Finding Young's Modulus for Steel from two graphs

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SUMMARY

The discussion focuses on estimating Young's Modulus for steel using two graphs: one plotting depression against load and the other plotting logarithmic values of depression against logarithmic values of cantilever length. The equation used for calculating Young's Modulus is Y = 4*L^3*m*g / D*a*b^3. The participant's calculation yielded a value of 1.067*10^11, which is significantly higher than the expected Young's Modulus for steel. The analysis highlights the importance of specifying fixed variables when interpreting the results from the graphs.

PREREQUISITES
  • Understanding of Young's Modulus and its significance in material science
  • Familiarity with linear regression and graph interpretation
  • Knowledge of cantilever beam mechanics and related equations
  • Basic proficiency in logarithmic functions and their applications
NEXT STEPS
  • Review the derivation of Young's Modulus from experimental data
  • Learn about the significance of fixed variables in experimental setups
  • Explore the relationship between load and deflection in cantilever beams
  • Investigate common errors in calculating material properties from experimental graphs
USEFUL FOR

Students in engineering and physics, material scientists, and anyone involved in experimental mechanics or structural analysis will benefit from this discussion.

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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