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In the hydraulic press shown, a force of 100 N is applied to piston A and it moves down 10 cm. Calculate the work done by both pistons.

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here are the answers to the remaining questions:

2.3.2 Calculate the output force, if the input force is 50N, the input piston's area is 100mm² and the output piston's area is 800mm².
This was calculated in the previous response as part of 2.3.1.
The output force is 400 N\boxed{\text{400 N}}.

2.3.3 Draw a systems diagram for the above hydraulic system.

  • INSET: Draw a small piston with an arrow indicating an input force (effort) being applied downwards.
  • PROCESS: Draw a container filled with fluid, connected by a pipe to both pistons. Indicate that pressure is transmitted through the fluid.
  • OUTPUT: Draw a larger piston with an arrow indicating an upward output force (load) being exerted.

2.4 In the hydraulic press below; a force of 100 N is applied to piston A and it moves down 10 cm.

2.4.1 Calculate the work done by both pistons.

  1. Calculate the work done by piston A (input work).

    Work done (WW) is calculated as force (FF) multiplied by distance (dd).

    WA=FA×dAW_A = F_A \times d_A

    Given:
    FA=100 NF_A = 100 \, \text{N}
    dA=10 cm=0.1 md_A = 10 \, \text{cm} = 0.1 \, \text{m}
    Substitute the values:

    WA=100 N×0.1 mW_A = 100 \, \text{N} \times 0.1 \, \text{m} WA=10 JW_A = 10 \, \text{J}

  2. Calculate the work done by piston B (output work).

    In an ideal hydraulic system, the work input equals the work output due to the conservation of energy.

    WB=WAW_B = W_A WB=10 JW_B = 10 \, \text{J}

    The work done by both pistons is 10 J\boxed{\text{10 J}}.

    2.4.2 Calculate the pressure of the fluid.

  3. Convert the area of piston A to square meters.

    AA=10 cm2A_A = 10 \, \text{cm}^2
    1 cm=0.01 m1 \, \text{cm} = 0.01 \, \text{m}
    1 cm2=(0.01 m)2=0.0001 m2=10−4 m21 \, \text{cm}^2 = (0.01 \, \text{m})^2 = 0.0001 \, \text{m}^2 = 10^{-4} \, \text{m}^2

    AA=10×10−4 m2=10−3 m2A_A = 10 \times 10^{-4} \, \text{m}^2 = 10^{-3} \, \text{m}^2

  4. Calculate the pressure (PP) using the force and area of piston A.

    P=FAAAP = \frac{F_A}{A_A}

    Given:
    FA=100 NF_A = 100 \, \text{N}
    AA=10−3 m2A_A = 10^{-3} \, \text{m}^2
    Substitute the values:

    P=100 N10−3 m2P = \frac{100 \, \text{N}}{10^{-3} \, \text{m}^2} P=100×103 PaP = 100 \times 10^3 \, \text{Pa} P=100000 PaP = 100000 \, \text{Pa}

    The pressure of the fluid is 100000 Pa\boxed{\text{100000 Pa}} or 100 kPa\boxed{\text{100 kPa}}.

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