Answer to Question #131181 in Physics for Koketso Rangongo

Question

In the sketch, the cylinder L has a mass of 1300kg and cross sectional area 0.2m^2. The piston S has a cross sectional area of 30cm^2 and negligible weight. If the apparatus is filled with oil, RD=0.78, calculate the force F requires for equilibrium

Answer 1

The pressure in both sides is equal:

$$\frac{Mg}{A_1}=\frac{F}{A_2}+h_\text{oil}g\rho,\\\space\\ F=A_2g\bigg(\frac{M}{A_1}-h_\text{oil}\rho\bigg),\\\space\\ F=30\cdot10^{-4}\cdot9.8\bigg(\frac{1300}{0.2}-h_\text{oil}\cdot780\bigg),\\\space\\ F=(191.1-22.93h_\text{oil})\text{ N}.$$

As we see, the force depends on the height of oil in the piston.