Energy stored while loading a spring

[nokia8650]

I am doing a question which asks to plot a graph of Force vs. extension; it then asks how can the graph be used to estimate the energy stored during the loading process. I thought that this would simple be the area under the graph, however the markscheme says "the area under the graph at any given point." Can anyone explain the reason for this please?

Thanks

 

[lzkelley]

This means the area under the graph up to the given point. For instance if you have a graph that looks like a triangle, one corner at the origin, sloping up to some maximum x and maximum y; if you want to know the energy stored when the extension (or compression) is at x/2 (half the maximum) you only want to know the area up till that point, i.e. 1/8*x*y

 

[nokia8650]

thanks, where did you get 1/8 xy from? wouldn't it be 1/4 xy?

Thanks

 

[lzkelley]

np,
1/2*base*height right? base = x/2 ; height = y/2 --> 1/8xy

 

[nokia8650]

Yes, my mistake. Thank you.