A swimming pool has the shape of a box with a base that measures 25 m by 11 m and a uniform depth of 3.1 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. Draw a y-axis in the vertical direction (parallel to gravity) and choose one corner of the bottom of the pool as the origin. For 0 less than or equals y less than or equals 3.1 , find the cross-sectional area A (y).

Question

Gemma Spears

Mathematics

9 May, 09:48

A swimming pool has the shape of a box with a base that measures 25 m by 11 m and a uniform depth of 3.1 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. Draw a y-axis in the vertical direction (parallel to gravity) and choose one corner of the bottom of the pool as the origin. For 0 less than or equals y less than or equals 3.1 , find the cross-sectional area A (y).

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Answers (1)

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Skyler Randall · Answer 1

Step-by-step explanation:

Volume of water in the swimming pool

= 25 x 11 x 3.1

= 852.5 m³

mass of water in the pool

= volume x density of water

m = 852.5 x 10³ kg

We shall consider the height H by which the centre of mass of the water-body is increased to lift the water.

H = 3.1 / 2 = 1.55 m

Work done in pumping the water out of pool

mgH,

= 852.5 x 10³ x 9.8 x 1.55

= 13 x 10⁶ J