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Question

Figure 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 coefficient between the road and the bigger block is μ and that between the block is μ/2. Find the time elapsed before the smaller blocks separates from the bigger block.
782261_11bda58a8cc7472ea98617645401de11.png

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Solution

N1=mg

N2=(m+m)g

a1=-μ/2 N1/m

=-μg/2

a2=(μN1/2 -μN2)/M

=(μmg/2 -μ(m+m)g)/M

initial velocity of smaller block with respect to biggere =v-v =0

acceleration of smaller block w.r.t bigger = a1-a2

so smaller block sepeate

S=l =0*t +1/2 (a1-a2) t2

t2 =2l/(a1-a2)

6611-315_7662_untitled.JPG


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