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Simple energy question with rotation

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data
    a small solid sphere of mass m and radius r starts from rest and rolls down a hill without slipping. the sphere encounters a loop of radius R where R >> r.

    Given R determine the min height h such that the ball remains on the track throughout the loop


    2. Relevant equations

    I = 2/5 mR^2

    ω = v/r
    3. The attempt at a solution

    highest point requiring most energy is at top of loop:

    mgh = mg2R + 1/2 Iω^2

    mgh = mg2R + 1/2 * 2/5 m r^2 *v^2/r^2

    gh = 2Rg + 1/5*v^2



    at top of loop, normal force is 0,

    Fy = N + mg
    ma = mg

    m*v^2/R = mg
    v^2 = gR


    ...

    gh = 2Rg + 1/5 Rg

    h = 11/5 R

    this is correct?
     
  2. jcsd
  3. Nov 10, 2012 #2

    Simon Bridge

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    To check your results - it is useful to compare to something:

    i.e. If this were a block sliding around the track without friction, then what would the minimum h have to be?
    (for the ball, some energy is stored in rotation - so you need to start higher than this.)

    How fast is the ball rolling at the top of the hoop?
    (i.e. is the kinetic energy a lot or a little more than the potential energy there? says if you should start a little higher or a lot higher.)
     
  4. Nov 10, 2012 #3

    TSny

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    Have you included all of the kinetic energy at the top?
     
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