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Using Specific Volume, Volume, and PressureFigure P1.30
Chapter 1, Problem 30P(choose chapter or problem)
Figure P1.30 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 N, required if the gas pressure is \(3 \mathrm{bar}\). 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 \(g=9.81 \mathrm{~m} / \mathrm{s}^2\).
Questions & Answers
QUESTION:
Figure P1.30 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 N, required if the gas pressure is \(3 \mathrm{bar}\). 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 \(g=9.81 \mathrm{~m} / \mathrm{s}^2\).
Step 1 of 4
Draw the free-body diagram of the piston and the shaft together.
Step 2 of 4
Consider the equilibrium of forces along the vertical direction as,
\({\sum F _y} = 0\)
Solve it as,
\({F_P} - \left( {{F_{atm}} + W + F} \right) = 0\)
\({F_P} = \left( {{F_{atm}} + W + F} \right)\)
\(p{A_p} = \left( {{p_{atm}}\left( {{A_p} - A} \right) + {m_{piston}}g + {m_{shaft}}g +