What mass can a hydraulic press lift if the area of the small piston is 1.3 cm2, the large one is 1300 cm2

| January 8, 2021 | education

What mass can a hydraulic press lift if the area of the small piston is 1.3 cm2, the large one is 1300 cm2, and the force acting on the small piston can reach 900N.

g = 9.8 m / s2.
Sm = 1.3 cm2 = 0.00013 m2.
Sb = 1300 cm2 = 0.13 m2.
Fm = 900 N.
m -?
The hydraulic press uses Pascal’s law, according to which the pressure on the small Pm and the large piston Pb are the same: Pm = Pb.
Pressure P is the ratio of the force F to the area S, on which this force acts: P = F / S.
Fm / Sm = Fb / Sb.
The load acts with its weight on the large piston, therefore Fb = m * g, where m is the mass of the load, g is the acceleration of gravity.
Fm / Sm = m * g / Sb.
We find the mass of the cargo m by the formula: m = Fm * Sb / Sm * g.
m = 900 N * 0.13 m2 / 0.00013 m2 * 9.8 m / s2 = 91836.7 kg.
Answer: a hydraulic press can lift a load weighing m = 91836.7 kg.



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