Finding Young's Modulus for Steel from two graphs

AI Thread Summary
To estimate Young's Modulus for steel from the provided graphs, the relationship between depression and load is expressed through a linear equation, while the logarithmic relationship between depression and cantilever length shows an exponent of 2.5, deviating from the expected value of 3. The formula for Young's Modulus is derived from the depression equation, but the calculated value of 1.067*10^11 is significantly higher than the known value for steel. The discussion highlights the importance of fixing one variable when plotting the graphs to ensure meaningful results. Clarifying the fixed variable is essential for accurately combining the equations to determine Young's Modulus.
Kieran12
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Homework Statement



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.

Homework Equations


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

Where
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

The Attempt at a Solution



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

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.
 
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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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