Kinetic+Energy

The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.



The adjective kinetic has its roots in the Greek word κίνησις (kinesis) meaning motion.

The principle in classical mechanics that E ∝ mv² was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force, vis viva. Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Willem 's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation.

The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term "kinetic energy" c. 1849–51.

Kinetic energy of rigid bodies
In [|classical mechanics], the kinetic energy of a //point object// (an object so small that its mass can be assumed to exist at one point), or a non-rotating [|rigid body] , is given by the equation where is the mass and  is the speed (or the velocity) of the body. In [|SI] units (used for most modern scientific work), mass is measured in [|kilograms], speed in metres per [|second] , and the resulting kinetic energy is in [|joules]. For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as //E////k// = (1/2) · 80 · 182 J = 12.96 kJ  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. The kinetic energy of an object is related to its [|momentum] by the equation: where: is momentum is mass of the body For the //translational kinetic energy,// that is the kinetic energy associated with rectilinear motion, of a [|rigid body] with constant [|mass], whose [|center of mass] is moving in a straight line with speed , as seen above is equal to where: is the mass of the body is the speed of the [|center of mass] of the body. The kinetic energy of any entity depends on the reference frame in which it is measured. However the total energy of an isolated system, i.e. one which energy can neither enter nor leave, does not change in whatever reference frame it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the [|Oberth effect]. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames disagree on the value of this conserved energy. 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, i.e. the reference frame in which the total momentum of the system is zero. This minimum kinetic energy contributes to the [|invariant mass] of the system as a whole.

[ [|edit] ] Derivation
The work done accelerating a particle during the infinitesimal time interval //dt// is given by the dot product of //force// and //displacement//: where we have assumed the relationship **p** = //m// **v**. (However, also see the special relativistic derivation [|below] .) Applying the [|product rule] we see that: Therefore (assuming constant mass), the following can be seen: Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call the result kinetic energy: This equation states that the kinetic energy (//Ek//) is equal to the [|integral] of the [|dot product] of the [|velocity] (**v**) of a body and the [|infinitesimal] change of the body's [|momentum] (**p**). It is assumed that the body starts with no kinetic energy when it is at rest (motionless).