Chapter 4, Problem 36P

To determine

The minimum coefficient of static friction exists between feet and the floor.

Answer to Problem 36P

Solution:

0.20

Explanation of Solution

Given:

The train is accelerating at $a=0.20g$ .

Where, g is the acceleration due to gravity.

Formula used:

Frictional force F is obtained by:

  $F=\mu N$

Where, $\mu$ is the coefficient of friction and N is the normal reaction force.

The normal force would be equal to the weight of the person.

  $\begin{array}{l}N=mg\\ F=\mu mg\end{array}$

From Newton’s second law of motion.

  $F=ma$

Where, m is the mass and a is the acceleration.

Calculation:

The minimum frictional force would equal to the force acting on the person as he stands on the moving train.

  $\mu mg=ma$

The minimum coefficient of static friction is

  $\mu =\frac{a}{g}$

  $\mu =\frac{0.20g}{g}$

  $\mu =0.20$

Conclusion:

Thus, the minimum coefficient of friction is 0.20.