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Question

Block A, as shown in the figure weighs 2 N and block B weighs 6 N. The coefficient of kinetic friction between all surfaces is 0.25. Find the magnitude of the horizontal force necessary to drag block B to the left at constant speed if A and B are connected by a light, inextensible cord passing around a fixed, frictionless pulley.


A
2 N
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B
3 N
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C
5 N
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D
6 N
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Solution

The correct option is B 3 N
Drawing FBD of the blocks,


Friction force on block A f1=μkmAg=(0.25)(2)=0.5 N.
and friction force on block B f2=μk(mA+mB)g=(0.25)(2+6)=2 N.

From the FBD of A,
T=f1=0.5 N

From FBD of B,
Ff2Tf1=0
F=f2+2f1 (T=f1)
F2=2+1=3 N

The force F must then have magnitude 3 N

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