Question

A gas in confined in a 0.5 ft. diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 300 lbm. The local acceleration of gravity is 32.16 ft/s^2, and atmospheric pressure is 1 atm (14.7 psi). What is the force in lbf and Newton exerted on the gas by (1) the piston and the weight (F1); (2) P2, the atmosphere (F2), respectively? Compare the two forces.

Answer 1

We have piston,schematic diagram as follows:

force by piston and weight = mg

m = mass

g = acceleration due to gravity

300 lbm = 136.078kg

32.16 ft/s² = 9.802368 m/s²

force due to piston and weight(F₁) = 136.078 kg x 9.802368 m/s² = 1333.89 N

2.

force due to atmosphere = pressure x cross section area of cylinder

1 atm = 101325 Pa

0.5 ft = 0.1524 m

area = pi/4 x d² = 3.14/4 x (0.1524m)² = 0.01823m²

Force due to atmospheric pressure(F₂) = pressure x area =  101325 Pa x 0.01823m² = 1847.38 N

force due to piston and weight is less than due to pressure

Difference = F₂ - F₁ = 1847.38 N- 1333.89N = 513.5 N