How to find tension in a spring?

[nikkii128]

This is more of a general question, but it relates to a school assignment...

So I am trying to find a mathematical relationship between tension in a spring and the firing range of a device that works basically the same way that a slingshot does.

The setup is basically just two springs on each side a guide and when pulled back and released they propel the object (placed where they join) through the guide.

So far I've got:

PE_{(in a spring)} = (1/2).k.x²
KE=(1/2).m.v²

and just said that ideally, all PE (from both springs) would be converted to KE when the object is propelled.

(btw, x is distance springs are drawn back, m is mass of object propelled, v is velocity and k is the spring force constant)

so I equated them and ended up with:

v² = C.k

where C is a constant of (x²)/m

and then range of projectile motion is:

R=[v².sin(2.theta)]/g

and by subtituting v² from before, i just get

R=ak

where a is just another constant

so to my actual question... does the variable k constitute 'tension in a spring' or is there some other equation I should know about that has the proper variable?

also, were there any errors in my calculations/understanding?

thankyou! :)

 

[Doc Al]

so to my actual question... does the variable k constitute 'tension in a spring' or is there some other equation I should know about that has the proper variable?

I'm not quite sure what you are asking. "k" is the spring constant of the spring you are using. The maximum tension in the spring will be kx, where x is the initial stretch of the spring. (See Hooke's law.)

also, were there any errors in my calculations/understanding?

You mentioned two springs, but it looks like you only considered the PE from one spring.

To make your analysis more accurate, you may want to consider the change in gravitational PE of the object during its propulsion by the spring.