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The hydraulic jack shown below consists of a master cylinder with a diameter of 60mm and a lifting (or slave) cylinder with a diameter of 150mm. The two cylinders are connected by a flexible high pressure hose with a diameter of 10mm.The density of the hydraulic fluid that fills the jack is 15,000kg/m3.
The jack is being used to lift a 5 tonne mass through a vertical distance of 50mm. Initially the hydraulic fluid heights are hA=150mm and hB=400mm.
What is initial force that is required to be applied at location B to lift the weight off the ground?
Develop and expression for the force at B that varies with the lift height at location A Hint: From the conservation of mass and the fact that the hydraulic fluid is incompressible, the volume of fluid displaced at locations A and B must be the same.
What is percentage increase in the force that is required to be applied at location B when the mass is 50mm off the ground compared to the initial force?
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