Question
Asked Nov 3, 2019
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You pull on a string with a horizontal force of magnitude Fyb = 32 N that is attached to a block of mass mb = 6.5 kg, then to the axle of a solid cylinder of mass mc = 4.0 kg and radius r = 0.4 m, then to a spring of spring constant k = 185 N/m. This is all done on an inclined plane where there is friction ( μs = 0.69 and μk = 0.40 ), and the incline angle is θ = 28 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches.

  • First, what is the speed of the block and cylinder after you have pulled the block and cylinder 6 cm down the plane?
  • How far have you pulled the block and cylinder when everything stops?
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рооо0000- с b yb

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Step 1
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000000000 X Frbsin28 Fyb 28e mbgsin28 289 FrbCos28 28° mbgcos28° mbg.

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Step 2

Frictional force:

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4 (m,gcos28 - F,sin28°) Energy due to frictional force = f2.d (m,gcos28° - Fsin28)d U Plugging in the given values U0.40(6.5 x9.8x cos 28°-32x sin28x 6x 10 0.989296 Joules

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Step 3
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Trans lational kinetic energy of block and cylinder (m, + m.)v U,(6.5-4) = 5.25v2 Joules Rotational kinetic energy of the cylinder =-I' 1 1 U, xx Mi 2 2 1 4 4 1 :41 = v2 joules

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