Finding Young's Modulus for Steel from two graphs

In summary: That's probably because you didn't know to keep the other variable fixed. If you had, you would have found a much better fit for the data.In summary, the conversation discusses estimating the value for Youngs Modulus from two graphs, one plotting depression against load and the other plotting log of depression against log of length. The equations for each graph are given, but it is noted that there are two independent variables in the experiment and the observed equations are not meaningful without specifying the value for the fixed variable. It is also mentioned that the observed exponent for length is off from the expected value due to not keeping the other variable fixed.
  • #1
Kieran12
6
0

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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  • #2
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.
 

1. What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It is defined as the ratio of stress to strain within the elastic limit of a material.

2. Why is it important to find Young's Modulus for steel?

Young's Modulus is an important material property as it helps engineers and scientists understand how a material will behave under stress and how it will deform when subjected to a force. It is particularly important for steel, which is commonly used in construction and engineering projects.

3. How do you find Young's Modulus for steel from two graphs?

To find Young's Modulus for steel from two graphs, you will need to plot stress (y-axis) against strain (x-axis) for the material. The slope of the linear portion of the stress-strain curve is equal to Young's Modulus. If you have two stress-strain curves for the same material but with different dimensions, you can use the ratio of the slopes to calculate the Young's Modulus.

4. What factors can affect the accuracy of finding Young's Modulus for steel?

The accuracy of finding Young's Modulus for steel can be affected by several factors, including the quality of the material, the temperature at which the test is conducted, and the strain rate. Other factors such as surface defects, impurities, and sample preparation can also impact the accuracy of the results.

5. Can Young's Modulus for steel change over time?

Yes, Young's Modulus for steel can change over time due to various factors such as fatigue, creep, and temperature variations. These changes can affect the stiffness and strength of the material, making it important to consider the age and history of the steel when determining its Young's Modulus.

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