Question

A cyclist comes to skidding stop in 10m. During this process, the force on the cycle due to the road is 200 N and is directly opposed 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?

• A. -2000 J,2000J
• B. -2000 J,1000 J
• C. 0J,2000J
• D. -2000 J,0 J

Answer 1

Answer: (D)

=10m,ForceF=200N

$\text{Step 1: Work done on the cycle by road:}$

The force acting on the cycle by the road opposes the motion and thus angle between force and displacement will be ${180}^0$

$F=200N$

$d=10$

Work done on the cycle by road $W=F.d\cos \theta =200\times 10\cos \left({180}^0\right)=-2000J$

$\text{Step 2: Work done on the road by cycle :}$

The corresponding displacement in the road is zero (Road is at rest)

Work done on the road by cycle = F×0 = 0J

Hence, option D is correct.

[Note: The force acting on the road by the cycle will have the same magnitude as that of the force acting on the cycle by the road but will be opposite in direction.

Fc→r=20