Chapter 11, Problem 78A

To determine

To explain:The comparison of the stopping distance of two skaters.

Answer to Problem 78A

The heavier person among the skaters, will have the longer stopping distance in comparison with the lighter skater.

Explanation of Solution

Given:

Two skaters have unequal masses. But the speed in same of both the skaters.

Formula used:

The expression for the work done $\left(W\right)$ is,

$W=Fd$

Consider two skaters A and B of unequal mass moving with same speed and in same direction.

Consider the friction force acting on each skater A and B are the same.

The work done by the skater is the product of the frictional force $\left(F\right)$ and the stopping distance of the skater $\left(d\right)$ .

The work done will be,

$W=Fd$

The kinetic energy $\left(K.E\right)$ of the skater is dissipated by negative work done by the skater.

$\begin{array}{l}W=-K.E\\ Fd=-\frac{1}{2}mv\\ d=-\frac{1}{2F}mv\end{array}$

The velocity $\left(v\right)$ and frictional force $\left(F\right)$ of the two skaters are equal.

The stopping distance $\left(d\right)$ of the two skaters A and B depends on their mass. The heavier the mass of the skater more will be the stopping distance of the skater.

Conclusion:

Thus, the heavier person among the skaters, will have the longer stopping distance.