Chapter 5, Problem 72A

To determine

Force required to start the motion.

Answer to Problem 72A

  $F_{\text{refrigerator}}=181.1\text{N}$

Explanation of Solution

Given:

Mass of refrigerator, $m=88\text{kg}$

Coefficient of kinetic friction, ${\mu }_k=0.13$

Coefficient of static friction, ${\mu }_S=0.21$

Formula Used:

Force required is

  $F=F_{\text{friction}}$

Calculation:

The free body diagram of the refrigerator is shown below,

  $F_N=mg$ and $F=F_f$

Since, the refrigerator is initially as rest. So, static friction will be in action.

After start of motion, kinetic friction will be in action.

So, to just start the motion

  $\begin{array}{l}{F}_{\text{refrigerator}}=F_{\text{friction}}\\ ={\mu }_S{F}_N\left(\because F_{\text{friction}}={\mu }_S{F}_N\right)\\ ={\mu }_{S}mg\left(\because F_N=mg\right)\\ =0.21\times 88\times 9.8\\ =181.1\text{N}\end{array}$

Conclusion:

Therefore, to get the refrigerator start moving the minimum required force is $F_{\text{refrigerator}}=181.1\text{N}$ .