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Potential energy for near Earth gravity

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For small height changes, gravitational potential energy can be computed using U g = m g h , {\displaystyle U_{g}=mgh,} where m is the mass in kg, g is the local gravitational field (9.8 metres per second squared on earth), h is the height above a reference level in metres, and U is the energy in joules. In classical physics, gravity exerts a constant downward force F =(0, 0, F z ) on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r (t) = ( x (t), y (t), z (t)), such as the track of a roller coaster is calculated using its velocity, v =( v x , v y , v z ), to obtain W = ∫ t 1 t 2 F ⋅ v d t = ∫ t 1 t 2 F z v z d t = F z Δ z . {\displaystyle W=\int _{t_{1}}^{t_{2}}{\boldsymbol {F}}\cdot {\boldsymbol {v}}\mathrm {d} t=\int _{t_{1}}^{t_{2}}F_{z}v_{z}\mathrm {d} t=F_{z}\Delta z.} where the integral of the vertical...
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Potential energy

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U = ½ · k · x 2(elastic) U = ½ · C · V 2 (electric) U = - m · B (magnetic) In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these ...
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Overview

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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 called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of configurations of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from a potential are also called conservative forces. The work done by a conservative force is W = − Δ U {\displaystyle \,W=-\Delta U} w...
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