Question

A bicyclist comes to a skidding stop at 10 m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is:
A. $+ 2000\,{\text{J}}$
B. $- 200\,{\text{J}}$
C. Zero
D. $- 2000\,{\text{J}}$

Answer 1

Examine what really does the work, road or cycle? To do work on the road, the cycle has to move the road by a certain distance as per the expression for work done. The force which acts on the cycle is the force due to friction.

Complete step by step solution:
We know the formula for work done by the force is given as,
$W = fd\cos \theta$
Here, f is the force and d is the distance moved by the force.
Now, we take a close look at our given question. The questions ask us to determine the work done by the cycle on the road. To do work on the road, the cycle has to move the road by a certain distance. But we can see the road never moving, only the cycle skid. Since the distance moved by the road is zero, from the above equation, we have,
$W = \left( {200} \right)\left( 0 \right)\cos \left( {180} \right)$
$\therefore W = 0\,J$
Therefore, the work done by the cycle on the road is zero.

So, the correct answer is option (C).

Additional information:
We can calculate the work done by the road on the cycle as follows,
$W = fd\cos \theta$
Substituting 200 N for f, 10 m for d and $180^\circ$ for $\theta$ in the above equation, we get,
$W = \left( {200} \right)\left( {10} \right)\cos \left( {180^\circ } \right)$
$\therefore W = - 2000\,{\text{J}}$
Therefore, the road does work on the cycle to halt its motion.

Note: While solving these types of questions, students must notice what really does the work. In this case, according to Newton’s third law of motion, the cycle also exerts the same amount of force on the road but it cannot move the road. Note that, when the work done is negative, the motion of the body decelerates.