Kinetic energy Guide, Meaning , Facts, Information and Description
Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. The kinetic energy of a body is equal to the amount of work needed to establish its velocity and rotation, starting from rest.
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2 Heat as kinetic energy 3 See also |
For non-relativistic mechanics, the total kinetic energy of a body can be considered as the sum of the body's translational kinetic energy and its rotational energy, or angular kinetic energy:
If a body is rotating, its rotational kinetic energy or angular kinetic energy is calculated from:
In Einstein's relativistic mechanics, (used especially for near-light velocities) the kinetic energy of a body is:
Relativity theory states that the kinetic energy of an object grows towards infinity as its velocity approaches the speed of light, and thus that it is impossible to accelerate an object to this boundary.
Where gravity is weak, and objects move at much slower velocities than light (e.g. in everyday phenomena on Earth), Newton's formula is an excellent approximation of relativistic kinetic energy.
The next term in the approximation is 0.375 mv4/c², e.g. for a speed of 10 km/s this is 0.04 J/kg, for a speed of 100 km/s it is 40 J/kg, etc.
Equations
Definition
In words the above 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 of the body's momentum (p).Newtonian mechanics
where:
For the translational kinetic energy of a body with mass m, whose centre of mass is moving in a straight line with linear velocity v, we can use the Newtonian approximation:
Thus, for a speed of 10 m/s the kinetic energy is 50 J/kg, for a speed of 100 m/s it is 5 kJ/kg, etc.
where:
Relativistic mechanics
It is an edifying exercise to show that the ratio of this relativistic kinetic energy to the Newtonian kinetic energy given by (1/2)mv2 approaches 1 as v approaches 0, i.e.,
This can be done by the techniques of first-year calculus.Heat as kinetic energy
Heat is a form of energy due to the total kinetic energy of molecules and atoms of matter. The relationship between heat, temperature and kinetic energy of atoms and molecules is the subject of statistical mechanics. Heat is more akin to work in that it represents a change in internal energy. The energy that heat represents specifically refers to the energy associated with the random translational motion of atoms and molecules in some identifiable matter within a system. The conservation of heat and mechanical work form the first law of thermodynamics.