Chapter 5, Problem 46P

To determine

To Calculate: The minimum coefficient of static friction between the turtle and the truck bed surface that is needed to prevent the turtle from sliding.

  $0.21$

Given Information:

Mass of the turtle $m=12\text{kg}$

Initial speed $u=55\text{mi/h}$

  $=24.6\text{ m/s}$

Final speed, $v=0$

Time $t=12\text{s}$

Formula Used:

First equation of motion:

  $a=\frac{v-u}{t}$

Calculation:

Let the acceleration be ‘a’

  

Therefore, acceleration

  $\begin{array}{c}a=\frac{v-u}{t}\\ =\frac{0-24.6}{12}{\text{m/s}}^{\text{2}}\\ =-2.05{\text{m/s}}^{\text{2}}\end{array}$

The required force $=ma$

Here, normal reaction, $R=mg$

Frictional force $f_s={\mu }_{s}R$ ( $\mu$ is the co-efficient of static friction)

Condition for the turtle to slide.

  $\begin{array}{l}{f}_s\ge ma\\ {\mu }_{s}mg\ge ma\\ {\mu }_s\ge \frac{a}{g}\end{array}$

Therefore, ${\mu }_{s\left(\min \right)}=\frac{a}{g}$

  $\begin{array}{l}=\frac{2.05{\text{ m/s}}^2}{9.81{\text{ m/s}}^2}\\ =0.21\end{array}$