Kinetic energy
Kinetic energy is a fundamental concept in physics describing the energy an object possesses by virtue of its motion. Every moving body, whether a particle, a vehicle, or a planet, carries kinetic energy that depends on its mass and speed. In classical mechanics this energy is expressed through a simple mathematical relationship, while developments in relativity and quantum mechanics have refined the concept for extreme speeds and microscopic scales.
Historical Background and Conceptual Origins
The term kinetic derives from the Ancient Greek kinesis, meaning movement, and has long been associated with theories of motion. The broad distinction between kinetic and potential energy can be traced to Aristotle’s differentiation between actuality and potentiality, illustrating that ideas surrounding motion and stored energy have deep philosophical roots.
The foundations of kinetic-energy theory emerged during the seventeenth and eighteenth centuries. Gottfried Leibniz and Johann Bernoulli developed the principle that mv²—the vis viva or “living force”—is conserved in mechanical processes. They argued that this quantity better represented the effect of motion than linear momentum alone. The Dutch physicist Willem ’s Gravesande provided key experimental evidence in 1722, demonstrating that objects dropped into clay penetrated to depths proportional to the square of their speed. This finding supported the view that kinetic energy increases rapidly with velocity.
Émilie du Châtelet gave a clear theoretical explanation of these results, reinforcing the importance of the v² term in describing dynamical processes. By the nineteenth century, the modern concept of kinetic energy began to take shape. Thomas Young used the term energy in its present scientific sense in an 1802 lecture to the Royal Society. Gaspard-Gustave Coriolis later formalised the mathematical description of the work done by moving bodies in his 1829 paper Du Calcul de l’Effet des Machines. The expression kinetic energy is credited largely to William Thomson (later Lord Kelvin), who employed it between 1849 and 1851. William Rankine, who introduced potential energy in 1853, also adopted the terminology that distinguished between energy of activity (kinetic) and energy of configuration (potential).
Overview of Energy Forms
Energy appears in numerous forms, including chemical, thermal, electrical, gravitational, elastic, nuclear, and rest energy. These forms broadly fall into two categories: potential energy, associated with the position or configuration of a system, and kinetic energy, associated with motion. Energy can neither be created nor destroyed; it can only be transferred or transformed from one form to another.
Kinetic energy offers abundant examples of such transformations. A cyclist converts the chemical energy of food into muscular work, increasing the speed of the bicycle and thus accumulating kinetic energy. As the cyclist ascends a hill, this kinetic energy is gradually converted into gravitational potential energy. When descending, some of this potential energy is reconverted into kinetic energy; however, frictional losses in the tyres, gears, and air resistance convert part of the energy into heat. Alternatively, a dynamo attached to the wheel converts some of the cyclist’s kinetic energy into electrical energy.
Kinetic energy is also central in orbital mechanics. Spacecraft expend chemical energy to achieve high orbital speeds. In a circular orbit the kinetic energy remains effectively constant, although it becomes dramatically apparent during atmospheric re-entry when much of it is transformed into heat. In elliptical or hyperbolic trajectories kinetic and potential energy continually exchange; highest speed occurs at the point of closest approach to the central body.
Classical Description of Kinetic Energy
In classical mechanics the kinetic energy of a non-rotating body of mass m moving with speed v is
Ek=12mv2.E_{\text{k}} = \frac{1}{2} mv^{2}.Ek=21mv2.
This relationship shows that kinetic energy increases with the square of the velocity. Doubling the speed results in four times the kinetic energy, a fact with practical consequences: a car travelling twice as fast requires approximately four times the braking distance when decelerated with the same force.
The International System of Units expresses energy in joules, derived from kilograms for mass and metres per second for velocity. For example, an 80-kilogram person travelling at 18 metres per second possesses:
Ek=12×80×182=12 960 J,E_{\text{k}} = \frac{1}{2} \times 80 \times 18^{2} = 12\,960\ \text{J},Ek=21×80×182=12960 J,
which corresponds to 12.96 kilojoules.
Kinetic energy equals the work required to accelerate an object from rest to speed v. Equivalently, it represents the work the object can perform while being brought to rest. Work is computed as the force applied in the direction of motion multiplied by the displacement through which it acts.
Kinetic energy is further related to momentum p by the expression:
Ek=p22m,E_{\text{k}} = \frac{p^{2}}{2m},Ek=2mp2,
valid for classical, non-relativistic motion. This connection highlights how kinetic energy depends not only on motion but also on the distribution of mass.
Kinetic Energy in Collisions and Transfers
Kinetic energy can be transferred from one object to another. In billiards a cue delivers kinetic energy to the cue ball, which in turn transfers energy to other balls upon collision. Idealised billiard collisions are considered elastic, meaning kinetic energy is conserved. In inelastic collisions, some kinetic energy is transformed into heat, sound, deformation, or other forms, although the total energy of the system remains constant.
Rotational motion also carries kinetic energy, represented in rigid bodies by the expression:
Ek,rot=12Iω2,E_{\text{k,rot}} = \frac{1}{2} I \omega^{2},Ek,rot=21Iω2,
where I is the moment of inertia and ω the angular velocity. Flywheels exemplify the storage of energy in rotational form, providing a practical means of buffering energy supply and demand in mechanical systems.
Relativistic and Quantum Considerations
The classical expression for kinetic energy holds only when the speed of the object is much less than the speed of light. At speeds approaching this limit, relativistic mechanics becomes essential. In special relativity, kinetic energy is derived from the relativistic expression:
Ek=(γ−1)mc2,E_{\text{k}} = (\gamma -1)mc^{2},Ek=(γ−1)mc2,
where γ is the Lorentz factor. This formula reduces to the familiar 12mv2\tfrac{1}{2}mv^{2}21mv2 for everyday velocities but accounts for the immense energy required to accelerate particles to near-light speeds.
On atomic and subatomic scales, quantum mechanics governs particle behaviour. Electrons in atoms exhibit kinetic energy associated with their quantised motion, and phenomena such as tunnelling and discrete energy levels arise from quantum mechanical principles unavailable to classical physics.
Frame of Reference and Observational Dependence
Kinetic energy is not invariant under a change of reference frame. An object at rest relative to one observer may possess substantial kinetic energy from the perspective of another observer in motion. This dependence illustrates that kinetic energy is meaningful only with respect to a chosen frame, although energy conservation holds in all inertial frames when all relevant forms of energy are included.
| Related | |
|---|---|
