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Homework Help: Young's Modulus (E)

  1. Jul 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Determine Young's Modulous (E) for the following materials:
    Metal alloy - Test Piece 1 (TP1)
    Low Carbon Steel - Test Piece 2 (TP2)
    Copper - Test Piece 3 (TP3)

    Each test piece has the same following dimentions - Length 25mm Diamter 4mm

    Data:

    TP1 = Force(kN) - 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 | 7.5 | 8.0 | 8.5 |
    Extension (mm) - 0.012 | 0.024 | 0.040 | 0.046 | 0.60 | 0.072 | 0.084 | 0.093 | 0.11 | 0.13 |

    TP2 = Force(kN) - 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
    Extension (mm) - 0.005 | 0.009 | 0.015 | 0.02 | 0.024 | 0.028 | 0.037 | 0.045 |

    TP3 = Force(kN) - 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
    Extension (mm) - 0.0014 | 0.003 | 0.0045 | 0.006 | 0.0075 | 0.0092 | 0.0108 | 0.0122| 0.014 | 0.018 |


    2. Relevant equations

    Don't really know but my guess is something along the lines of:

    E = Tensile Stress / Tensile Strain ??

    Would apreciate if i could have the correct equation for this.

    3. The attempt at a solution

    Just playing a guessing game and don't really know what im doing, so not really looking for answers but mainly how to equate it all, if you could give me an example using the first one 'Metal Alloy' showing from start to finish with the answer then i'll figure out how to do the last two.

    Then if i do get stuck i'll come back and let you guys know :)
     
  2. jcsd
  3. Jul 2, 2010 #2
    What is tensile stress? What is tensile strain? Expand the formula and you will have an equation connecting them (Young modulus, force, area, extension, length) all.
    I suggest you then plot a force-extension graph. From the graph, you will find E. Hint: The graph should be a line, though all the points are not on the line. The data is not really nice.
     
  4. Jul 3, 2010 #3
    Hey, i've done the graphs, i know what im looking at, but it's what exactly am i looking for on the graph to take note of to put into the equation.

    Length = 25mm

    Cross-Section will be the diameter 4mm or the radius of that??

    There is an extension but i don't know what the measurement for that is, the tests pieces themselves i don't have with me to measure. So for the extension how do i read from the graph to figure out what it is?

    The forces are different for each subject, do i add into the equation the top force on the tale of data for each? or am i looking for the maximum force before breaking point?

    As for the data, that can't be helped now that theres a massive advertisement on it. I'll try and clear it up a bit.

    Thanks for your reply though much appreciated :)
     
  5. Jul 3, 2010 #4
    Cross-sectional diameter = 4mm as given in the problem.

    The data has already given you extension of each measurement, and you use it to plot the graph, so what's the point of finding it in the graph?

    No. All you need to do with the data is to use it to plot a graph of force versus extension.

    What is the equation you got anyway? (the one relates force, E, area, length and extension) This equation should be written with notations only; don't hastily plug the data in it as it's unnecessary. The data is only for plotting the graph.
     
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