Hydraulic systems utilize Pascal's principle by transmitting pressure from one cylinder (called the primary) to another (called the secondary). Since the pressures will be equal, if the surface areas are different then the forces applied to the cylinders' pistons will be different. Suppose in a hydraulic lift, the piston of the primary cylinder has a 2.25-cm diameter and the piston of the secondary cylinder has a 24.5-cm diameter. What force, in newtons. must be exerted on the primary cylinder of this lift to support the weight of a 2200-kg car (a large car) resting on the secondary cylinder?

Question

Engineering

Tess Moyer

27 February, 01:54

Hydraulic systems utilize Pascal's principle by transmitting pressure from one cylinder (called the primary) to another (called the secondary). Since the pressures will be equal, if the surface areas are different then the forces applied to the cylinders' pistons will be different. Suppose in a hydraulic lift, the piston of the primary cylinder has a 2.25-cm diameter and the piston of the secondary cylinder has a 24.5-cm diameter. What force, in newtons. must be exerted on the primary cylinder of this lift to support the weight of a 2200-kg car (a large car) resting on the secondary cylinder?

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Steven · Answer 1

182 N

Explanation:

The pressure in both pistons will be the same.

The areas will be:

A = π/4 * D^2

P = F / A

F1 / A1 = F2 / A2

F1 = F2 * A1 / A2

F1 = F2 * (π/4 * D1^2) / (π/4 * D2^2)

F1 = F2 * D1^2 / D2^2

The weight of the car will be:

F = m * a

F2 = 2200 * 9.81 = 21.6 kN

F1 = 21.6 * 2.25^2 / 24.5^2 = 0.182 kN = 182 N