Answer to Question #97785 in Physics for Nyx

Question

A block of mass m is pushed a horizontal distance D from position A to position B, along
a horizontal plane with friction coefficient µ.
Then the mass is pushed from B to A.
If the horizontal force pushing the mass
from A to B is P~ , and the force pushing the
mass from B to A is −P~ , what is the total
work done by friction?
1. +2 µ m g D
2. −2 µ m g D
3. 2 (P − µ m g) D
4. 2 (µ m g − P) D
5. 0

Answer 1

The work done

$$W=Fd\cos\theta$$

$$W_{AB}=-\mu mgD$$

$$W_{BA}=-\mu mgD$$

So, the total work done by friction

$$W=W_{AB}+W_{BA}=-2\mu mgD$$