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Finding Young's Modulus for Steel from two graphs

  1. Nov 30, 2014 #1
    1. The problem statement, all variables and given/known data

    Estimate the value for Youngs Modulus from the two following graphs:
    Graph 1: Plot a graph of depression in metres (D) against load in kilograms (M)
    Graph 2: Plot a graph of log_10(D) against log_10 of Length of cantilever.

    2. Relevant equations

    D = 4*L^3*m*g / Y*a*b^3

    D = depression
    L = length of cantilever
    m = mass of load on free end of cantilever
    a = width of cantilever
    b = thickness of cantilever

    Equation for Graph 1: y = 0.9843x + 0.001, where y = depression and x = load
    Equation for Graph 2: log(y) = 2.5074 * log(x) + 0.2922, where y = depression and x = length of cantilever

    3. The attempt at a solution

    I've attempted to get Y by re-arranging the straight line equation for Y.

    Y = 4*L^3*m*g / D*a*b^3

    But this gives me 1.067*10^11. Which is quite a way off Youngs Modulus for steel.
  2. jcsd
  3. Nov 30, 2014 #2


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    Gold Member

    There are two independent variables in your experiment: length and weight. If you plotted a graph for each then you must be holding the other value fixed, yes? Your observed equations aren't meaningful unless you specify the value for the variable that was held fixed. Without that, you cannot combine them into a single equation.
    I note that the observed exponent for length is 2.5, which is rather a long way off the expected 3.
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