Question

two blocks A) 4 kg and (B) 6 kg rest one over the other on a smooth horizontal plane. The coefficient of static and dynamic friction between (A) and (B) is the same and equal to 0.3. The maximum horizontal force F that can be applied to (B) in order that both (A) and (B) do not have any relative motion is​

Answer 1

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Now both should move with same acceleration.

So,

Fr = ma = 2a

F - Fr = 5a

A = umg/m = ug = 6m/2

F - 6×2×10×=5×6=42N

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Answer 2

Given: two blocks of mass A 4kg, B 6kg rest one over the other on a smooth plane. The coefficient of static and dynamic friction between (A) and (B) is the same and equal to 0.3.

To find: The maximum horizontal force F that can be applied to (B) so that both (A) and (B) do not have any relative motion is

Solution: There will be no relative motion between the blocks. Therefore we can say that both the blocks will move with the same acceleration.

For making Block A not move in relative to block B, the external force that will be applied needs to balance the frictional force between these two blocks.

Common acceleration of the blocks will be

a= F/(4+6)

a= F/10 ms^-2

we also know that force will act in such a way it will balance the frictional force

F = f

Mass of A × a = Mass of A × μg

a = μg = 0.3× 10= 3

F/10 = 3

F = 30N

The maximum horizontal force F that can be applied to (B) so that(A) and (B) do not have any relative motion is will be 30 N.