Question

In the figure shown, the coefficient of static friction between the blocks is $0.1$, while the floor is frictionless. Find the minimum value of force $F$ (in $N$ ) to cause sliding between the blocks $A$ and $B$ of masses $5 \,kg$ and $10 \,kg$, respectively, when the angle of string is $53^{\circ}$ with horizontal. (Use $\sin 53^{\circ}=4 / 5$ and $\cos 53^{\circ}=3 / 5$ )

Answer 1

$f_{1} \leq \mu N_{1}$
or $f_{1} \leq 5$
For minimum $F$ to cause sliding,
$a_{A}=a_{B} $ and $ f=f_{\max }$
or $\frac{f_{\max }}{m_{A}}=\frac{F \cos \theta-f_{\max }}{m_{B}}$
or $\frac{5}{5}=\frac{F\left(\frac{3}{5}\right)-5}{10}$
or $F=25 \,N$