A box-shaped metal can has dimensions 6 in by 2 in by 12 in high. All of the air inside the can is removed with a vacuum pump. Assuming norm

Question

A box-shaped metal can has dimensions 6 in by 2 in by 12 in high. All of the air inside the can is removed with a vacuum pump. Assuming normal atmospheric pressure outside the can.

a. Find the total force on one of the 6 in by 12 in sides.
b. Find the gauge pressure at the bottom of a swimming pool that is 17 feet deep.

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Xavia 3 years 2021-07-20T20:47:30+00:00 1 Answers 30 views 0

Answers ( )

  1. Orla
    0
    2021-07-20T20:49:23+00:00
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    Answer:

    a) The total force is 4659.8 N

    b) The gauge pressure is 50764 Pa

    Explanation:

    Given:

    Pressure inside = 0

    Patm = pressure outside = 1.013×10⁵Pa

    Pressure difference = ΔP = 1.013×10⁵ – 0 = 1.013×10⁵Pa

    a) The area is equal:

    A=12*6=72in^{2} =0.046m^{2}

    The force is:

    F=delta-P*A=1.013x10^{5} *0.046=4659.8N

    b) The gauge pressure at the bottom is equal:

    P=\rho gh

    Where:

    ρ = density = 1000 kg/m³

    h = 17 ft = 5.18 m

    Replacing:

    P=1000*9.8*5.18=50764Pa

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