Question

A 2 kg block is placced over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to (a) the upper block, (b) the lower block. Take $g=10m/s^2$

Answer 1

(i) $R_1-2g=0\Rightarrow R_1=2\times 10=202a+0.2R_1-12=0$

$\Rightarrow 2a+0.2\left(20\right)=12\Rightarrow 2a=12-4\Rightarrow a=4m/s^2$
Again $4a-\mu R_1=0$
$\Rightarrow 4a=\mu R_1=0.2\left(20\right)=4\Rightarrow a_1=1m/s^2$

2 kg Block has acceleration $4m/s^2$ and that of 4 kg is 1 $m/s^2$
(ii) $R_1=2g=2gma=\mu R_1=0ma=\mu R_1=0a=0$