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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 v. The friction coefficientbetween the road and the bigger block is μ and that between the block is μ2. Find the time elapsed before the smaller blocks separates from the bigger block.

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Solution

Let a1 and a2 be the accelerations of m and M respectively.
Here,a1>a2, so taht m moves on M Suppose, after time 't' m is separated from M.
In this time, m covers vt+12a1t2 and
Sv=vt+12a1t2
For m to separate from M,
vt+12a1t2=vt+12a2t2+1
Again from free body diagram,
ma1+μ2R=0ma1=(μ2)mg=(μ2)m×10a1=o5μ

Again, Ma2+μ(M+M)g(μ2)mg=02Ma2+2μ(M+m)gμmg=02Ma2=μmg2μmg2μmga2=μmg2μMg2M
Putting values of a1 and a2 wwe get,

t=4Ml(M+m)μg


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