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Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to U: Wherever the force is zero, its potential energy is defined to be zero as well. Whenever the force does work, potential energy is lost.
The kinetic energy of the system is: = (˙ + ˙) where is the mass of the bobs, is the length of the strings, and , are the angular displacements of the two bobs from equilibrium. The potential energy of the system is: E p = m g L ( 2 − cos θ 1 − cos θ 2 ) + 1 2 k L 2 ( θ 2 − θ 1 ) 2 {\displaystyle E_{\text{p}}=mgL(2-\cos ...
The total energy is given by the sum of the kinetic and potential energies = + and the Lagrangian by their difference =. The total energy is conserved in a mathematical pendulum, so time t {\displaystyle t} dependence of the potential E P O T {\displaystyle E_{\mathrm {POT} }} and kinetic E K I N {\displaystyle E_{\mathrm {KIN} }} energies is ...
The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is ...
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 ...
The quantum pendulum is fundamental in understanding hindered internal rotations in chemistry, quantum features of scattering atoms, as well as numerous other quantum phenomena. Though a pendulum not subject to the small-angle approximation has an inherent nonlinearity, the Schrödinger equation for the quantized system can be solved relatively ...
Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, the internal energy contained within a ...
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 ...
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