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There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is ...
where is the kinetic energy and is the potential energy. Hooke's law is the potential energy of the spring itself: = where is the spring constant. The potential energy from gravity, on the other hand, is determined by the height of the mass. For a given angle and displacement, the potential energy is:
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is = where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The potential energy of the system is: = ( ) + () where g {\displaystyle g} is the gravitational acceleration , and k {\displaystyle k} is the spring constant . The displacement L ( θ 2 − θ 1 ) {\displaystyle L(\theta _{2}-\theta _{1})} of the spring from its equilibrium position assumes the small angle approximation .
The potential energy within a spring is determined by the equation =. When the spring is stretched or compressed, kinetic energy of the mass gets converted into potential energy of the spring. By conservation of energy, assuming the datum is defined at the equilibrium position, when the spring reaches its maximal potential energy, the kinetic ...
While some of the energy transferred can end up stored as the kinetic energy of acquired velocity, the deformation of component objects results in stored elastic energy. A prototypical elastic component is a coiled spring. The linear elastic performance of a spring is parametrized by a constant of proportionality, called the spring constant.
Assuming that the masses are constant, G is one-half the time derivative of this moment of inertia: = = = = = = =. In turn, the time derivative of G is = = + = = = + = = + =, where m k is the mass of the k th particle, F k = dp k / dt is the net force on that particle, and T is the total kinetic energy of the system according to the v k ...