FrictionHard

Question

An arrangement of the masses and pulleys is shown in the figure. Strings connecting masses A and B with pulleys are horizontal and all pulleys and strings are light. Friction coefficient between the surface and the block B is 0.2 and between blocks A and B is 0.7. The system is released from rest. (use g = 10 m/s2)

Options

A.The magnitude of acceleration of the system is 2 m/s2 and there is no slipping between block A and block B.   
B.The magnitude of friction force between block A and block B is 42 N.
C.Acceleration of block C is 1 m/s2 downwards.
D.Tension in the string connecting block B and block D is 12 N.

Solution

Suppose blocks A and B move together. Applying NLM on C, A + B, and D 
60 − T = 6a
T − 18 − T′ = 9a
T′ − 10 = 1a
Solving
a = 2 m/s2
To check slipping between A and B, we have to find friction force in this case. If it is less than limiting static friction, then there will be no slipping between A and B. 
Applying NLM on A. 
T − f = 6(2)
as T = 48 N
f = 36 N
and fs = 42 N hence A and B move together.
and  T′ = 12 N.

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