Problem 8.75 Part A Find d such that the block\'s speed after crossing the rough

Question

Problem 8.75 Part A Find d such that the block's speed after crossing the rough patch is 2.0 m/s Express your answer using two significant figures in the figure(Eigure 1) a 1.3 kg block is held at rest against a spring with a force constant k . 720N/m initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless except for a rough patch of width 5.0 em that has a coeficient of knete fricton#x-0.44. I13 My Answers Give Up Incorrect; Try Again; 8 attempts remaining Equilibrium position Rough 5.0 2

Explanation / Answer

m=1.3kg, k=720N/m, x=0.5m, vf=2.0m/s, uk=0.44

We use law of conservation of energy

Initial KE before the rough patch = Work done by friction on rough patch + Final KE

KEi = Wf + KEf -----------(1)

But For spring mass system

KEi = spring PE = 1/2kd^2 --------(2)

Combining () and (2),

1/2kd^2 = Wf + KEf

1/2kd^2 = uk*Fn*x + 1/2mvf^2

1/2kd^2 = uk*mg*x + 1/2mvf^2

Plugging values,

½*720*d^2=0.44*1.3*9.8*0.05+1/2*1.3*2.0^2

d=0.089m= 8.9cm

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