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Minimum Vo for a hoop to get to the top

  1. Jun 20, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-6-20_22-1-39.png upload_2016-6-20_22-1-50.png
    part(b) and (c)
    2. Relevant equations
    Conservation of momentum
    Conservation of angular momentum
    Conservation of mechanical energy

    3. The attempt at a solution
    So first I thought that I could do it by just using the conservation of mechanical energy, but then I realized that since the lower part of the hoop hits the platform, the energy can't be conserved (there's energy lost):

    1/2 mv^2 + 1/2 Iw^2 = mgh + Energy lost
    mv^2 = mgh + Energy lost

    I think that part (b) and (c) is very related, once we know the energy lost, we can determine the v needed, however I don't really understand how to find its value. Any suggestion ??
     
  2. jcsd
  3. Jun 20, 2016 #2

    haruspex

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    You are right that KE will not be conserved. What other conservation possibilities are there?
    You mentioned two. What is stopping you from trying to use them?
     
    Last edited: Jun 20, 2016
  4. Jun 20, 2016 #3
    Well, conservation of momentum:
    m1v1 + m2v2 = (m1+m2)v3
    But this is if the object experiences inelastic collision, I don't know how to apply it when the other object is just a small bump.
    Conservation of angular momentum:
    Iw1= Iw2
    since the hoop will rotate about the edge of the bump during collision, parallel axis theorem:
    mr^2 w1= 2mr^2 w2
    w1= 2w2

    At this time I can't seem to figure out what to do afterwards.
     
  5. Jun 20, 2016 #4

    haruspex

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    The problem with those two conservation laws here is that you have an unknown impulse from the step. So you need to find a way of applying one of them in which that impulse makes no contribution.
    If you knew the direction of the impulse you could consider momentum orthogonal to it; but you don't.
    Angular momentum is always relative to some chosen axis. Can you choose an axis such that the impulse has no moment about it?
     
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