Question

$\sf \orange{♡ } \: Question$
Explain Conservative Force as Negative Gradient of Potential Energy (Optional)
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Comment upon the statement in detail :-
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Answer 1

Question

Explain Conservative Force as Negative Gradient of Potential Energy (optional) :-

☆ Concept

When a body is taken from one position to other against a conservative force (such as elastic, gravitational or electrical), then the work done in this process is stored as potential energy in the body (provided no work has been done in overcoming frictional or other dissipating forces). Thus, the difference in the potential energy of a body at two positions is defined as the work done in moving the body from one position to the other in the absence of dissipating forces.

It can be shown that negative work done by the conservative force increases the potential energy of the particle.

$\bf \: F = - \dfrac{dU}{dx}$

i.e the conservative force is given by the negative gradient of potential energy.

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More to know

Conversely, the potential energy may be defined as a function of position whose negative gradient gives the conservative force.

Answer 2

More to know

Conversely, the potential energy may be defined as a function of position whose negative gradient gives the conservative force.

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