Atmospheric Pressure on Shaft of piston cylinder assembly

[dkjjjj0302]

Homework Statement

In a vertical piston cylinder assembly, a vertical shaft whose cross sectional area is 0.8 cm^2 is attached to the top of the piston. Determine the magnitude F, of the force acting on the shaft, in N, required if the gas pressure inside the cylinder is 3 bar. The masses of the piston and attached shaft are 24.5 and 0.5 kg respectively. The piston diameter is 10 cm. The local atmospheric pressure is 1 bar. The piston moves smoothly in the cylinder and g=9.8 m/s^2

Homework Equations

P=F/A

The Attempt at a Solution

I converted the atmospheric pressure and gas pressure to forces. I summed all the forces acting on the cylinder. F= -Wshaft - Wpiston + Fgas -Fatm -F=0 Now my problem is, when I find the force caused by atmospheric pressure, do I subtract the area of the shaft from the area of the piston >> Fatm = Pressure (Area(piston)-Area(shaft)) ? How does atmospheric pressure not act on the top of the shaft, shouldn't Fatm = Pressure(Area(piston))?

 

[Nidum]

How does atmospheric pressure not act on the top of the shaft, shouldn't Fatm = Pressure(Area(piston))?

If there is no seal or other pressure controlling feature at the top of the shaft then atmospheric pressure acts on the shaft end in the normal way .

Area to be used for calculating atmospheric pressure force is effectively just the total area of the piston - the hatched area shown in diagram below .

 

[Nidum]

 

[Chestermiller]

You should be considering the equilibrium force balance on the combined piston and shaft, not the cylinder.