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16 May, 20:05

What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the slave cylinder? the master cylinder has a 2.00-cm diameter and the slave has a 24.0-cm diameter?

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  1. 16 May, 21:04
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    Archimedes principle states that

    F1 / A1 = F2 / A2

    F2 = (A2 / A1) * F1

    Also, formula for the force is F = mg. Formula for the area of the cylinder is A = πr^2, therefore we get

    F2 = (πr2^2 / πr1^2) * mg

    Since the diameter of the cylinders are 2 cm and 24 cm, r1 = 12 and r2 = 1.

    Substituting the values to the derived equation, we get

    F2 = (π 1^2 / π 12^2) * 2400 * 9.8

    F2 = 163.3333 N
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