Chapter 4, Problem 38P

To determine

The maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck.

Answer to Problem 38P

Solution:

The maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck is 7.35m/s².

Explanation of Solution

Given:

The coefficient of static friction between the crate and the bed of the truck (µ) is 0.75.

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.

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

From Newton’s second law of motion.

  $F=ma$

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

Calculation:

The maximum decelerating force that can be applied is equal to the static frictional force.

  $\mu \times mg=m\times a$

  $a=0.75\times 9.8$

  $a=7.35{\text{m/s}}^{\text{2}}$

Conclusion:

Hence the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck is 7.35m/s².