-atomic scale, quantum mechanical effects are significant. In quantum mechanics, observables like kinetic energy are represented as operators. The kinetic energy operator appears as a term in the Hamiltonian and is defined in terms of the more fundamental momentum operator. The expectation value of the electron kinetic energy for a system of N electrons described by the wavefunction is a sum of 1-electron operator expectation values. This mathematical framework allows physicists to calculate energy at scales where classical formulas fail completely.
Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. A cyclist transfers chemical energy provided by food to the bicycle and cyclist's store of kinetic energy as they increase their speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction. The chemical energy has been converted into kinetic energy, but the process produces thermal energy within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to gravitational potential energy when coasting up a hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. If the cyclist applies the brakes, the kinetic energy would be dissipated through friction as heat. These scenarios illustrate how energy changes form while remaining conserved in total.
The kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant. For example, a bullet passing an observer has kinetic energy in the reference frame of this observer. The same bullet is stationary to an observer moving with the same velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame unless all the objects have the same velocity. In any other case, the total kinetic energy has a non-zero minimum. This minimum kinetic energy contributes to the system's invariant mass, which is independent of the reference frame. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space. However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat.
In fluid dynamics, the kinetic energy per unit volume at each point in an incompressible fluid flow field is called dynamic pressure. Dividing by V, the unit of volume, yields the formula for dynamic pressure where rho is the density of the incompressible fluid. A. M. Kuethe and J. D. Schetzer published foundational work on aerodynamics that defines these relationships. Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is also stored in rotational motion. The kinetic energy of such systems depends on the choice of reference frame. The reference frame that gives the minimum value of that energy is the center of momentum frame. This minimum kinetic energy contributes to the invariant mass of the system as a whole. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. All internal energies of all types contribute to a body's mass, inertia, and total energy.
Common questions
What is the origin of the word kinetic energy?
The adjective kinetic has its roots in the Greek word kinesis, meaning motion. This linguistic origin traces back to Aristotle's concepts of actuality and potentiality.
Who developed the principle that energy is proportional to mass times velocity squared?
Gottfried Leibniz and Johann Bernoulli developed the principle that energy is proportional to mass times velocity squared. Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship in 1722.
How do you calculate the kinetic energy of an 80 kg mass traveling at 18 metres per second?
One would calculate the kinetic energy of an 80 kg mass traveling at 18 metres per second as 13 kilojoules. The formula for non-rotating objects equals one half mv squared with mass measured in kilograms and speed in metres per second.
When does relativistic mechanics become necessary for calculating kinetic energy?
If a body's speed relative to an inertial frame is a significant fraction of the speed of light it is necessary to use relativistic mechanics. In relativistic mechanics energy combines with momentum in a way analogous to the combination of time and space into spacetime.
What happens to the kinetic energy of a car when its speed doubles?
Since the kinetic energy increases with the square of the speed an object doubling its speed has four times as much kinetic energy. A car traveling twice as fast as another requires four times as much distance to stop assuming a constant braking force.