To calculate the work done in moving a mass within a gravitational field, we utilize the formula:

When a mass is displaced in a gravitational field, work is performed against the force of gravity. The total work done is equal to the force exerted multiplied by the distance moved in the direction of that force. For an object in a gravitational field, the force corresponds to its weight, which can be expressed with the equation:

Here, $m$ represents the mass of the object and $g$ denotes the acceleration due to gravity.

The work done in moving the object a vertical distance $h$ against the gravitational force is thus given by:

This equation indicates that the work performed is directly proportional to the mass of the object, the height it is raised, and the strength of the gravitational field.

It is crucial to understand that the work done in displacing an object within a gravitational field depends solely on its initial and final positions, independent of the specific path taken between these two points. This characteristic arises because gravity is a conservative force, meaning that the net work done in moving an object along a closed path is always zero.

In summary, to determine the work done in moving a mass in a gravitational field, we apply the formula:

where $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height to which the object is lifted.