Calculating Young's Modulus (E) for Metal Alloy, Low Carbon Steel, Copper

[MathsRetard09]

Homework Statement

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 |

Homework 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.

The Attempt at a Solution

Just playing a guessing game and don't really know what I am 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 :)

 

[hikaru1221]

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.

 

[MathsRetard09]

Hey, I've done the graphs, i know what I am 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 there's a massive advertisement on it. I'll try and clear it up a bit.

Thanks for your reply though much appreciated :)

 

[hikaru1221]

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

Cross-sectional diameter = 4mm as given in the problem.

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 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?

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?

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.

 

[paranormal]

Thank you for your question and your attempt at finding a solution. As a scientist, it is important to have a clear understanding of the concepts and equations being used in any experiment or calculation. In this case, you are correct in thinking that Young's Modulus (E) can be calculated using the equation E = Tensile Stress / Tensile Strain. However, it is important to understand what these terms mean and how to obtain them from the data provided.

Tensile stress is the force per unit area applied to a material, and can be calculated using the equation Stress = Force / Area. In this case, the area is the cross-sectional area of the test piece, which is given as 4mm^2 (since the diameter is 4mm, the cross-sectional area is πr^2 = π(2)^2 = 4π ≈ 12.57 mm^2). So, for each force value in the data, we can calculate the corresponding tensile stress by dividing the force by 12.57 mm^2.

Tensile strain is the change in length of a material per unit length, and can be calculated using the equation Strain = Change in Length / Original Length. In this case, the original length is given as 25 mm, so we can calculate the strain for each extension value by dividing it by 25 mm.

Now, we can plug these values into the equation E = Tensile Stress / Tensile Strain for each test piece. For TP1, the first data point would be:

E = (1.0 kN / 12.57 mm^2) / (0.012 mm / 25 mm) = 208.3 kN/mm^2

We can repeat this calculation for all the data points in TP1 and then take the average to get an overall value for E for this metal alloy. You can then follow the same process for TP2 and TP3 to calculate the values for E for low carbon steel and copper respectively.

I hope this helps to clarify the process and equations used in calculating Young's Modulus. If you have any further questions or need clarification, please don't hesitate to ask. As a scientist, it is important to have a thorough understanding of the concepts and methods used in any experiment or calculation. Keep up the good work!