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Simple Experimental Error Problem

  1. Aug 19, 2009 #1
    I have two values:

    r = 12.3 ± 0.2m
    d = 0.57 ± 0.03mm

    I want to divide the two values to find theta (d/r = theta), how do I go about this?
    I assume that I add the experimental error margins together after the division of 12.3 and 0.57? Giving me:

    4.63 x 10^-5 ± 2.0003m
     
  2. jcsd
  3. Aug 19, 2009 #2

    kuruman

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    I cannot figure out what you've done here but 2.0003 m does not look like an appropriate uncertainty for an angle. The way this is usually done is through fractional uncertainties. The fractional uncertainty for the radius is

    [tex]\delta_{r}= \frac{\delta r}{r} = \frac{0.2}{12.3} [/tex]

    and for the arclength

    [tex]\delta_{d}= \frac{\delta d}{d} = \frac{0.03}{0.57} [/tex]

    Then the fractional uncertainty for the angle is

    [tex]\frac{\delta\theta}{\theta} = \sqrt{\delta^{2}_{r}+\delta^{2}_{d}}[/tex]
     
  4. Aug 19, 2009 #3

    Kurdt

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    For division of variables on would normally treat the erros like so.

    [tex]\frac{\delta q}{q} = \sqrt{\left(\frac{\delta r}{r}\right)^2 + \left(\frac{\delta d}{d}\right)^2}[/tex]
     
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