Question

Figure P1.30 (attached) shows a gas contained in a vertical piston-cylinder assembly. A vertical shaft whose cross-sectional area is0.8 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

Answer 1

Draw the free body diagram of the piston and the shaft together.

Consider the equilibrium of forces along the vertical direction.

…… (1)

Here, is the external force acting on the shaft, is the force due to atmospheric pressure, is the weight of the piston and the shaft together,is the gas pressure, is the cross sectional area of the piston, is the atmospheric pressure, is the cross sectional area of the shaft, is the mass of the piston, is the mass of the shaft, and is the acceleration due to gravity.

Calculate the cross sectional area of the piston.

Here, is the diameter of the piston.

Substitute 0.1 m (10 cm) for

Convert the units of gas pressure from bar to N/m².

Convert the units of atmospheric pressure from bar to N/m².

Substitute for for for for 24.5 kg for 0.5 kg for and for in equation (1).

Therefore, the force acting on the shaft is.