The area of the smaller piston of a hydraulic press is 4 cm2 and the area of a larger one is 100 cm2

The area of the smaller piston of a hydraulic press is 4 cm2 and the area of a larger one is 100 cm2, a force of 200 N acts on the smaller piston. Find out how much weight the large piston can lift. Friction is not included.

Sm = 4 cm2 = 0.0004 m2.

Sb = 100 cm2 = 0.01 m2.

Fm = 200 N.

g = 10 m / s2.

m -?

In the device of a hydraulic press, Pascal’s law is used, according to which the fluid pressure is transmitted in different directions in the same way.

The pressure of the small piston Pm and the large piston Pb are equal to each other: Pm = Pb.

The pressure of the liquid 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 by the force of its weight Fb on the larger piston: Fb = m * g.

Fm / Sm = m * g / Sb.

The mass of the cargo m will be determined by the formula: m = Fm * Sb / g * Sm.

m = 200 N * 0.01 m2 / 10 m / s2 * 0.0004 m2 = 500 kg.

Answer: the mass of the load that can be lifted with a press is m = 500 kg.