Question

A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open at the top. Friction is absent. The spring constant of the spring is 3900 N/m. The piston has a negligible mass and a radius of 0.020 m.

a) When 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

a) We know that:
Pressure = Force / Area

And for a spring,
F = kx, where k is the spring constant and x is the change in length.

P = kx/A; P = 101325 Pa
101325 = 3900x / (0.02²π)
x = 0.033 m or 3.3 cm

b) Work = 1/2 kx²
= 1/2 * 3900 * (0.033)²
= 2.12 Joules