A particle moves in x-y plane in figure under the influence of a friction force with magnitude `3.00N` and acting in the direction opposite to the particle's displacement. Calculate the work done by the friction force on particle as it moves along the following closed paths: (a) path OA followed by AC and return path AO, (b) path OA followed by AC and the return path CO, (c) path OC followed by the return path CO, and (d) each of your three answers should be non-zero. What is the significant of this observation?

Explanation

Along each step of motion, the frictional force is opposite in direction to the incremental displacement, so in the work `cos 180^@=-1`
a. `W=(3N)(5m)(-1)+(3N)(5m)(-1)=-30.0J`
b. The distance CO is `(5^2+5^2)^(1//2)m=7.07m`
`W=(3N)(5m)(-1)+(3N)(5m)(-1)+(3N)(7.07m)(-1)`
`=-51.2J`
c. `W=(3N)(7.07m)(-1)+(3N)(7.07m)(-1)=-42.4J`
d. The force of friction is a non-conservative force.