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Very Frustrated here A gas is contained in a vertical, frictionless,piston-cycli

ID: 1815573 • Letter: V

Question

Very Frustrated here A gas is contained in a vertical, frictionless,piston-cyclinder. The piston (m = 10kg, A = 75x10^-3m^2) isattached to a spring, and the back-side of the piston is exposed toatmospheric pressure. Initially the piston is at x = 0m, and thespring is not deformed. Thereafter the gage pressure in thecylinder is increased to 0.75bar, until the final volume of the gasincreases by 3.75x10^-3m^3. The local acceleration of gravity is9.81 m/s^2. Determine the following: i) the initial cylinder gage pressure(kPa) ii) the linear spring constant k(N/m) this is not out of a textbook, very confused, pleasehelp!! Very Frustrated here A gas is contained in a vertical, frictionless,piston-cyclinder. The piston (m = 10kg, A = 75x10^-3m^2) isattached to a spring, and the back-side of the piston is exposed toatmospheric pressure. Initially the piston is at x = 0m, and thespring is not deformed. Thereafter the gage pressure in thecylinder is increased to 0.75bar, until the final volume of the gasincreases by 3.75x10^-3m^3. The local acceleration of gravity is9.81 m/s^2. Determine the following: i) the initial cylinder gage pressure(kPa) ii) the linear spring constant k(N/m) this is not out of a textbook, very confused, pleasehelp!!

Explanation / Answer

m= 10 kg A=75*10^-3 Pg=0.75 bar = 75 kpa V=3.75*10^-3 m^3 i)   Pg1* A = m*g     (Pg1=initial pressure gage)     Pg1 * 75*10^-3 = 10 * 9.81     Pg1 = 1308 pa = 1.308 kpa ii)   Pg2 * A = m*g + Fs      Pg=Pg2-Pg1         75 = Pg2 -1.308                   Pg2= 76.308 kpa       so,   Pg2 * A = m*g +Fs      (76.308*10^3)*(75*10^-3) =(10)*(9.81) + Fs      Fs= 5625 N (springforce)       Fs= k*x      A= (pi/4)*D^2      V= V2-V1     V= A*h2-A*h1    V= A (h2-h1)     V= A*x     (3.75*10^-3)= (75*10^-3)*x    x= 0.05 m     Fs= k* x      5625 = k * (0.05)      ( k= 112500 N/m )      Good luck