Gravitational Potential Energy and Work Done

Gravitational Potential Energy (GPE) is the energy an object possesses because of its position in a gravitational field. It quanties the energy stored by lifting an object against the force of gravity.

Defining Potential Energy

The potential energy at a certain height is fundamentally linked to the effort required to place the object at that height from a reference point (usually the ground).

Work Done Against Gravity

To lift an object vertically, one must exert a force to counteract the pull of gravity. The work done ($W$) in lifting an object is calculated as the force applied multiplied by the vertical distance moved.

• The force required to lift the object (ideally at constant velocity) is equal to its weight, which is mass ($m$) times the acceleration due to gravity ($g$), i.e., $F = mg$.
• The vertical distance moved is the height ($h$).
• Therefore, the work done is $W = F \times h = mgh$.
• This work done against the gravitational force is stored in the object as gravitational potential energy ($U$). Hence, $U = mgh$.
• The key aspect is that this work is done specifically against gravity.

Moving the object with constant velocity or along a curved path describes the motion, but the definition of potential energy relies solely on the work done against the conservative force (gravity) over the vertical displacement.

Work done *in the direction of gravity* would mean gravity is doing the work, which decreases potential energy.