Calculating Final Height with Piston Design

[jonathan102]

Homework Statement

As a mechanical design project, we have to design a device that will lift a 1kg weight off the ground as high as possible when the only source of energy provided is 1.35L of 80psi compressed air. (it has to stay there so a slingshot/cannon is out of the equation) We are currently in the design process and would like to know how high it would go with the amount of compressed air. Our current design is to use a piston to push the weight up. My question is, if we know the dimension of the piston we are using, can we simply use P_1*V_1 = P_2*V_2 to give us an approximation of the final height?

Homework Equations

P₁V₁=P₂V₂
P = mg/A

The Attempt at a Solution

P₁ = 80psi = 551580 Pa
V₁ = 1.35L = 0.00135m³
P₂ = mg/A = 9.81/(0.025² $\times$$\pi$)
V₂ = (0.025²$\pi$$\times$h)$\times$2+0.00135

Assuming there are two 0.025m radius pistons pushing the weight up, i got a height of 37.6m.

 

[gneill]

The compressed air container is probably heavier than 1kg. Tie it to one end of a rope that goes over a pulley to the 1kg weight on the other end. Make the rope as long as you like!

Place the weight at the bottom of a very deep lake. Use some of the 1.35L of air to inflate a balloon to raise the weight by buoyancy.

But seriously, don't forget that there will be frictional losses between the cylinders and pistons, and that gas cools as it expands. Your P_o*V_o = P₁*V₁ assumes a constant temperature for the gas. You may get mediocre results unless you let the gas expand slowly and use a metal with high heat conductivity for the cylinders. Don't let on that you're sneaking extra energy into the system