Question

A plank of mass 10 kg rests on a smooth horizontal surface. two blocks A & B of masses 2kg & 1kg lies at a distance of 3m on the plank. The Friction coefficient between the plank & blocks are0.3 & 0.1. Now a force F=15 N is applied to the plank in horizontal direction.Find the time in which the block A collides with B.​

Answer 1

Time in which the block A collides with B = 6 seconds

Explanation:

Please refer to the attached pictures for the diagrams.

Maximum friction force between the plank (P) and A = Fa =  μa.ma.g = 6N

Maximum friction force between the plank (P) and B i= Fb =  μb.mb.g = 1N

Then acceleration of the system = a = F / (ma + mb +M) = 15/13 m/s

Friction force on mb = fb = mba = 15/13N

Friction force on ma = fa = ma.a = 30/13N

We find fb > Fb, so B will not move with the plank.

fa < FA, so A will move with the plank.

ab = Fb/ mb = 1 m/s2

Ap = F-Fb / ma +M = 7/6 m/s2

FBD of the plank and A&B are accelerated of B with respect to plank.

abp = 1 - 7/6 = -1/6 m/s2

Lbp = 1/2. abp. L = -3 = 1/2 (x-6)

Time of collision t = 6 seconds

Answer 2

Answer:

6 secs

Explanation:

Please see this attached image for solution.