A cyclist comes to a skidding stop in `10m`. During this process, the force on the cycle due to the road is `200N` and is directly opposite to the motion.
a. How much work does the road do on the cycle?
b. How much work does the cycle do on the road?

Explanation

a. The work done on the cycle by the road is the work done by the frictional force exerted by the road on the cycle.
Now, `W=vecF.vecS=F.Scos 180^@`
`=-FS`
`=-200Nxx10m`
`=-2000J`
It is this negative work which brings the cycle to rest. This is clearly in accordance with work-energy theorem.
b. The displacement of the road is zero. So, work done by the cycle on the road is zero.
(According to Newton's third law of motion, an equal and opposite force acts on the road due to the cycle. The magnitude of this force is `200N`).