Question

The pressure gauge shown below has a spring for which k = 60 N/m, and the area of the piston is 0.50 cm2. Its right end is connected to a closed container of gas at a gauge pressure of 30 kPa. How far will the spring be compressed if the region containing the spring is (a) in vacuum, and (b) open to the atmosphere? Atmospheric pressure is 101 kPa; *Use Hooke’s law*

Answer 1

a) -0.1092 m

b) - 0.00283 m

Step-by-step explanation:

Given:

A_p = 0.5 cm^2 = 0.00005 m^2

P_g = 30 KPa , P_abs = 30KPa + 101 KPa = 131 KPa

k = 60 N /m

Equations used:

F_net = Δ P * A_p Δ P: Absolute Pressure

F_net = k*x (Hooke's Law)

x = Δ P * A_p / k

part a (P_ext = 0 Pa)

x = ((0 - 131)*10^3 * 0.00005) / 60 = - 0.1092 m (compression)

part b (P_ext = 101 KPa)

x = ((101 - 131)*10^3 * 0.00005) / 60 = - 0.002583 m (compression)