): Air contained within a vertical piston–cylinder assembly is shown in the
figure. On its top, the 10 kg piston is attached to a spring and exposed to an atmospheric pressure
of 1 bar.
Initially, the bottom of the piston is at x=0, and the spring exerts a negligible force on the piston.
The valve is opened and air enters the cylinder from the supply line, causing the volume of the
air within the cylinder to increase by 3.9 x10-4 m3
. The force exerted by the spring as the air
expands within the cylinder varies linearly with x according to
=
where k = 10,000 N/m. The piston face area is 7.8 x10-3 m2
. Ignoring friction between the piston
and the cylinder wall,