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 4900 N/m. The piston has a negligible mass and a radius of 0.029 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress

Answer 1

Answer:

x = 0.0537 m or 5.37 cm

Explanation:

Given:

spring constant'k'= 4900 N/m

radius 'r' =0.029 m

Area 'A' =r²π = 0.029²π => 2.6 x $10^{-3}$ m²

Here, Pressure 'P' is given by,

Pressure = Force / Area

And we know that, for a spring :

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

P = kx/A

As P = 101325 Pa

101325 = 4900x / ( 2.6 x $10^{-3}$)

x = 0.0537 m or 5.37 cm