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Question

Find the accelerations of the blocks A and B for the figure shown, if the system is initially at rest. Take g=10 m/s2.


A
43 m/s2, zero
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B
zero, 53 m/s2
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C
3 m/s2,3 m/s2
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D
3 m/s2, zero
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Solution

The correct option is D 3 m/s2, zero
The FBDs of the blocks are as shown.
Given, force applied on the block A is F=50 N


We have from the FBDs of the blocks
N1=10g=100 N
f1max=0.2×100=20 N
N2=N1+20g=100+200=300 N
f2max=(0.4)(300)=120 N

Since, f2 max>f1 max, block B will be at rest.
acceleration of the block B will be zero.

For block A: Since, F>f1 max, it will accelerate and the friction will be kinetic in nature
Kinetic friction acting on block A is fk=μN1=0.2×10g=20 N
So, acceleration of the block A is given by,
aA=FfkmA=502010=3 m/s2

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