Spring to propel object at specific velocity

In summary, the conversation discusses using the conservation of energy principle to calculate the appropriate spring constant for a small spring piston. The formula for potential energy is (1/2)kx^2, and the speed of the ball can be determined using the equation v= x√(k/m). The conversation also mentions the density of steel and provides a link for finding the correct potential energy of a spring.
  • #1
Becky6
3
0
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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  • #2
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.
 
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  • #4
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.
 
  • #5
Thank you both so much! That makes sense. With your help I was able to figure out what I need.
 

FAQ: Spring to propel object at specific velocity

1. How does a spring work to propel an object?

A spring is an elastic object that stores potential energy when compressed or stretched. When released, this stored energy is converted into kinetic energy, causing the spring to push or pull an object attached to it. This motion can be used to propel an object at a specific velocity.

2. What factors affect the velocity of an object propelled by a spring?

The velocity of an object propelled by a spring is affected by factors such as the strength and stiffness of the spring, the mass of the object, and the distance the spring is compressed or stretched. These factors determine the amount of potential energy stored in the spring, which is converted into kinetic energy to propel the object.

3. Can the velocity of an object propelled by a spring be adjusted?

Yes, the velocity of an object propelled by a spring can be adjusted by changing the factors that affect it. For example, increasing the strength or stiffness of the spring, decreasing the mass of the object, or compressing or stretching the spring to a greater distance can result in a higher velocity.

4. Are there any limitations to using a spring to propel an object at a specific velocity?

Yes, there are limitations to using a spring to propel an object at a specific velocity. The strength and stiffness of the spring have a maximum limit, and compressing or stretching the spring too far can cause it to lose its elasticity. Additionally, external factors such as friction and air resistance can also affect the velocity of the object.

5. How is the velocity of an object propelled by a spring calculated?

The velocity of an object propelled by a spring can be calculated using the equation v = √(kx²/m), where v is the velocity, k is the spring constant, x is the distance the spring is compressed or stretched, and m is the mass of the object. This equation is derived from the conservation of energy principle, where the potential energy stored in the spring is converted into kinetic energy to propel the object.

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