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A Level Physics: Errors And Uncertainties Part 2.
A brief guide to a tricky topic which catches out a lot of A Level Students.
Date : 02/12/2019
Part 2: Compound Uncertainties. Where a result is calculated using a formula, every measurement used in the calculation contributes to the uncertainty of the result. This is what we mean by compound uncertainties. The method used at A Level is actually a fairly crude estimate for the uncertainty but is sufficient for the degree of precision which you re working to. The rules are fairly simple: If the formula only involves adding or subtracting, you can add the absolute uncertainties in the measurements used. (It s hard to think of an example where you would actually do this for A Level physics!)If the formula involves anything other than adding or subtracting, so multiplying, dividing, indices (powers), you can only add the percentage uncertainties in the measurements. Example:R = V/ILet s say your measurement for P.d. (V) is 2.0 0.1 v and your measurement for current (I) is 5.0 0.1 A (I ve kept the numbers fairly simple here to avoid confusion)Percentage uncertainty in V = 0.1 2.0 = 5%Percentage uncertainty in I = 0.1 5.0 = 2%So R = V/I = 2.0 5.0 = 0.40 And the percentage uncertainty in R = %U(V) + %U(I) = 5 + 2 = 7%So R = 0.40 7%If we want the absolute uncertainty in R, we can calculate it as follows:Absolute uncertainty = ([%-uncertainty] 100%) x resultUncertainty in R = (7 100) x 0.40 = 0.028R = 0.40 0.03 (Note that the uncertainty is typically rounded to one s.f. less than the result) For formulae involving indices (powers) we have to multiply the percentage uncertainty by the index.Example:KE = mv2 = x m x v x vSo %-uncertainty in KE = %U(m) + 2 x %U(v)
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