Spring to propel object at specific velocity

AI Thread Summary
To propel a 3 mm stainless steel ball at 15 m/s using a spring piston, one can apply the conservation of energy principle. The potential energy stored in the spring, calculated as (1/2)kx², converts into the kinetic energy of the ball, expressed as (1/2)mv². The formula v = x√(k/m) can be used to determine the necessary spring constant (k) based on the desired compression distance (x) and the mass of the ball (m). The discussion highlights the importance of using the correct potential energy formula, which was initially misstated. Overall, the calculations and corrections provided led to a clearer understanding of the requirements for the spring mechanism.
Becky6
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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?
 
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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.
 
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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.
 
Thank you both so much! That makes sense. With your help I was able to figure out what I need.
 

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