# Spring to propel object at specific velocity

1. Jul 22, 2009

### Becky6

I want to make a small spring piston to propel a 3 mm stainless steel ball to hit a target at a velocity of 15 m/s from just a few inches away. How can I calculate/determine the right spring to use?

2. Jul 22, 2009

### HallsofIvy

Staff Emeritus
Well, you ought to be able to do this using "conservation of energy". If the spring has spring constant k, and you compress it a distance x, it gains potential energy (1/2)kx2. When it is released, that potential energy goes into the kinetic energy of the ball, (1/2)mv2: (1/2)kx2= (1/2)mv2 so the speed with which the ball leaves the spring is $v= x\sqrt{(k/m)}$. I don't think the ball will lose much speed in "just a few inches". The density of steel varies a little depending on the kind of steel- I'll let you look that up.

Last edited: Jul 23, 2009
3. Jul 23, 2009

### Bob S

4. Jul 23, 2009

### HallsofIvy

Staff Emeritus
Oh, blast- I knew better than that!
The potential energy is $(1/2)kx^2$, not $(1/2)kx$. That doesn't even have the correct units!

Thanks for the correction, Bob S, I have edited my post to correct that.

5. Jul 24, 2009

### Becky6

Thank you both so much! That makes sense. With your help I was able to figure out what I need.