A car comes to a sliding stop in 5 m. During this process, the force on the car due to road is 100 N and is directed opposite to the motion.
(a) How much work done the road do on the car?
(b) How much work done the car do on the road?

Explanation

(a) The st opping force and displacement make an angle of `180^(@)` with each other `W_(r)=Fdcostheta`
`F=100N,d=5m, cos180^(@)=-1`
(b) An equal and opposite force acts on the road due to the car but road undergoes no displacement.
(a)Work done by the road, `W_(r)=Fd cos theta`
`=100xx5xx(-1)=-500J`
It is this negative, work that brings the car to rest in accordance with W-E theorem
(b) According to Newton's III law, an equal and oposite force acts on the road due to the car i.e., 100 N However the road undergoes no displacement, so, work done on the road by the car is zero.
Note Work done on body A by B not necessarily equzal and opposite to the work done on B by A.