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Uncertainty of measurements

  1. Jan 3, 2013 #1

    trollcast

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    1. The problem statement, all variables and given/known data
    The experiment set up is a steel ball bearing is held from an electromagnet and above a switch at the bottom. When the electromagnet is switched off a timer starts and stops when it hits the switch.

    The height from the bearings initial position to the switch is measured.

    These 2 measurements are then used to calculate g using the formula, $$g=\frac{2s}{t^2}$$

    Which of your 2 variables uncertainties is the most significant in determining a value for g?

    2. Relevant equations



    3. The attempt at a solution

    I said the time taken as in our equation its squared whereas the distance is only multiplied by 2 so any error in the value will be magnified more.

    However the mark scheme says either is correct given a logically and scientifically correct reason.
     
  2. jcsd
  3. Jan 3, 2013 #2

    rock.freak667

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    Given that equation, how would you determine the uncertainty in g?
     
  4. Jan 3, 2013 #3

    trollcast

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    The uncertainty of g would be equal to $$ s / 2t $$

    Where s and t are the uncertainties of the same variables.
     
  5. Jan 3, 2013 #4

    rude man

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    g = 2s/t2
    dg = ∂g/∂s ds + ∂g/∂t dt

    So the absolute error dg is
    dg = 2/t2 ds due to an absolute error ds, and
    dg = -4s/t3 dt due to an absolute error dt.

    However, if we're talking percentage errors,

    dg/g = 2t-2/2st-2 ds = ds/s and
    dg/g = -4st-3/2st-2 dt = -2dt/t.

    Thus a percentage error in t is twice as bad as a percentage error in s. I don't know if that's what the problem was asking for ...
     
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