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The more accurate method?

  1. Nov 8, 2008 #1
    Well this isn't really a homework problem, just was curious behind the reasoning.

    In a lab we rolled a marble off the edge of a table, and measured the velocity using: Energy and Free fall trajectory. But when comparing the two there was something like a 60% error, between the two.

    My Physics teacher doesn't do much, so when I asked him he just shrugged off the question. I think that Free Fall Trajectory is more accurate, but not sure why, its practically a guess.
     
  2. jcsd
  3. Nov 8, 2008 #2

    Hootenanny

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    Could you be more specific, what did you actually measure here?
     
  4. Nov 8, 2008 #3
    Oh sorry about that, we measured velocity.

    Energy using PE=KE

    Free fall trajectory d=.5*g*t^2

    Is that what you were asking?
     
  5. Nov 8, 2008 #4

    Hootenanny

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    When you say you "measured" velocity, how did you practically "measure" the velocity?
     
  6. Nov 8, 2008 #5

    LowlyPion

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    Unfortunately missing from the energy calculation was the effect that the friction had on the marble rolling down your ramp if I recall correctly.

    Since the ball was rolling without slipping there was some portion of the downward rolling that went into increasing angular velocity of the marble.
    Your equation for PE = KE was incomplete then because not only was there the horizontal v from the mv2/2 as it left the table
    but there was the energy contained in the rotational kinetic energy I*w2/2
    which is the moment of inertia of the marble times the angular velocity squared.
     
  7. Nov 8, 2008 #6
    Oh alright:

    I attached some images of the work. Seemed easier than typing it out.
     

    Attached Files:

  8. Nov 8, 2008 #7

    LowlyPion

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    I think the measurement was of the distance from the edge of the table given the measured height of the table.

    The marble that was measured had been released down a ramp, and the horizontal velocity was calculated on that basis.
     
  9. Nov 8, 2008 #8
    Yea, sorry. lowlypion is correct. The marble was rolled down a curved ramp, which was on a table. we measured the horizontal velocity when it was at the edge of the ramp, before it rolled off of the table. In the trajectory equation, vx=d/t "d" is the distance that we measured when the marble hit the ground (measurement by Carbon Paper).
     
  10. Nov 8, 2008 #9
    Ok, that makes sense. I was thinking friction. But I had no idea on how to explain it. Thanks.
     
  11. Nov 8, 2008 #10

    Hootenanny

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    Ahh, I was labouring under the impression that they were measuring the velocity and then either infering the energy from their measurements or comparing their measurements to theoretical predictions.
     
  12. Nov 8, 2008 #11

    LowlyPion

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    Note that the moment of inertia of a sphere is 2/5*m*r2 and of course w = v/r, making 1/2*I*w2 = 1/5*m*v2

    Hence a better expression might have been

    m*g*h = 1/2*m*v2 + 1/5*m*v2

    with v = (10*g*h/7)1/2 as opposed to the more inexact (2*g*h)1/2
     
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