Question

A small block of mass $20 \,kg$ rests on a bigger block of mass $30 \,kg$, which lies on a smooth horizontal plane. Initially the whole system is at rest. The coefficient of friction between the blocks is $0.5$. The horizontal force, $F=50\, N$, is applied on the lower block. The work done by frictional force on upper block in $t=2 \,s$ is $n \times 10\, J$. Find $n$.

Answer 1

Assuming both Block are moving together
$ a =\frac{50}{50}=1 \,m / s ^{2} $
$ f =20 \times 1=20\, N$
$ f_L =0.5 \times 20 \times 10 $
$\Rightarrow 100\, N$

$f_{\text {required }}=20 N$ which is less than $F _{ L }$ so block move together
$S_{\text {upper }} =\frac{1}{2} \times 1 \times 2^{2}=2 $ metre
$f =20 \,N$
$W =20 \times 2=40$ Joule