Potential energy increases with height in a gravitational field.

When an object is lifted to a greater height within a gravitational field, its potential energy increases. This increase occurs because work is performed against the force of gravity to raise the object to a higher position. The potential energy of an object is directly proportional to its height above a reference point, such as the ground.

The formula for gravitational potential energy is given by

where $PE$ represents potential energy, $m$ denotes the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height above the reference point. This equation illustrates that potential energy increases linearly with height.

The relationship between potential energy and height can also be represented graphically. In a graph of potential energy versus height, the resulting line is straight with a positive slope. The slope of this line indicates the strength of the gravitational field, which is defined as the force per unit mass exerted by gravity. A steeper slope corresponds to a stronger gravitational field.

Comprehending how potential energy varies with height is crucial in various physics applications, including the design of roller coasters and the calculation of the energy required to lift objects to different elevations.