Chapter 6.2, Problem 12PP

To determine

The centripetal acceleration of the runner and the agent which exerts the centripetal force on the runner.

Answer to Problem 12PP

The centripetal acceleration of the runner is $3.097{\text{ m/s}}^2$ .

Force of friction of the track which is acting on the shoes of the runner is responsible for centripetal force on the runner.

Explanation of Solution

Given:

Speed of the runner $v=8.8\text{ m/s}$

Radius of the curve, $r=25\text{m}$

Formula used:

Centripetal acceleration:

  $a_c=\frac{v^2}{r}$

Here, v is velocity and r is the radius.

Calculation:

Now, put the value of v and r and solve:

  $\begin{array}{l}{a}_c=\frac{{8.8}^2}{25}\\ =3.097{\text{ m/s}}^2\end{array}$

Conclusion:

Therefore, the centripetal acceleration of the runner is $3.097{\text{ m/s}}^2$ .

Force of friction of the track which is acting on the shoes of the runner is responsible for centripetal force on the runner.