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.