How does potential energy change with height in a gravitational field?

Potential energy increases with height in a gravitational field.

As an object is lifted higher in a gravitational field, its potential energy increases. This is because work is done against the force of gravity to lift the object to a higher position. The amount of potential energy an object has is directly proportional to its height above a reference point, such as the ground.

The equation for gravitational potential energy is PE = mgh, where PE is potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. This equation shows that potential energy increases linearly with height.

The change in potential energy with height can also be visualized using a graph. The graph of potential energy against height is a straight line with a positive gradient. The slope of the line represents the gravitational field strength, which is the force per unit mass due to gravity. The steeper the slope, the stronger the gravitational field.

Understanding how potential energy changes with height is important in many areas of physics, such as in the design of roller coasters and the calculation of the energy required to lift objects to different heights.