Question

# If μs and μk represent the coefficients of static and kinetic friction with appropriate suffixes for the two bodies shown, find the acceleration of the system. Take g=10 m/s2.

A
Zero
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B
4.2 m/s2
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C
5.2 m/s2
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D
10 m/s2
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Solution

## The correct option is C 5.2 m/s2The given system can be shown in the FBDs as So, we have from the above condition f1max=μs1(5g)=0.6×50=30 N f2max=μs2(2g)=0.5×20=10 N and, applied force =13g=130 N ∵ the applied force > Total friction force of the system, the system will acclerate ∴ we have fk1=μk1(5g)=(0.4)(5g)=20 N fk2=μk2(2g)=(0.3)(2g)=6 N So, from force equations: Taking the 5 kg and 2 kg masses as a system, we get 13g−T2=13a T2−fk1−fk2=(5+2)a13g−20−6=20a ⇒ a=130−2620=5.2 m/s2

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