(Solved): (a) The figure below shows a gas contained in a vertical piston-cylinder assembly. A vertical shaf ...

(a) The figure below shows a gas contained in a vertical piston-cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 ${\mathrm{cm}}^2$ is attached to the top of the piston. Determine the magnitude, $F$, of the force acting on the shaft, in $\mathrm{N}$, required if the gas pressure is 3 bar. The masses of the piston and attached shaft are $24.5\mathrm{kg}$ and $0.5\mathrm{kg}$, respectively. The piston diameter is $10\mathrm{cm}$. The local atmospheric pressure is 1 bar. The piston moves smoothly in the cylinder and $g=9.81\mathrm{m}/{\mathrm{s}}^2$.