Question

A cyclist comes to a skidding stop in ${{10 m}}$. 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?

Answer 1

Hint: First of all find the angle between the stopping force and the displacement. As the value of force and displacement are given. Substitute these values in the formula for work done, ${{W = Fd cos\theta }}$ and evaluate the values for work done on the cycle and work done on the road.

Complete step by step solution:
(A) Given: Stopping force (frictional force), ${{F = 200 N}}$
Stopping distance (due to skidding), ${{d = 10 m}}$
Formula for work done by a constant force is given by
${{W = Fd cos\theta }}$
Here, the angle between the stopping force and the displacement, ${{\theta = 18}}{{{0}}^{{0}}}$
On substituting the values in above formula, we get
$
  {{W = 200}} \times {{10 cos (18}}{{{0}}^0}) \\
   \Rightarrow {{W = 2000 \times ( - 1)}} \\
  \therefore {{W = - 2000 J}} \\
 $
Therefore, work done by the road on the cycle is ${{ - 2000 J}}$.
Here, the negative sign indicates that the applied force is in the opposite direction to the motion.

(B) An equal and opposite force acts on the road due to the cycle from Newton’s third law of motion. Thus, force is ${{200 N}}$. Well, the road does not undergo any displacement. Therefore, work done by the cycle on the road is zero.
Thus, Work done on the cycle by the road is ${{ - 2000 J}}$ and work done by the cycle on the road is ${{0 J}}$.

Note: It is advised to drive slowly in wet or icy conditions. In actual, skid occurs when there isn’t appropriate friction between the vehicle’s tyre and the road. Skidding occurs during driving in icy (wet) conditions or during high speed. So, drive slowly in wet or icy conditions. As a direct result of skidding, many motorcyclists who get into serious accidents can end up facing severe injuries. If someone comes into contact with the road and their skin is uncovered, there is no protective layer to keep them safe. This can result in great loss of money and health.