Chapter 5, Problem 73A

To determine

Coefficient of kinetic friction between tire and road.

Answer to Problem 73A

Coefficient of kinetic friction ${\mu }_k=0.4$ .

Explanation of Solution

Given:

Mass of car, $m=1200\text{kg}$

Initial velocity, $v_i=14\text{m/s}$

Final velocity, $v_f=0\text{m/s}$

Skid distance, $\Delta d=25\text{m}$

Formula Used:

From Newton’s second law, $F=ma$

Where, $F$ is force, $m$ is mass and $a$ is acceleration

Calculation:

The free body diagram of car after brake applied is,

  

From free body diagram,

  $F_N=mg$ and as force is acting opposite to direction of motion so,

  $\begin{array}{l}-F_f=ma\\ -{\mu }_k{F}_N=ma\left(\because F_f={\mu }_k{F}_N\right)\\ -{\mu }_{k}mg=\frac{m\left(v_f{}^2-v_i{}^2\right)}{2\Delta d}\left(\because a={\frac{v^2-u}{s}}^2\right)\\ \Rightarrow {\mu }_k=\frac{v_i{}^2}{2\Delta dg}\left(\because v_f=0\right)\end{array}$

On putting the values,

  $\begin{array}{l}{\mu }_k=\frac{{14}^2}{2\times 25\times 9.8}\\ \Rightarrow {\mu }_k=0.4\end{array}$

Conclusion:

Therefore, the coefficient of kinetic friction between tires and the road is ${\mu }_k=0.4$ .