Simple piston Pressure Problem

[engstud]

Homework Statement

Figure P1.30 (attached) shows a gas contained in a vertical piston-cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm² 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 is 3 bar. The masses of the piston and attached shaft are 24.5kg and 0.5kg respectively. The piston diameter is 10cm. The local atmospheric pressure is 1 bar. The piston moves smoothly in the cylinder and g=9.81 m/s²

Homework Equations

F=pA
F=ma

The Attempt at a Solution

I calculated the pressure exerted on the piston by the gas (I called it Fg) using Fg=pA which gave me Fg=(3 bar * 10⁵ Pa)*pi*(.05m)^2=23561.9 N

I then drew a free body diagram of the piston, applied Newton's second law and ended up with 0=Fg-F-Ws-Wp where Ws is the weight of the shaft and Wp is the weight of the piston. When I plug in all my numbers and solve for F I end up with 23316.7N. I do not know whether or not this is the correct answer but I am being thrown off by the fact that they gave me the cross-sectional area of the shaft and I did not use it. Can someone please check my logic?

 

[ee1215]

I have the calculations for the atm and gas force. I am not seeing how some get the formula, Fatm=F+Fgas+W. How do you come to this formula from the diagram? And then solve for F. Anyone.

 

[RTW69]

The area of the shaft is not needed. Convert the pressures to forces and do a free body diagram on the piston. I think the Force exerted by the gas is incorrect, decimal problem.