P.E of spring

[thespardian]

Hi there!

I want to know whether the spring in a springer airgun obeys the Hook's law. If yes, then how can i plot a graph for the energy stored in the spring of an airgun . The problem i m facing is, the spring is already a little compressed by the spring retainer. So how can i determine the energy stored in the spring when i chocked the gun. Theoretically i have the answer i.e using the hook's law, the useable energy of a chocked airgun can be determined by taking the triangle area under line between un-cocked and cocked airgun by the ignoring the initial compression (as the spring is a little compressed when we push the spring alongw ith spring retainer in the tube). But i don't know how to do it practically and how to draw a graph on a graph paper.
 Any help practical idea in this regard would be highly appreciated.

[rsterne]

Pretty easy calculation, as I recall....

PE = 1/2 k x^2

k is the spring rate (lb./ft.)
x is the distance the spring is compressed (ft.)

The PE (ft.lb.) plotted against compression is therefore a parabolic function....

I would think you would calculate the PE for the preload and subtract that from the total PE at full compression....

Bob

[thespardian]

Thanks a lot Bob for ur guidance
i m a little confused. According to hook's law the applied force is directly proportional to the displacement. it means that the i'll see a straight line while plotting a graph. Whereas the G.V. Cardew and G.M. Cardew plotted a curve instead of a straight line in his research work. Can not get it why there is a curve for the load upto 80 pounds and then a straight line ( I m on page No. 17 of " Airgun from Trigger to Target". and the graph is on page 16) Further to say, how to draw that curve at graph paper?   

[rsterne]

Correct, force is proportional to displacement.... and then to get the PE, you multiply that force by the compression distance again.... That is why the stroke is squared in the PE formula.... if that were not the case, shimming or preloading a spring would not increase the PE released by it....

Bob

[PakProtector]

Pretty easy calculation, as I recall....

PE = 1/2 k x^2

k is the spring rate (lb./ft.)
x is the distance the spring is compressed (ft.)

The PE (ft.lb.) plotted against compression is therefore a parabolic function....

I would think you would calculate the PE for the preload and subtract that from the total PE at full compression....

Bob

You have it right Bob...and the '1/2', and 'k' don't change...sooo, 1/2k(X-squared at cock minus x-squared at preload ) will do it...you take out the energy required to preload because you never get that back out is X_2 squared minus X_1 squared ) times 1/2k
cheers,
Douglas