# Does my elongation vs. load graph look right?

#### physicsss

This is a graphfor a bungee cord that is being tested by adding load to one end while fixing its other end on some support system

how I got the x-axis data: So say the initial length is 2 cm and after one pound is added to it it became 2.50cm. So I use 2.50cm-2cm and use it to find the elongation. so (0.5, 1) is the first point. and so on. I do the elongation measurement for every pound of loud I added.

y-axis is load. it goes up from 1 to 25.

But my graph here doesn't look right at all....is it supposed to go left to right and not left to right and left? Or it is the case with bungee cords? Please help...

TY.

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#### alpha_wolf

Given that you've taken the load as the variable, and the elongation as the function of the variable, you get a graph of elongation as a function of load, and not load as a function of elongation. If you switch the axes (put the load on the x axis, and the elongation on the y axis), then it will make more sense. But I'm not sure how useful such a graph would be.

If you want to study the cord's mechanical behavior, you need either a load-elongation graph (load as a function of elongation), or a stress-strain graph. The former tells you how this specific cord behaves, while the latter tells you how the cord's material behaves regardless of the shape of the actual cord.

To get these, first meassure the load as a function of elongation: stretch the bungee cord by a known amount, and measure the tension force it produces. Repeat for as many elongations as you need (in materials investigations, this is usually done until the model breaks).

Then, if you want the stress-strain graph, divide the load by the cord's initial cross-section area, and the elongation by the cord's inital length. I think you should get a graph similar to that of a typical elastomer.. I'll post a link to a sample graph in a few minutes.

edit:
ok. http://www.padtinc.com/epubs/focus/2002/0012_1125/article3_imgs/img001.gif [Broken], which gives a survey of the various elastomer testing techniques.

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#### Gokul43201

Staff Emeritus
Gold Member
It's also important to distinguish between "real stress" and "engineering stress".

Anyway physicsss, according to your graph, as you increase the load from 6 lbs to 7 lbs, the bungee cord gets shorter, and continues getting shorter as you add more load. Is this what really happens ? Also, you say that the first point was at (0.5,1) but on the graph, it's at (0,1). Will you please confirm that the cord gets shorter as you load it, finally returning to nearly its original length of 2 cm at 25 lbs ?

#### physicsss

how else can I calculate elongation? that point was made up to show what I did to get the calculations...the cord gets longer from 2 cm to 2.50 cm, but the elonation is the difference between the two, or am I doing this wrong?

#### brewnog

Gold Member
Physicsss, Gokul was pointing out that your graph shows that with increasing load, the cord extends reasonably steadily to a certain value, and then with even more load, it starts to contract back, eventually to its original size. I don't see how this happens.

Perhaps you want to try plotting a better graph? Define strain as extension/original length, and define stress as force/cross-sectional area, and feel free to neglect the change in area with extension as you see fit. Then plot stress/strain.

#### alpha_wolf

Gokul43201 said:
It's also important to distinguish between "real stress" and "engineering stress".
True. My description above was for engineering stress (and engineering strain), I don't really think the OP needs the real stress to real strain graph..

physicsss said:
how else can I calculate elongation? that point was made up to show what I did to get the calculations...the cord gets longer from 2 cm to 2.50 cm, but the elonation is the difference between the two, or am I doing this wrong?
The elongation is the current length minus the original length, not the current minus the previous.

#### Gokul43201

Staff Emeritus
Gold Member
alpha_wolf said:
The elongation is the current length minus the original length, not the current minus the previous.
Nice catch alpha. I think you have debugged the problem with the weird graph. The y-integral of that graph will look more like a regular load elongation curve, so I think you've cracked the source of the negative mudulus.

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