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18 July, 08:51

20 gallons of an incompressible liquid exert a force of 50 lbf at the earth's surface. What force in lbf would 3 gallons of this liquid exert on the surface of the moon? The gravitational acceleration on the surface of the moon is 5.51 ft/s^2.

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  1. 18 July, 10:50
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    1.29 lbf

    Explanation:

    Weight is a force, it is the product of a mass by the acceleration of gravity.

    f = m * a

    Gallons are a unit of volume. The relationship of volume with mass is:

    m = V * δ

    δ is the density (mass per unit of volume)

    Then the weight of a liquid is:

    w = V * δ * g

    Rearranging:

    δ = w / (V * g)

    The acceleration of gravity on Earth is 32.2 ft/s^2

    δ = 50 / (20 * 32.2) = 0.078 lbm/gallon

    Knowing this and the gravity on the Moon we can calculate how much would 3 gallons of this liquid weight on the Moon.

    w = V * δ * g

    w = 3 * 0.078 * 5.51 = 1.29 lbf
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