PlanetPhysics/1D Example of the Relation Between Force and Potential Energy

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For a simple one dimensional example of the relationship between force and potential energy, assume that the potential energy of a particle is given by the equation

The relationship between force and potential energy is

For our 1D example, where the potential energy is dependent only on the position,

Taking the derivative yields

Therefore, the force on the particle is governed by the equation

If we further assume that the constant C is so much larger than x, the force will simplify. Rearranging to get

Because , , we get

Further simplifying gives the force under this assumption