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 3400 N/m. The piston has a negligible mass and a radius of 0.028 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 =  0.0734 m = 7.34 cm

Explanation:

First we shall calculate the area of the piston:

$Area = \pi radius^2\\Area = \pi (0.028\ m)^2\\Area = 0.00246\ m^2$

Now, we will calculate the force on the piston due to atmospheric pressure:

$Atmospheric\ Pressure = \frac{Force}{Area}\\\\Force = (Atmospheric\ Pressure)(Area)\\Force = (101325\ N/m^2)(0.00246\ m^2) \\Force = F = 249.56\ N$

Now, for the compression of the spring we will use Hooke's Law as follows:

$F = kx$

where,

k = spring constant = 3400 N/m

x = compression = ?

Therefore,

x =  0.0734 m = 7.34 cm