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Energy conservation used to predict speed?

  1. Jan 23, 2009 #1
    1. The problem statement, all variables and given/known data
    I don't know if anyone can help me with this without having done the lab, but I thought I'd give it a shot. Ok, so I did a lab in my physics class where we used little rollercoasters to find the PE and KE of a marble at various heights and speeds. Here is the question in my lab write-up that has me stumped.

    How can you use energy conservation to predict the speed of the marble from the height?

    2. Relevant equations
    PEi + KEi = PEf = KEf

    3. The attempt at a solution
    I know that you can obtain the equation Vf = √2ghi from energy conservation, but that doesn't seem to be working when I plug in the height. It isn't coming out to the correct speed which I already calculated.
     
  2. jcsd
  3. Jan 23, 2009 #2

    rock.freak667

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    Well from the top of the roller coaster it would have 0 KE, and max PE. (At height h1). So the PE here is mgh1.

    When it moves from the initial height, h1 to another height, h2. The PE is mgh2. This change in PE, mg(h1-h2). Gives the change in kinetic energy.

    EDIT:

    So by conservation of energy:

    1/2 mv2=mg(h1-h2)
     
    Last edited: Jan 23, 2009
  4. Jan 23, 2009 #3
    you can use the equation 1/2mv^2+mgh=1/2mv^2+mgh
     
  5. Jan 23, 2009 #4

    LowlyPion

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    For one thing you have the angular kinetic energy of the marble.

    KE = 1/2*I*ω²

    For a sphere - the marble - I = 2/5*m*r²

    So the √2gh is really (2gh/(1+2/5*r))1/2
     
  6. Jan 23, 2009 #5
    Wouldn't that simplify to Vf = √2g(hi - hf) ?

    And @ LowlyPion, idk how to do angular KE, you're making it harder than it actually is. :bugeye:
     
  7. Jan 23, 2009 #6

    LowlyPion

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    I understand. But your marble rolls without slipping. That means as the speed increases, some of the PE is going to KEr.

    If you are wanting to determine why observation doesn't match the math, that's where some of your error is coming from.
     
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