Compressed air lift question (thermodynamics)

[hahaha158]

Homework Statement

A platform is supported on a piston by compressed air in a cylinder.
The mass of the platform and equipment being lifted is 1100kg. The pressure needed to
support this mass is 800kPa, and it rests initially at a height of 0.5m. The pressure supply
is closed so that no gas enters or leaves the cylinder. One of the pieces of equipment with a
mass of 50kg is moved o the platform. The entire system is at room temperature (300K)
(a) What is the new position of the platform? (b) What is its maximum velocity?

Homework Equations

W=PdV
PV=nRT

The Attempt at a Solution

I'm having trouble trying to find an equation that relates mass and height, that can also be related to pressure. There is no radius given, so I do not know how to find the volume of the ccylinder. Also, I am wondering what "no gas enters or leaves the cylinder" means in terms of pressure/temperature etc.

 

[Undoubtedly0]

Consider a force balance on the piston. The weight of the piston, mg, is balanced by what force?

 

[hahaha158]

Consider a force balance on the piston. The weight of the piston, mg, is balanced by what force?

It would be balanced by normal force given by f=-mg?

I can use this to calculate the area using P=F/A which is constant.

Given this I can find P when the 50kg mass is removed.

But how do I relate this to the height?

 

[Undoubtedly0]

It would be balanced by normal force given by f=-mg?

I can use this to calculate the area using P=F/A which is constant.

You are close. What you call a "normal force" is actually the force due to pressure, F_P = PA (where P=800\,\mathrm{kPa}). It is this force that balances the weight of the piston. In other words, this relationship allows you to find the area of the piston, and hence the initial volume of the cylinder.

 

[rude man]

I am butting in just to track this thread.