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Calculate speed of a hoop up an incline

  1. Nov 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Ok, I have attempted this problem, and believe I have the right answer. My work is not matching up though and I think I am missing something.

    Question:
    A hoop is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes and angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00m up the ramp?


    2. Relevant equations
    KE = 1/2*mv^2 + 1/2*I*w^2
    I = mR^2


    3. The attempt at a solution
    This is what I got.

    Total KE = 1/2*mv^2+1/2*Iw^2
    substituting the I = mR^2 and w = v/R

    Total KE = 1/2*m*v^2 + 1/2*(mR^2)*(v^2/R^2)
    = 1/2*m*v^2 + 1/2*m*v^2
    = mv^2

    at 3m up on the incline

    ke(bot) = pe(top)+ke(top)

    m*v(initial)^2 = mgh + 1/2*m*v(final)^2
    vi^2 = gh + 1/2*vf^2

    vf = sqrt(2(vi^2-gh))

    I believe at this point I am wanting vf = sqrt(vi^2-gh).. because the answer I believe is 2.80 m/s. sqrt(4.5^2 - (9.8*3sin25)) = 2.80 m/s

    Am I looking at this correctly?

    Any help would be appreciated.
     
  2. jcsd
  3. Nov 13, 2012 #2

    rcgldr

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    Homework Helper

    You calculated that total KE for the rolling hoop is m v2, and used m v2 for ke(bot) but then you used 1/2 m v2 for ke(top)?
     
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