Question

Find the friction force between block $A$ and the surface for system at rest given below:
$m_A=9\text{kg},m_B=4\text{kg},{\mu }_s={\mu }_k=0.8$

• A. $72\text{N}$
• B. $30\text{N}$
• C. $40\text{N}$
• D. $48\text{N}$

Answer 1

The correct option is C $40\text{N}$

From the FBD of Block $A$, to remain at rest:
$T=f...\left(i\right)$
$N=m_{A}g=90\text{N}...\left(ii\right)$
From FBD of block B, to remain at rest:
$T=m_{B}g=40\text{N}...\left(iii\right)$
$\therefore T=f=40\text{N}$

Now ${f_s}_{max}={\mu }_{s}N=0.8\times 90=72\text{N}$
$\because f\le f_{max}$, hence the frictional force will be equal to applied for, $f=40\text{N}$ will act on block A.

Hence option C is the correct answer