In the arrangement shown in the figure, friction exists only between the two blocks, A and B. The coefficient of static friction 
= 0.6 and coefficient of kinetic friction 
= 0.4, the masses of the blocks A and B are m 1 = 20 kg and m 2 = 30 kg, respectively. Find the acceleration (in m s -2 ) of m 1 , if a force F = 150 N is applied, as shown in the figure. [Assume that string and pulleys are massless]
Text Solution
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(1.5)
Let us assume that the two blocks move together, without slipping, relative to each other. The
acceleration of the system in that case is
In this case, if the frictional force acting between the two blocks is f, then writing the Newton's second
law of motion, for the block of mass m 1 , we get
T-f = m 1 a
150- f = 20 x 1.5 = 30
f = 120 N
f max = 0. 6 x 200 = 120 N
Since 
, our assumption about the two blocks moving together is correct and hence the
acceleration of the blocks is 1.5m s -2
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