A rectangular tank with length 3 m, width 2 m, and height h m is full of a certain synthetic oil whose mass density is 1 3 kg/m3. If the work required to pump all of the oil to the top and out of the tank is 90 J, how tall is the tank (i. e., what is the value of h) ? Use 10 m/s2 for the acceleration due to gravity.

Question

Sophie Small

Physics

25 April, 08:41

A rectangular tank with length 3 m, width 2 m, and height h m is full of a certain synthetic oil whose mass density is 1 3 kg/m3. If the work required to pump all of the oil to the top and out of the tank is 90 J, how tall is the tank (i. e., what is the value of h) ? Use 10 m/s2 for the acceleration due to gravity.

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Answers (1)

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Nathalie Olson · Answer 1

2.1 m

Explanation:

Work done = Weight of the liquid in the tank * height of tank

Weight = mass * acceleration due to gravity

Mass = density * volume

Since the tank was full, the volume = 3 m * 2 m * h m = 6h m³

Mass = 1/3 kg/m³ * 6h m³ = 2h kg

Weight = 2h kg * 10 m/s² = 20h N

Work = 20h N * h m = 90 J

20h² = 90

h² = 4.5 m²

h = 2.1 m