Why Is the Area Between Non-Hookean Material Graphs the Energy Lost?

[Abobaker Ugool]

So i have been given a practical for a non-hookean material i.e. polymer, we were to add weights progressively and then taking them off one by one. After doing so i plotted the weight attached to the polymer vs the length stretched for both adding and removing the weights on the same graph. The teacher told us the area inbetween the two curves is the energy lost/work done and and approximation of the spring constant are the tangents at which the graph curves, such that there are six tangents in total. But i don't understand why the area inbetween the two curves is the energy lost/work done and why the tangents at which the graph curve are approximations of the spring constant??
Please help!

 

[BvU]

Hello Abobaker, welcome to PF !

Interesting experiment. Difficult to answer your questions without knowing where you are in your education. That's why the template is so useful. It appears to have been lost in your post, an unfortunate accident, I hope. Because in PF its use is mandatory (see the guidelines for reasons why) They also require an effort on your part to come to a solution. That also helps us to provide more useful assistance.

Homework Equations

[/B] -- what equations do you have available relating force, distance, work ? And what do you have about ideal springs (Hooke ?, spring constant, force, distance, work ? )

The Attempt at a Solution

[/B]-- tell us what you know already about the work a weight does on a spring while loading.