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Homework Help: Inclined plane translational velocity

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data
    A hollow cylinder with a mass of 1.2 kilograms and a diameter of .25 m rolls down an inclined plane angled at 35 degrees. What is its translational velocity at the bottom of the incline plane if the distance traveled is 3 meters?


    2. Relevant equations
    v=[tex]\sqrt{gh}[/tex]
    ???

    3. The attempt at a solution
    sin35=h/3m
    h=1.72m
    v=[tex]\sqrt{9.8*1.72}[/tex]
    4.1 m/s
     
  2. jcsd
  3. May 6, 2010 #2

    rl.bhat

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    According to the conservation of energy,
    mgh = 1/2*Iω^2 + 1/2*m*v^2.
    here h = d*sinθ. The angular velocity v =ω*R, where R is the radius of the cylinder.
     
    Last edited: May 6, 2010
  4. May 6, 2010 #3
    I need translational velocity.
     
  5. May 6, 2010 #4

    rl.bhat

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    v is the translational velocity of the center of mass.
     
  6. May 6, 2010 #5
    Please explain more.
     
  7. May 6, 2010 #6

    rl.bhat

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    According to the conservation of energy
    K1 + U1 = K2 + U2
    0 + mgh = 1/2*m*v^2 + 1/2I*ω^2.
    mgdsinθ = 1/2*m*v^2 + 1/2MR^2(v/R)^2 + 0
    So mgdsinθ = mv^2.
    So what ever you have calculated is the required result.
     
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