Kracht en potentiële energie in drie dimensies

The force and potential energy expression can be extended to three dimensions.

Consider a particle moving in three-dimensional space due to a conservative force that is a function of all the three spatial coordinates.

Force along a spatial coordinate can be written as the negative ratio of potential energy change to the displacement along that coordinate. When the displacement is minimal, the ratios become derivatives.

Adding the force along the three spatial coordinates, the net force can be written as the vector sum of partial derivatives of potential energy with respect to each coordinate, multiplied by the corresponding unit vector.

Thus, force in three dimensions can be expressed as the negative of the gradient of the potential energy function.

For verification of the force and potential energy relationship, consider gravitational potential energy. When substituted into the force and energy relationship, expression for gravitational force is obtained.