A cylinder is fitted with a piston restrained by a spring. The spring is fully e

Question

A cylinder is fitted with a piston restrained by a spring. The spring is fully extended (exerting no force) when the piston rests on the bottom of the cylinder. It exerts a force that is linear with distance moved as the piston rises after the air supply line valve is opened. At the state shown in the figure, the pressure inside the cylinder is 300kPa and the volume is 0.5L. The piston diameter is 100mm, its mass is 5kg, and ambient pressure outside the cylinder is 100kPa. Additional air is admitted from the supply line, causing the piston to rise another 20mm. What is the pressure inside the cylinder at this point?
Answer: 360.9kPa

Explanation / Answer

the additional pressure created by the mass. P=mg/S=5*g/pi*r^2=6240(Pa). we have that P_inside=P_mass+P_spring+P_ambi. so 300e3=6.24e3+P_spring+100e3. so +P_spring = 193.8e3(Pa). --- the height of the air column before air is admitted. H=0.5e-3/pi*r^2=0.0637(m)=63.7(mm). we have. P_spring/H=const. so P_spring'=193.8e3*(63.7+20)/63.7=255e3(Pa). so P_inside=255e3+6.24e3+100e3=360.9e3(Pa)

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