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In a hydraulic press, the left cylinder L carries a piston of mass 600 kg on a cross-sectional area of 800 cm², while the right piston S has area 25 cm² and negligible weight. The two cylinders are connected and filled with oil of density 0.75 g/cm³, with both pistons at the same height. Find the downward force F that must be applied on the small piston S to keep the system in equilibrium.
- 187.5 N
- 375 N
- 750 N
- 1500 N
Correct answer: 187.5 N
Solution
With both pistons at the same height the hydrostatic head cancels, so by Pascal's law the pressure produced by the heavy piston equals that produced by F. Pressure on left = weight/A_L = (600*g)/(800 cm²). Setting F/A_S equal to this: F = (600*g)*(A_S/A_L) = 600*g*(25/800) = 600*g/32. Using g = 10, F = 187.5 N (with g = 9.8, F is about 183.75 N).
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