Question

In the figure shown, find the maximum value of $F$ (in $N$ ) for which both the blocks move together. Force $F$ is applied on upper block. (Take $g=10m/s^2$ )

Answer 1

Answer: 840

$f_{1s\max }=0.6\times 30\times 10=180N$
$f_{1k}=0.5\times 30\times 10=150N$
$f_{2s\max }=0.3\times 35\times 10=105N$
$f_{2k}=0.2\times 35\times 10=70N$

If the two blocks move together, they must have common acceleration.
$\therefore a=\frac{F-f_{2k}}{30+5}=\frac{F-70}{35}...(i)$
and $F-f_1=30a$
$\Rightarrow F-f_1=30\left(\frac{F-70}{35}\right)$[From (i)]
$\Rightarrow F-30\left(\frac{F-70}{35}\right)=f_1$
$\Rightarrow f_1=F-\frac{6}{7}(F-70)$
$f_1=\frac{F}{7}+60$
But $f_1$ is static
$\therefore \cdot f_1\le f_{1s\max }$
$\frac{F}{7}+60\le 180$
$\frac{F}{7}\le 120$
$\therefore F_{\max }=840N$