Potential energy is directly proportional to both the height of an object above the ground and its mass.

In physics, potential energy refers to the energy stored in an object due to its position relative to other objects, internal stresses, electric charges, or various other factors. The most commonly encountered type of potential energy is gravitational potential energy. This energy is associated with an object’s position within a gravitational field, typically defined in relation to its height above the ground.

The formula for gravitational potential energy is given by:

where

• $PE$ represents potential energy,
• $m$ is the mass of the object,
• $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$ on Earth), and
• $h$ is the height of the object above the ground.

This equation illustrates that potential energy is directly proportional to both the mass of the object and its height. Consequently, if either the mass or the height is doubled, the potential energy will also double.

For instance, if you lift a $1 \, \text{kg}$ object to a height of $1 \, \text{m}$ above the ground, it will possess a potential energy of $9.8 \, \text{joules}$ (calculated as $1 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 1 \, \text{m} = 9.8 \, \text{joules}$). If you raise the same object to a height of $2 \, \text{m}$, its potential energy will double to $19.6 \, \text{joules}$. Similarly, if you lift a $2 \, \text{kg}$ object to a height of $1 \, \text{m}$, its potential energy will also be $19.6 \, \text{joules}$.

It is crucial to understand that potential energy is a form of stored energy. It represents the work done in raising the object to a specific height against the force of gravity. When the object is released, this stored energy transforms into kinetic energy as the object accelerates toward the ground. This phenomenon exemplifies the principle of conservation of energy, which states that energy cannot be created or destroyed; it can only be transferred or transformed from one form to another.