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## Homework Statement

A simple pressure relief device is shown in Figure Q6.1 below. It consists of a

piston of mass 0.5 kg and thickness 3 cm sliding without leakage or friction into

a cylinder of diameter 5 cm. The bottom section of the cylinder can be exposed

to a varying source of pressure, while the upper section is open to the

atmosphere.

A spring is attached to the upper face of the piston at point A and to a fixed

frame at its other extremity. Without the piston attached, the spring rest

position of A is located up 15 cm from the bottom of the cylinder, as shown in

Figure Q6.1. When attached to the piston, A drops by 3 cm as shown in

Figure Q6.1. Assume that g = 9.8 m/s

1 -

Calculate the total length of the cylinder so that the bottom face of the

piston reaches the top of the cylinder (and therefore vents the pressure out)

when the internal pressure reaches 10 kPa gauge. Assume a spring

constant of 150 N/m for this question and a position of the piston point A at

rest of 12 cm from the bottom of the cylinder.

2 -

Consider the cylinder base open to atmosphere with a free flow of air. The

system of piston and spring is at rest. Calculate the natural frequency of

this system. Assume a spring constant of 150 N/m for this question.

Arrow on right is total length of cylinder, but the image was too big so I had to crop it.

Consider the cylinder base open to atmosphere with a free flow of air. The

system of piston and spring is at rest. Calculate the natural frequency of

this system. Assume a spring constant of 150 N/m for this question.w

## Homework Equations

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## The Attempt at a Solution

I don't even know where to begin to be honest.

Found Pressure upwards using F=PA, F=10,000 x pi (0.025)^2 = 19.63N which seems very low.

Then found force on hanging spring to beh 450N, F=kL = 150 x 3 = 450N

So I'm stuck because there isn't enough force to overcome the weight already on the spring so I've gone wrong somewhere.

Haven't even covered natural frequency to be honest.

Thanks