# Can the work by static friction on an object be negative?

We know that static friction acts between two surfaces in contact when they are not moving relative to each other (and when some other force is trying to move one object over the other). This question was inspired by my previous question - Can the work by kinetic friction on an object be zero? where I considered the cases of positive, negative and zero work done by kinetic friction. I did a similar analysis for static friction, and the following points discuss the case of zero and positive work:

• Zero work - Suppose a block is kept on a rough surface. When a small force is supplied the object does not move relative to the surface due to the static friction force supplied by the surface on the block which is equal and opposite to the applied force. Here, since the displacement is zero, the work done by either of the two forces (static friction or applied force) is zero.

• Positive work - The work done by static friction on an object moving along with (without slipping) an accelerating belt is positive with respect to the ground frame as the displacement and the friction force act along the same direction (along the direction of acceleration).

But, I'm unable to think of cases when the work done by static friction is negative. Is it possible for static friction to do negative work? If not, kindly specify the reason behind it.

Please note: I've read the answers for the following questions but none of them discuss the case of negative work done by static friction.

• Just change the belt from accelerating to decelerating. – BowlOfRed Nov 17 '19 at 6:39

## 3 Answers

Yes. Take your example of positive work. The reason that the amount of work done on the block is positive is that the force on the block is in the same direction as the block's motion. But the frictional force on the belt by the block is in the opposite direction of the belt's motion, and therefore the work done on the belt is negative.

If the belt is decelerating then static friction will be opposite to the motion of object and will do negative work. The free-body diagrams of both the blocks are shown below. Work done by static friction on A is positive and on B is negative and the examples you gave clearly depict that work done by static friction can be zero, positive or negative.