Question

When force applied is not in the direction of displacement of an object, is there any work done?

Why work is said to be negative when force is applied opposite to the direction of displacement?

Answer 1

When a body is moving, all forces produce work. It may be negative, positive or null.

Suppose we’re both pushing a huge box from the opposite sides: since you’re probably stronger than me, the box will move in my direction. However, I am still applying a force. My force and the displacement go in opposite directions, so my work is negative.

The same thing happens with friction: it goes against the movement, and it’s a force, so the work it does is negative.

What about putting a book in the top shelf? You’re pushing, and your force is parallel to the displacement (since you push upwards and the book goes up) but gravity is pushing down: it goes against the displacement. Once again, the work is negative.