I attempted the problem and got an answer, although I have no idea if its right

Question

I attempted the problem and got an answer, although I have no idea if its right since there was no example in lecture and nothing similar in the book.

I did a equilibrium analysis on the piston and got something like : Fsubstance = mg + Fatmosphere - kx

I'm not sure if I used the correct formula for the area the piston, pi(d^2)/4?

Thanks.

Consider a vertically aligned piston/cylinder/spring assembly shown below. The mass of the piston is 2.5 kg and has a diameter of 0.1 m. The spring constant is 100 N/m and the spring is stretched by 0.03 m. If the absolute pressure of the surroundings is 100 kPa. what is the absolute pressure of the substance inside the piston/cylinder/spring assembly? Hint, consider free body diagram of the piston and perform static force balance. What is the relative pressure of the substance inside the cylinder? Is the relative pressure a gage value or vacuum value? What had to be assumed to conduct this analysis? I attempted the problem and got an answer, although I have no idea if its right since there was no example in lecture and nothing similar in the book.I did a equilibrium analysis on the piston and got something like : Fsubstance = mg + Fatmosphere - kx I'm not sure if I used the correct formula for the area the piston, pi(d^2)/4?

Explanation / Answer

Balancing the force on mass

Po*area + mg = kx + Pin *area

where Po = pressure outside

Pin = pressure in cyclinder

100*10^3 *area + 2.5*9.8 = 100*0.03 + Pin*area

putting area = 3.14*0.1^2/4

Pin = 102.74 kpa

relative pressure = 2738 pa

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