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 3300 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 = 0.081 m.

Explanation:

a) To find how much does the atmospheric pressure cause the spring to compress we need to use the following equation:

$F = k*x$    (1)

Where:

F: is the force

k: is the spring constant = 3300 N/m

x: is the distance of compression =?

The force can be found as follows:

$F = P*A$    

Where:

P: is the atmospheric pressure = 101325 Pa

A: is the area of the piston = πr²

r: is the radius = 0.029 m

$F = 101325 Pa*\pi*(0.029 m)^{2} = 267.7 N$    

Now, from equation (1) we can find x:

$x = \frac{F}{k} = \frac{267.7 N}{3300 N/m} = 0.081 m$    

Therefore, the atmospheric pressure causes the spring to compress 0.081 m.      

I hope it helps you!