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Define potential energy. Derive an expre...

Define potential energy. Derive an expression for the potential energy of a body of mass m, at a height h above the surface of the Earth.

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Suppose a body of mass m is raised to a height h above the surface of the ground as shown in figure. The force applied just to overcome the gravitational attraction is
`F = m xx g " " . . . (ii)`
where g = acceleration due to gravity

As the distance moved is in the direction of the force applied, work is said to be done. The object gains energy equal to the work done on it. Let the work done on the object against gravity by W,so
Work done = Force ` xx` Displacement
`W = F xx h " ". . . (ii)`
Substituting the value of F from eqn (i) in eqn. (ii) we get
`W = m xx g xx h`
This work gets stored up in the body as gravitational potential energy . Thus,
Work done on the object against gravity = Gravitational potential energy
Gravitational potential energy (P.E) ` = m xx g xx h`
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