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Question

Each of the three plates has a mass of 10 kg. If the coefficients of static and kinetic friction at each surface of contact are μs=0.3 and μk=0.2, respectively (g=10 ms2). Find the acceleration of block B.
828803_0e7d7c07e417464ca674faf7f06720b4.png

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Solution

a) f1static=μsN1=0.3×10g=0.3××10=30N

if F=18<f1static, then block D doesn't slip on C.

b) Considering C

f2static=μsN2=μs(10g+N1)=μs(10g+10g)=0.3×20×10=60N

Here, f2=100N>(f2static+f) then blockC slips on B

Let acceleration of C and D is a2 towards right then

a2=100Ff2staticMC+MD=100180.2×20g10+10=100184020=4220=2.1m/s

c) Consider block B,

f2kinetic=40N

f3<f2kinetic

f3static=μ3N3=0.3(20g+10g)=0.3×30g=90N

f3static>[f2kinetic(f3=15N)]

Hence, block B doesn't move.

Acceleration of B is zero.



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