system
Given the following post, respond as if you're commenting on Reddit:
human
What's the physics behind shooting a plastic bottle cap?

Hey everyone, hope you're having a good day!
I very much like this subreddit because of the wide variety of questions that are asked here, from really theoretical questions to daily applications of science.

The thing I woud like to talk about belongs in the second category of daily applications of science in shooting plastic bottle caps. I am sure that a lot of you have tried this at some point, but let me explain what I mean exactly: If you take an empty plastic bottle (for example a water bottle or a soda bottle) and try to crunch it as much as you can with the cap still on it, you will be able to build up a lot of air pressure inside the bottle. If you then quickly unscrew the cap while the air is compressed, the cap will shoot off!

I do not know a lot of physics myself, but most of the fluid dynamics that I have heard of revolved around incompressible fluids and not gases, so I was wondering if there were any formulas or calculations one could make to figure out things like the **compressibility of the air** inside a plastic bottle, the built up **potential energy** in compressing the bottle and the conversion from potential to **kinetic energy** when you shoot the cap.
I hope you guys will enjoy this topic!
gpt
Well you have:

P1*V1 = P2*V2

Basically as volume decreases from the initial state, the pressure will have to increase. When you scrunch the bottle down, you are decreasing the volume and causing an increase in pressure. 

Pressure can be expressed as:

P = Force/Area

Since the area of the bottle cap doesn't change, as pressure goes up, so does the force on the cap. 

Force is defined as:

F = mass * acceleration

Since the mass of the bottle cap doesn't change, then acceleration has to. Increase in force causes an increase in acceleration.

In conclusion, decreasing the volume causes an increase in pressure which increases the force on the bottle cap. The higher forces give the bottle cap a higher acceleration and send it flying.