Simple problem here boys. I'm currently in the process of making a high powered and hand held potato gun. Essentially, it'll function just as a regular paintball gun would but on a slightly larger scale. Now....What makes this a rather hard endeavor is that I want to shoot a whole potato; and that is some serious weight. So before I start construction I want to get the physics behind the gun down pat.

It'll be a bolt like design whereby a pressure source pushes the bolt forward into a spring that later retracts the bolt into its original position but not before the bolt hits and ejects the potato out the barrel.

Here's what I got. Okay so the Kinetic Energy of the Bolt when it hits the patato is

Where Fpvc = force of friction done on the bolt by the PVC pipe (probable material)

And again, we equate K1 to

Which is the equation for the potato when it exits the pipe. This, so we can calculate the velocity at the time of exist.

That's not to complicated; unless i'm forgetting something in that calculation? I don't think so because

Where M1 = mass of patato and M2 = mass of bolt. Therefore M1V2 = 0 and M2V2` = 0.

Hence

And the only reason Kinetic Energy wouldn't be conserved is due to Friction correct?

Okay so assuming the above calculations are right (if there not do let me know) I need to know the relationship between pressure, the resistance of the spring that the bolt is propelled into, and the weight of the bolt.

Because I need to calculate the minimum pressure to meet my goals (in terms of distance and speed). Does anyone know the constraint relation for those 3 things? The mass of the bolt, the resistance of the spring and the weight of the bolt?