Question

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=0⇒ma1=−(μ2)mg=(μ2)m×10⇒a1=o−5μ

Again, Ma2+μ(M+M)g−(μ2)mg=0⇒2Ma2+2μ(M+m)g−μmg=02Ma2=μmg−2μmg−2μmg⇒a2=−μmg−2μMg2M

Putting values of a1 and a2 wwe get,

t=√4Ml(M+m)μg

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