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23 April, 22:00

Two hydraulic piston/cylinders are connected with a line. The master cylinder has an area of 5 cm2, creating a pressure of 1000 kPa. The slave cylinder has an area of 3 cm2. If 25 J is the work input to the master cylinder, what is the force and displacement of each piston and the work output of the slave cylinder piston?

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  1. 23 April, 23:56
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    Work done by slave cylinder = 25J

    Displacement of the piston of master cylinder = 0.05m

    Displacement of the piston of slave cylinder = 0.08m

    Force of master cylinder = 500 N

    Force of slave cylinder = 300 N

    Explanation:

    Given-

    Area of master cylinder, A1 = 5cm²

    Area of slave cylinder, A2 = 3cm²

    Pressure, P1 = 1000 KPa

    Work, W1 = 25J

    Force, displacement and work output = ?

    If one cylinder is connected to another, then the pressure created in both the cylinders are same.

    P2 = P1 = 1000 kPa

    Therefore, work done by both the cylinders are also same

    W1 = W2 = 25J

    Displacement of first cylinder, s1:

    W1 = P1 X A1 X s1

    s1 = W1 / P1 X A1

    s1 = 25 / 1000000 X 0.0005

    s1 = 0.05m

    Force on first cylinder:

    F1 = W1 / s1

    F1 = 25 / 0.05

    F1 = 500N

    Force on second cylinder:

    F2 = P2 X A2

    F2 = 1000000 X 0.0003

    F2 = 300N

    Displacement on second cylinder:

    F1 X s1 = F2 X s2 (work done on both the sides are same)

    s2 = F1 X A1 / F2

    s2 = 500 X 0.05 / 300

    s2 = 0.08m
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