# 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.

Arun Kumar IIT Delhi
10 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
Ankit Jaiswal
165 Points
8 years ago
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