How is gravitational potential energy calculated?

Gravitational potential energy is calculated using the formula E_potential = mgh, where E_potential represents the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of the Earth), and h is the height of the object above a reference point, typically the ground or the lowest point in a given context.

This equation reflects the concept that the energy stored in an object due to its position in a gravitational field depends directly on both its mass and its height. As the height increases, the gravitational potential energy also increases proportionally. The acceleration due to gravity remains constant near the surface of the Earth for most practical applications, making this equation very useful for calculating changes in potential energy in various scenarios, such as lifting heavier objects or understanding the energy transformations involved in falling bodies.

Other potential formulas listed do not correctly represent gravitational potential energy. For instance, the first option lacks the height factor entirely, and the third option introduces an incorrect coefficient. Therefore, using mgh provides a comprehensive and accurate means to compute gravitational potential energy in a gravitational field.