Question

Two blocks ($m=0.5\text{kg}$ and $M=4.5\text{kg}$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $3/7$. Then the maximum horizontal force that can be applied on the larger block so that blocks move together is ______$\text{N}$.

$($Round off to the nearest integer$)$
$($Take $g$ as $9.8{\text{ms}}^{-2})$

Answer 1

Maximum acceleration for both blocks to move together,
$a_{max}=\mu g$
$\Rightarrow a_{max}=\frac{3}{7}\times 9.8$

$a_{max}=4.2{\text{m/s}}^2$

Now, considering both blocks are moving together with the acceleration of $4.2{\text{m/s}}^2$,

$F_{max}=(M+m)a_{max}$

$\Rightarrow F_{max}=(4.5+0.5)\times 4.2=21\text{N}$