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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 which is on a horizontal surface such tha the system can slide.The system is started towards right with an initial velocity v.The friction coefficient between the surface and the larger block is x and the friction coefficient between the blocks is x/2.Find the time elapsed before the smaller block separates from he bigger block.

A small block of mass m is kept at the left end of a larger block of mass M and length L which is on a horizontal surface such tha the system can slide.The system is started towards right with an initial velocity v.The friction coefficient between the surface and the larger block is x and the friction coefficient between the blocks is x/2.Find the time elapsed before the smaller block separates from he bigger block.

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hello Student,

Let a1 and a2 be the accelerations of ma and M respectively.
Here, a1 > a2 so that m moves on M
it would be easiest if we see this in relative frame of M
see in relative frame
relative distance to be covered is l wrt to M
so we find a rel to M =a1-a2
and 1/2 a*t^2 = l
and for the force lower body M will have two force friction from the box below =-k(M+m)g
and fromt the upper body -k/2(mg)
a2=-(kmg-2kMg)/2M
a1=-k/2g
take the difference
-kg(M+m)/2M
now apply the kinematics formulae
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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