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? wouldnt 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.