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Standard XII

Physics

Newton's Second Law

A plank of ma...

Question

A plank of mass 10 kg rests on a smooth horizontal surface.Two blocks A and B of masses m_a = 2 kg and m_b =1 kg lies at a distance of 3 m on the plank. The friction coefficient between the blocks and plank are f_a=0.3 and f_b=0.1.Now a force F=15 N is applied to the plank in horizontal direction.Find the time (in sec) after which block A collides with B.

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Solution

Considering the plank and the blocks to be a system,

F=m.a

15N = 13.a

a=15/13 ms-2 [ a is the acceleration of the system]

Now, considering the blocks...

Block A

f ≤ μN
≤ 0.3 * 20 ≤ 6N

Force acting on the block due to motion of plank,

F= m.aA = 2.15/13 = 2.30 N

Hence, force of friction balances this force and hence there is no relative motion between the block A and the plank.

Block B

f ≤ μN
≤ 0.110 ≤ 1 N

Force acting on the block = m.aB = 115/13= 1.153N

Net force,

m.aB= 1.15 - 1
= 0.15
aB= 0.15/1

Time taken ≈ 6s

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