# How can work be negative?

1. ### Ellipses

17
Hello everyone.

I understand the concept of work in general, but the concept of negative work still somewhat baffles me. One of my main problems is this: according to my textbook, 3 conditions must be met in order for work to be done, and one of them is "at least part of the force must be in the same direction as the displacement."

Well, how can negative work occur if the force in displacement are going in opposite directions?

Thanks for the help!

2. ### cjl

That's a poorly worded condition. I would reword it to say that in order for work to be done, the force must not be normal to the displacement (in other words, the dot product of the force and displacement must be nonzero). It can be in the same direction as the displacement or the opposite direction, so long as it isn't directly perpendicular.

3. ### maverick_starstrider

As has been said, that's not correct. Imagine a force directed in a certain direction and label that direction with an arrow. If the displacement is a 90 degree angle from that arrow (perpendicular) than no work is done. However, if the displacement is, at least a little bit, pointing along OR OPPOSITE to the force arrow than work is done. In the opposite direction case that work is negative. Intuitively you can say that this force is giving energy BACK to the system.

4. ### sarosh

1
Work is done by a particular force. This can be either done by imparting energy to the system or by extracting energy from the system. The former case we say the work done is positive and the latter it is negative.