7.13: Work Done by Gravity

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.

Like other forces, gravity does work on an object if it displaces it toward the Earth's center. In this case, the work done by gravity is said to be positive. If an external force acts on the object against the pull of gravity and manages to lift it away from the Earth's center, work is done against gravity. In this case, the net work done is said to be negative. If an object moves along the Earth and has no displacement toward or away from the Earth's center, then no work is done by or against gravity.

Of course, no object on Earth is a particle. The center of mass framework developed in studying composite objects bypasses this problem. A single particle of mass equal to the object's total mass can be considered to be present at the object's center of mass before considering the effect of external forces, including gravity.

When an object is thrown upward, the gravitational force acts against its displacement.

So, the work done by the gravitational force is the dot product of the gravitational force and displacement vectors.

Since these vectors point in opposite directions, the work done is negative.

The gravitational force does work on the object by transforming the objects' kinetic energy to potential energy.

After reaching the maximum height, the object falls back. The gravitational force acts  in the direction of the displacement, and the work done is positive.

Suppose an object is lifted, both the applied force and the gravitational force do work on the object.

The net work done on the object is given by the work-energy theorem.

If the object is stationary before and after a lift, the net change in kinetic energy is zero.

So, the work done by applied force is negative of the work done by the gravitational force.