Question

A block of mass $m$ is placed on another block of mass $M$ lying on a smooth horizontal surface as shown in the figure. The coefficient of friction between the block is $\mu$. Find the maximum horizontal force $F$ (in Newton) that can be applied to the block $M$ so that the blocks move together with same acceleration? $(M=3kg,\mu =0.1,g=10{m/s}^2)$.

Answer 1

When both blocks moves together $a=\frac{F}{M+m}$
From $FBD$ of $m$ relative to $M$ so that the blocks to move together
$ma<f$
$m\left(\frac{F}{M+m}\right)<\mu mg$
$F<(M+m)\mu g$
$F<5N$
$\therefore F_{max}=5N$