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Spring to propel object at specific velocity

  1. Jul 22, 2009 #1
    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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  3. Jul 22, 2009 #2

    HallsofIvy

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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 [itex]v= x\sqrt{(k/m)}[/itex]. 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
  4. Jul 23, 2009 #3
  5. Jul 23, 2009 #4

    HallsofIvy

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

    Thanks for the correction, Bob S, I have edited my post to correct that.
     
  6. Jul 24, 2009 #5
    Thank you both so much! That makes sense. With your help I was able to figure out what I need.
     
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