Question

A swimming pool has the shape of a box with a base that measures 30 m by 10 m and a uniform depth of 2.5 m. How much work is required to pump the water out of the pool when it is​ full? Use 1000 kg divided by m cubed for the density of water and 9.8 m divided by s squared for the acceleration due to gravity.

Answer 1

Explanation:

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Answer 2

Answer:

18,375 kJ

Explanation:

Parameters given:

Density of water: 1000 kg/m³

Acceleration due to gravity = 9.8 m/s²

Dimensions of pool = 30m × 10m × 2.5m

Depth of pool = 2.5 m

First we need to find the mass of the water in the pool:

Density = mass/volume

Mass = density * volume

Since the pool is full of water, the volume of the water is equal to the volume of the pool:

Volume = 30 * 10 * 2.5 = 750 m³

Mass = 1000 * 750

Mass = 750,000 kg

We can now find the force required to pump the water out of the pool:

F = m * g

Where m = mass of water

g = acceleration due to gravity

F = 750,000 * 9.8 = 7,350,000 N

The work needed to be done is the product of the force required by the distance the water would need to move to be pumped out (depth of pool):

Work = F * d

Work = 7,350,000 * 2.5

Work = 18,375,000 J = 18,375 kJ