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# Projectile acceleration question

## Projectile acceleration question

(OP)
Also posted here.

I am trying to determine what the acceleration of a projectile would be if failure happened on an aluminum container that contains 300 PSI compressed air. I'll have to make some assumptions so I would assume that a small piece of 20 grams broke off and the gas inside the chamber propelled it forward horizontally. The gas is not constrained in any way after it leaves the container. The container holds 0.5 cubic feet of compressed gas.

I understand that mass * acceleration = force. If I know the weight of the broken piece all I need is acceleration. I need to estimate acceleration to derive force.

Any help would be appreciated.

### RE: Projectile acceleration question

I'm not quite following you, but I think you mean what happens if your container catastrophically disintegrates?

You know the force - pressure x area, plus the mass should give you acceleration. The force will rapidly diminish once the container fails and the fragment accelerates, but will start to get you in the feel of it.

The other way is to look at energy of the gas and allowing some factor (75%??) to be transferred into movement of the mass of metal.

You might need to draw it out so that we can understand your scenarios.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Projectile acceleration question

(OP)
You are correct - catastrophic failure of the container.

#### Quote (LittleInch)

You know the force - pressure x area, plus the mass should give you acceleration.

Basically a piece at rest acted instantaneously with 300 lbs will strike another object with 300 lbs of force (ignoring air resistance) regardless of mass???

### RE: Projectile acceleration question

No.

The force on your particle depends on the area exposed to the gas pressure - it might be 300 lbs force if it is 1 sq inch.

The mass is known therefore you can calculate acceleration. In a vacuum then yes the piece would hit another piece with that force once it reached terminal velocity. There is a lot of energy in a gas at 300 psig.

The issue is normally how long does the piece of shrapnel see the force. Once there is no force left, there is no acceleration, only deceleration.

I haven't read this, but it looks like what you need. http://www.dtic.mil/dtic/tr/fulltext/u2/a207549.pd...

It looks fairly key as to how the disintegration happens and whether the material is ductile or brittle. I know from painful experience that a brittle material (PVC pipe in my case), when it disintegrates small particles travel very fast and over a surprisingly wide area.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Projectile acceleration question

flycast,
You might have missed one of LittleInch's points. If the shard is 1 sq inch then the force is 300 lbf. If the shard is 2 sq inch then the force is 600 lbf. If a 2 sq inch shard weighs .25 lbm, then your initial acceleration could be as much as 77,000 ft/s2. Even if that force is only applied for 0.01 s, you get an initial velocity of nearly 400 ft/s.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

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