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Formulae from Experimental Data

Formulae from Experimental Data. When scientists & engineers try to find relationships between variables in experimental data the figures are often very large or very small and drawing meaningful graphs can be difficult. The graphs often take exponential form so this adds to the difficulty.

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Formulae from Experimental Data

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  1. Formulae from Experimental Data When scientists & engineers try to find relationships between variables in experimental data the figures are often very large or very small and drawing meaningful graphs can be difficult. The graphs often take exponential form so this adds to the difficulty. By plotting log values instead we often convert from to

  2. Example The variables Q and T are known to be related by a formula in the form T = aQn The following data is obtained from experimenting Q 5 10 15 20 25 T 300 5000 25300 80000 195300 Plotting a meaningful graph is too difficult so taking log values instead we get …. log10Q 0.7 1 1.2 1.3 1.4 log10T 2.5 3.7 4.4 4.9 5.3

  3. This gives us the following graph from which we can get a line of best fit log10T log10Q

  4. m = 5.3 - 2.5 1.4 - 0.7 = 2.8/0.7 = 4 (a,b) = (1,3.7) Since the graph does not cut the y-axis use Y – b = m(X – a) where X = log10Q and Y = log10T , Y – b = m(X – a) log10T – 3.7 = 4(log10Q – 1) log10T – 3.7 = 4log10Q – 4 log10T = 4log10Q – 0.3 log10T = log10Q4 – log10100.3 law3 log10T = log10Q4 – log102 log10T = log10(Q4/2) law2 T = 1/2Q4

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