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# Young's modulus help. watch

1. So I'm doing a project for my advanced higher physics and one of the ways I have used to calculate Young's modulus of a mild steel wire is by Searle's method. I have already calculated it using the equations stress/strain but in my instructions sheet it told me to plot mass(x-axis) against change in length(y-axis) which I have done and it says that the gradient of the graph can also be used to calculate Young's modulus. The units I used for mass were kg and for change in length it was mm. Can anyone help me with calculating it by using the gradient of the graph ? And also should it be mm on the y-axis or something different because my gradient was like 0.161 which seems way too small a value to be used for a calculation. Cheers.
2. Anyone ?
3. (Original post by RossB1702)
So I'm doing a project for my advanced higher physics and one of the ways I have used to calculate Young's modulus of a mild steel wire is by Searle's method. I have already calculated it using the equations stress/strain but in my instructions sheet it told me to plot mass(x-axis) against change in length(y-axis) which I have done and it says that the gradient of the graph can also be used to calculate Young's modulus. The units I used for mass were kg and for change in length it was mm. Can anyone help me with calculating it by using the gradient of the graph ? And also should it be mm on the y-axis or something different because my gradient was like 0.161 which seems way too small a value to be used for a calculation. Cheers.
Write out the full equation of the function you are plotting:

,

where is mass, is a product of constants and is the displacement.

The gradient of your graph is . Additionally, you should know that is a function of the Young's modulus .

You should equate the parameters which compose with the gradient of your graph and then solve for .
Write out the full equation of the function you are plotting:

,

where is mass, is a product of constants and is the displacement.

The gradient of your graph is . Additionally, you should know that is a function of the Young's modulus .

You should equate the parameters which compose with the gradient of your graph and then solve for .
Hey thanks for the help! Would you mind clarifying on what you mean by "You should equate the parameters which compose with the gradient of your graph and then solve for . ". Also wouldn't m=s/c not cs ? And is the deflection being in mm okay ? Cheers for the help.

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5. (Original post by RossB1702)
Hey thanks for the help! Would you mind clarifying on what you mean by "You should equate the parameters which compose with the gradient of your graph and then solve for . ". Also wouldn't m=s/c not cs ? And is the deflection being in mm okay ? Cheers for the help.

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Using Searle's method, you should be able to rearrange the fundamental equation to the form of:

,

where will be a function of the Young's modulus and other relevant parameters (which you should know).

Hence, when you plot your graph, the gradient will be . Equate with the numerical value of your gradient and then rearrange for .

The displacement for this sort of experiment is usually plot in [mm]. However, you should convert the displacement to [m] when performing your calculations. This will result in the resulting value of with units [Pa].

If you look up a reference book for materials (or do a quick search online), you can see that for Young's modulus of metals is typically in the order of [GPa]. Hence, you should convert your answer from [Pa] to [GPa] when presenting it in your report or whatever you may be doing.

You have not previously defined , so I do not understand what you are referring to. I have yet to develop the ability to read minds.
6. (Original post by RossB1702)
So I'm doing a project for my advanced higher physics and one of the ways I have used to calculate Young's modulus of a mild steel wire is by Searle's method. I have already calculated it using the equations stress/strain but in my instructions sheet it told me to plot mass(x-axis) against change in length(y-axis) which I have done and it says that the gradient of the graph can also be used to calculate Young's modulus. The units I used for mass were kg and for change in length it was mm. Can anyone help me with calculating it by using the gradient of the graph ? And also should it be mm on the y-axis or something different because my gradient was like 0.161 which seems way too small a value to be used for a calculation. Cheers.
Mass/change in length. Modulus = (F/A)/strain strain= (F/A)/modulus.
Strain = (mass*9.81/A)/modulus.
Strain/mass = (9.81/A)/modulus

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Updated: February 11, 2017
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