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Question

For the figure shown below, the coefficient of friction between 2 kg and 4 kg block is 0.1 and between 4 kg and ground is 0.2. The graph of friction force acting on 4 kg block by the ground as a function of time is


A
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B
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C
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D
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Solution

The correct option is A

f1max=μ1N1=0.1×2g=2 N
f2max=μ2N2=0.2×6g=12 N


For 0<F<2 N:
f1=F
i.e Tension will be zero
and f2=f1
f2=02 N (rightward)

For 2 N<F<4 N:
F=f1max+T
i.e Tension is 0<T<2 N.
f2=f1maxT=2T
f2=20 N (rightward)


For 4 N<F<16 N:
F=f1max+T
i.e tension T will be 2 N<T<14 N
f2=Tf1max=T2
f2=012 N (leftward)


For F>16 N:
Lower block will start moving since T>f1max+f2max. Hence friction will be kinetic (constant) and act leftward.

Graph (a) matches these values.

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