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Finding uncertainty of a measurement

  1. Sep 22, 2016 #1
    1. The problem statement, all variables and given/known data
    What is your average reaction time? What is the uncertainty?

    2. Relevant equations
    To find time I used the following equation:
    [tex]t=\sqrt{\frac{2(\frac{D}{100})}{9.81}}[/tex]
    D is measured in cm, hence the division by 100 (to get meters).
    9.81 is acceleration due to gravity (this comes from [itex] x = \frac{1}{2}at^2[/itex])
    While measuring D, I used a measuring stick with smallest unit 1cm. Therefor, uncertainty of D is [itex]\pm[/itex]0.05cm.
    My average time and distance are 15.48cm and 0.17s.
    3. The attempt at a solution
    I'm not certain what the best way to go about this is. So, the first thing I do is convert the absolute uncertainty to a relative uncertainty: [itex]\pm 0.05cm \longrightarrow \frac{0.05}{15.48} \times 100 = \pm 0.32[/itex]%.

    With a relative uncertainty, multiplication and division by a constant no longer matter, so far as my understanding goes. So, this simplifies down to a square root with a relative uncertainty. Therefore I just multiply my uncertainty by 0.5: [itex]\frac{1}{2} \times 0.32 = \pm 0.16[/itex]%.

    Is this the correct answer? Something about this whole process just didn't seem right to me, but I've never been good at uncertainties and whatnot.
     
  2. jcsd
  3. Sep 23, 2016 #2

    DrClaude

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    Staff: Mentor

    That's not correct. Even though you are using relative uncertainties, the uncertainty on t depends on the absolute value of D. Have a look at http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html [Broken]
     
    Last edited by a moderator: May 8, 2017
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