Question

Can the normal force on an object ever do work? Explain.

Short answer

Yes, the normal force can do work on an object.

Step-by-step solution

Meaning of normal force

Normal force may be described as the kind of force exercised upon a body that is in connection with another stable body.

It is also known as the support force and always acts perpendicular to the body's contact surface.

Formula for work done

The expression for work done is given by:

$W=Fd\cos \theta$

Here, $F$ is the applied force and $d$ is the displacement.

The value of the work done by the normal force will be zero if the angle between the displacement vector and the normal force vector is 90°.

Condition when a normal force can do work on an object

If the normal force has one of its components in the direction of the object’s displacement, then it can do work on an object. If a person jumps up in the air, in such a situation, the force vector and displacement vector share the same direction.

Thus, the floor pushing the person in the upward direction would do positive work.

Furthermore, the force vector and displacement vector act in the opposite direction when the person hits the floor. The force of the floor is pushing upward, and the displacement of the person is downward directed; the normal force does negative work in this case.