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A small block of mass m is 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 coeffecient between the road and the bigger block is x and that between the two blocks is x/2.Find the time elapsed before the smaller block separate from the bigger block.

A small block of mass m is 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 coeffecient between the road and the bigger block is x and that between the two blocks is x/2.Find the time elapsed before the smaller block separate from the bigger block.
 

Grade:9

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
or the block M,
Ma2 = μ(M+m)g - μmg/2
a2 = Acceleration of M w.r.t. ground is μg(1+m/2M) towards right.
For the block m,
ma1 = μmg/2
a1 = acceleration of m w.r.t M is μg/2 towards right.

l = ut + 0.5a1 t2
u=0 so l = 0.5 μg/2 t2
t = (4l/μg)1/2

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