Question

Figure shows a small block of mass $m$ kept at the left end of a larger block of mass $M$ and length $L$. The system can slide on a horizontal road. The system is started towards right with an initial velocity $v$. The friction coefficient between the road and the bigger block is $\mu$ and that between the block is $\mu /2$. Find the time elapsed before the smaller blocks separates from the bigger block.

Answer 1

N1=mg

N2=(m+m)g

a1=-μ/2 N1/m

=-μg/2

a2=(μN1/2 -μN2)/M

=(μmg/2 -μ(m+m)g)/M

initial velocity of smaller block with respect to biggere =v-v =0

acceleration of smaller block w.r.t bigger = a1-a2

so smaller block sepeate

S=l =0*t +1/2 (a1-a2) t²

t² =2l/(a1-a2)