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.

Question

Aussie

Engineering

22 June, 18:50

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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Answers (1)

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Mason · Answer 1

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