Power band rubber from around the world has different properties and different soak off times depending on percentage elongation of the specimen length. The modulus of elasticity even varies from batch to batch from the same balk rubber supplier. There can be no generalization here that will apply to shaft impact force without knowing all the gun specs.
Cheers, Don Paul
Hi Don
I can give you an example that you can apply and see if you can find a law for this rubber or no. First of all you need to bring the below:
1- Weight of 2 kgs 5kgs and 8 kgs.
2- Bring 3 rubber bands same length and same diameter but from different suppliers i.e different stretching behavior.
3- A bench to hang the rubber vertically.
4- you need meter tape for measuring the length.
If you connect the rubber from one side and put a weight of 2 Kgs from the other side vertically the rubber will stretch in specific X value. Going back to Hooks law F = K(X-X1) and as you said we will find that each brand will stretch in a small difference, but still we can apply this law since the stretch value will be different and the constant K therefore will be different and this proves what you said K is different from one factory to another depnds on how they make the rubber. Lets take it like this K will define the power of the band so if we have weight of 2 Kgs which will produce a force of F= mass x Gravity Then F= 2 x 9.81= 19.62 N If the power K= 5 for Brand A and K = 6 Then it will be like this:
Case A K = 5 and F= 19.62 = K(X-X1)= 5 (X-X1) then (X-X1) = 3.924
Case B K = 6 and F = 19.62 = K(X-X1) = 6 (X-X1) then (X-X1) = 3.27
As we can see when K was more which is the rubber band power was high we got less stretching (X-X1)
You can do it on different weights and see the difference while applying different weights how it will affect. Hooks law will be applied till the spring lose its elasticity, and here till it reach it is maximum point of stretching.
So despite all of the very good points made the original question is would a spear fire at the same speed and with the same range with the 80lb force applied by a 16mm rubber stretched 2.2 times as with a 14mm rubber stretched 2.8 times?
Not always right 100% as bill says work = force x distance so if you take the values for the same gun it will be right because same stretching distance will be there approximately(Shaft will be same), but for different guns it will be different since the shaft length and weight will make the difference.