Question

A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3100 N/m. The piston has a negligible mass and a radius of 0.025 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?

Answer 1

Atmospheric Pressure at STP = 1.01325*10^5 Pa

The force due to the atmosphere on the piston = Pressure*Area of the piston

F = 101325*pi*0.035^2

F = 198.95 N

This forces acts on the spring below the piston to compress.

When the piston reaches equilibrium force due to spring = force due to atmosphere

F = kx

x = 198.95 / 3100 = 0.06417 m

b)

By conservation of energy

The work done by atmospheric pressure compressing the spring = Potential energy of the spring

W = 1/2*3100*0.06417^2 = 6.38 J