# Length vs force graph

1. Apr 11, 2006

### jimmy_neutron

I have a graph question. I am given the values of Force and the values of length of a rubber band stretching and contracting and am told to plot the data in a length vs force graph.
Here is the data:

And using the data in the plot I have to calculate the work done by the rubber band as it stretches from 10 to 87. I know to do this I just have to caluclate the area under the graph, but my question is how do I plot the graph when the force at force 10 is both 18 and 33.
Sorry if this sounds confusing, hope someone can help.

2. Apr 11, 2006

### DaveC426913

I presume you mean "...as it stretches from 10 to 87... and back to 10..."

3. Apr 12, 2006

### jimmy_neutron

yes that is what i meant

4. Apr 12, 2006

### Staff: Mentor

That's a case of a graph of a quantity that exhibits hysteresis. You'll see this effect in magnetic materials and in stretchy things like rubber bands. I googled hysteresis plot, and the first hit is very helpful:

http://en.wikipedia.org/wiki/Hysteresis

5. Apr 12, 2006

### jimmy_neutron

hmm, I'm only in a basic physics class, that topic seems pretty advanced, thanks for the web site though.

6. Apr 12, 2006

### Staff: Mentor

If that one website isn't enough help, just try the google search that I mentioned to see if there are other sites with explanations that make more sense to you.

Basically hysteresis has to do with the fact that the motion (or whatever) of something can be different based on the history of the motion. In the case of your rubber band, the act of stretching it changes its spring constant, so the position versus force diagram changes after it's been stretched out. So when you do a plot of position versus force, you trace out a different line on the initial stretch-out path than you do on the returning path. And you will be left with a residual extra length (or residual magnetic field in the case of permanent magnets) after the intial stretch (or magnetic field application).