# Positive work done by friction

Can work done by friction be positive? Please explain with an example. Is the work done by friction on a moving car positive?

## 2 Answers

Work done by force $\mathbf F$ on a material point whose velocity is $\mathbf v$ is, in the time interval $t_1..t_2$

$$\int_{t_1}^{t_2} \mathbf F\cdot\mathbf v\,dt.$$

This number depends on the velocity of the point. The velocity in turn depends on the frame of reference. There is always a frame of reference where the force and the velocity have the same direction and the work is thus positive.

For example, if you try to pull top sheet off table while dishes still rest on it, the dishes will begin to move as a result of the friction forces from the sheet. The work done by friction on the dishes will be positive.

Yes friction can be a mechanism that transfers energy from one body onto another. For example place a block on rotating disk. Without friction the block is going remain still at the initial position because the contact force will only counter act gravity. Now with friction the block will start moving and the disk will start to slow down. Initially the body is going move tangentially and as it picks up speed it will start moving radially out to. The friction force is going to oppose the relative motion between the block on the disk imposing work on the block.