Question

A cyclist comes to a skidding stop at 10 m. During this process, the force on the cycle due to the road is 200 N and is directly opposite to the motion. Find (a) the work is done by the road on the cycle and (b) the work done by the cycle on the road.
A) $- 2000{\text{J, }}2000{\text{J}}$
B) $- 2000{\text{J, 1}}000{\text{J}}$ by each tyre.
C) $0{\text{J, }}2000{\text{J}}$
D) $- 2000{\text{J, }}0{\text{J}}$

Answer 1

The work done by a force acting on an object depends on the applied force and the displacement it causes. Here the force applied by the road is opposite in direction to the displacement of the cyclist and hence the work done in that case will be negative.

Formula used:
The work done by a force acting on an object is given by, $W = Fd$ where $F$ is the force acting on the object and $d$ is the displacement of the object.

Complete step by step answer:
The force acting on the cycle causes a displacement of the cycle and is given to be $d = 10{\text{m}}$.
The force acting on the cycle by the road opposes the motion and thus will be negative. It is given to be ${F_{r \to c}} = - 200{\text{N}}$.
Then 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 i.e., ${F_{c \to r}} = 200{\text{N}}$.
However, the corresponding displacement in the road is zero.
The work done by the road on the cycle will be
${W_{r \to c}} = {F_{r \to c}}d$-------- (1)
Substituting the values for $d = 10{\text{m}}$ and ${F_{r \to c}} = - 200{\text{N}}$ in equation (1) we get,
$\Rightarrow {W_{r \to c}} = - 200 \times 10 = - 2000{\text{J}}$
Thus the work done by the road on the cycle is ${W_{r \to c}} = - 2000{\text{J}}$.
The work done by the cycle on the road will be ${W_{c \to r}} = {F_{c \to r}}d$-------- (2)
Substituting the values for $d = 0$ and ${F_{c \to r}} = 200{\text{N}}$ in equation (2) we get, ${W_{c \to r}} = 200 \times 0 = 0{\text{J}}$

Thus the work done by the cycle on the road is ${W_{c \to r}} = 0{\text{J}}$. So the correct option is D.

Note:
The force acting on an object may or may not cause a displacement of the object. Here the force acting on the cycle resulted in a displacement of the cycle but the force acting on the road did not cause the road to move. The force on the cycle is frictional in nature and it is what caused the cycle to skid and eventually come to a rest. Hence the mechanical energy of the system will not be conserved.