Figure (6-E12) 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 u. The friction coefficient between the road and the bigger block is i and that between the block is μ/2. Find the time elapsed before the smaller blocks separates from the bigger block.
Let masses m and M are having acceleration a1 and a2 respectively.
a1 should be greater than a2 so that mass m can move on mass M.
Suppose, after time ‘t’, the mass m separates from mass M
Using the equation of motion.
During this time, mass m covers the distance s
s=vt + 
a1t2
and sm=ut + 
a2t2
For mass m to separate from mass M, we can write,
vt + 
a1t2 = vt + 
a2t2 +1
From the free body diagram, figure (b), we can write,
ma1+(1/2)μR=0
⇒ma1=-(1/2)μmg=(1/2)μm×10
⇒a1=-5μ
Also from figure (a),
Ma2+μ(M+m) g-(μ/2) mg=0
⇒ 2Ma2 + 2μ (M + m)g − μmg = 0
⇒ 2Ma2 = μmg − 2μmg − 2μmg
Substituting the values of a1 and a2 in equation (i), we get:
