The hydraulic press must produce a force of 2.7 · 10⁵N. The diameter of the small piston is 3 cm

| May 10, 2021 | education

The hydraulic press must produce a force of 2.7 · 10⁵N. The diameter of the small piston is 3 cm, and the diameter of the large one is 90 cm. What force should be applied to the small piston?

Fb = 2.7 10⁵H
Dm = 3 cm = 0.03m
Db = 90cm = 0.9m
Fm-?
Let us express the pressure of the large Pb and the small piston Pm. Pb = Fb / Sb, Pm = Fm / Sm, where Fb is the force with which the large piston presses, Sb is the area of the large piston, Fm is the force with which the small piston presses, Sm is the area of the small piston. The pistons are circular so the area of the circle is (P * D ^ 2) / 4, where P = 3.14. Sb = (P * Db ^ 2) / 4, Sm = (P * Dm ^ 2) / 4. According to Pascal’s law, pressure in liquids and gases is transmitted in all directions in the same way, therefore Pb = Pm, Fb / Sb = Fm / Sm; Fb / (P * Db ^ 2) / 4 = Fm / (P * Dm ^ 2) / 4; Fb / Db ^ 2 = Fm / Dm ^ 2; Fm = Fb * Dm ^ 2 / Db ^ 2. Fm = 2.7 10⁵H * 0.0009m2 / 0.81m2 = 300 N.
Answer: Fm = 300 N.



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