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Branches Tags. Could not load branches. Could not load tags. Latest commit. Git stats 43 commits. Failed to load latest commit information. View code. Keenetic SDK Step 1. In relativistic mechanics , this is a good approximation only when v is much less than the speed of light. The standard unit of kinetic energy is the joule , while the English unit of kinetic energy is the foot-pound. The dichotomy between kinetic energy and potential energy can be traced back to Aristotle 's concepts of actuality and potentiality.
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. The terms kinetic energy and work in their present scientific meanings date back to the midth century.
Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis , who in 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.
Energy occurs in many forms, including chemical energy , thermal energy , electromagnetic radiation , gravitational energy , electric energy , elastic energy , nuclear energy , and rest energy. These can be categorized in two main classes: potential energy and kinetic energy. Kinetic energy is the movement energy of an object.
Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen 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, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top.
The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction.
Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat.
Like any physical quantity that is a function of velocity, 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. 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. If the orbit is elliptical or hyperbolic , then throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance.
Disregarding loss or gain however, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another. In the game of billiards , the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it.
Collisions in billiards are effectively elastic collisions , in which kinetic energy is preserved. In inelastic collisions , kinetic energy is dissipated in various forms of energy, such as heat, sound and binding energy breaking bound structures. Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is also stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation.
However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale , quantum mechanical effects are significant, and a quantum mechanical model must be employed. 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 depends on the mass of the body as well as its speed.
In formula form:. In SI units, mass is measured in kilograms , speed in metres per second , and the resulting kinetic energy is in joules. 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. 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. As a consequence of this quadrupling, it takes four times the work to double the speed. The kinetic energy of an object is related to its momentum by the equation:. 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. 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.
Different observers moving with different reference frames would however 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. This minimum kinetic energy contributes to the invariant mass of the system as a whole. The work W done by a force F on an object over a distance s parallel to F equals.
Using Newton's Second Law. The work done in accelerating a particle with mass m during the infinitesimal time interval dt is given by the dot product of force F and the infinitesimal displacement d x. However, also see the special relativistic derivation below.
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. Assuming the object was at rest at time 0, we integrate from time 0 to time t because the work done by the force to bring the object from rest to velocity v is equal to the work necessary to do the reverse:.
This equation states that the kinetic energy E k 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. A system of bodies may have internal kinetic energy due to the relative motion of the bodies in the system. For example, in the Solar System the planets and planetoids are orbiting the Sun. In a tank of gas, the molecules are moving in all directions.
The kinetic energy of the system is the sum of the kinetic energies of the bodies it contains. A macroscopic body that is stationary i. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However, all internal energies of all types contribute to a body's mass, inertia, and total energy. In fluid dynamics , the kinetic energy per unit volume at each point in an incompressible fluid flow field is called the dynamic pressure at that point.
The speed, and thus the kinetic energy of a single object is frame-dependent relative : it can take any non-negative value, by choosing a suitable inertial frame of reference. 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.
In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's invariant mass , which is independent of the reference frame. The total kinetic energy of a system depends on the inertial frame of reference : it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass.
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