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AP Physics C rotational Energy

  1. Nov 5, 2009 #1
    1. A uniform solid sphere of radius r starts from rest at a height h and rolls without slipping along the loop-the-loop track of radius R as shown.
    a) What is the smallest value of h for which the sphere will not leave the track at the top of the loop?



    Attempt:

    2. Relevant equations
    [tex]\Delta[/tex]PE = mgh - 2mgR
    [tex]\Delta[/tex]KE = 1/2 mv2 + 1/2 Iw2
    ac = v2/R
    v = rw

    3. The attempt at a solution
    mgh = 2mgR + 1/2 Iw2 + 1/2 mv2
    I = 2/5 mr2
    mgh = 2mgR + 1/5 mr2w2 + 1/2 mv2
    N = mg - mac = mg - mv2/R = 0
    v2 = gR
    mgh = 2mgR + 1/2 mv2 + 1/5 mv2 +2mgR = 2.7mgR
    h = 2.7R

    however, this answer is wrong, and the correct one is h = 2.7R - 1.7r. can anybody correct me on this?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 5, 2009 #2
    N is the force of norm exerted by the track on the cart at the top of the loop by the way
     
  4. Nov 5, 2009 #3
    haha, nvrmind, i figured out what i did wrong.
     
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