Air is contained in a vertical piston-cylinder assembly such that the piston is in static equilibrium. the atmosphere exerts a pressure of 14.7 lbf/in2 on top of the 6-in-diameter piston. the absolute pressure of the air inside the cylinder is 16 lbf/in2. the local acceleration of gravity is g= 32.2 ft/s2. determine (a) the mass of the piston, in lb, and (b) the gage pressure of the air in the cylinder, in psig

Refer to the diagram shown.

p₁ = 14.7 psia,atmospheric pressure
p₂ = 16 psia, absolute pressure in the cylinder

The weight of the piston is
W = mg
where m =  mass of the piston.
g = 32.2 ft/s² = 386.4 in/s²

The area of the piston is
A = (π/4)*(6 in)² = 28.273 in²

Part a:
For equilibrium,
(p₂ - p₁)A = W
(16 - 14.7)*(28.273) = (386.4)*(m)
m = 0.095 lb

  m = 0.095 lb

Part b:
The gage pressure in the cylinder is
p₂ - p₁ = 16 - 14.7 = 1.3 lb/in²

1.3 lb/in²

The relationship of both of them

B. conditioned response