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A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 8.0 cm. What force must be applied to the smaller piston to obtain a force of 1600 N at the larger piston?
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A hydraulic press has one piston of diameter 2.0 cm and the other pist...
Hydraulic Press Calculation


Introduction


A hydraulic press is a machine that uses hydraulic pressure to increase force. It works on the principle of Pascal's Law, which states that when pressure is applied to a confined fluid, the pressure is transmitted equally in all directions.

Given Information


Diameter of smaller piston (d1) = 2.0 cm

Diameter of larger piston (d2) = 8.0 cm

Force at larger piston (F2) = 1600 N


Calculation


Area of smaller piston (A1) = π(d1/2)2 = π(1 cm)2 = 3.14 cm2

Area of larger piston (A2) = π(d2/2)2 = π(4 cm)2 = 50.27 cm2


According to Pascal's Law:

Pressure at smaller piston (P1) = Pressure at larger piston (P2)


Force at smaller piston (F1) = Pressure x Area of smaller piston (A1)


Force at larger piston (F2) = Pressure x Area of larger piston (A2)


Substituting the values:


F2 = P x A2

1600 N = P x 50.27 cm2

P = 31.8 N/cm2


F1 = P x A1

F1 = 31.8 N/cm2 x 3.14 cm2

F1 = 100 N


Conclusion


Therefore, to obtain a force of 1600 N at the larger piston, a force of 100 N must be applied to the smaller piston.
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A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 8.0 cm. What force must be applied to the smaller piston to obtain a force of 1600 N at the larger piston?
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