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A swimming pool has the shape of a box with a base that measures 22 m by 11 m and a uniform depth of 2.4 m. How much work is required to pump the water out of the pool when it is full? Use 1000 kg/m for the density of water and 9.8 m/s 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 Osys 2.4, find the cross-sectional area Aly) Aly) = 6,8 x 106 (Simplify your answer.)

User Sunkas
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To calculate the work required to pump the water out of the pool, we need to determine the volume of water in the pool and then multiply it by the product of the density of water and the acceleration due to gravity.

First, let's calculate the cross-sectional area of the pool's base (Aly):

Aly = length x width = 22 m x 11 m = 242 m²

The volume of water in the pool can be found by multiplying the cross-sectional area (Aly) by the uniform depth (2.4 m):

Volume = Aly x depth = 242 m² x 2.4 m = 580.8 m³

Next, we can calculate the mass of water in the pool by multiplying the volume by the density of water:

Mass = Volume x density = 580.8 m³ x 1000 kg/m³ = 580,800 kg

Finally, we can calculate the work (W) required to pump the water out of the pool using the formula:

Work = force x distance

In this case, the force is equal to the weight of the water, which can be calculated using the mass and the acceleration due to gravity:

Force = Mass x gravity = 580,800 kg x 9.8 m/s² = 5,691,840 N (Newtons)

The distance in this case is the height of the pool, which is 2.4 m.

Work = Force x distance = 5,691,840 N x 2.4 m = 13,660,736 J (Joules)

Therefore, the work required to pump the water out of the pool when it is full is approximately 13,660,736 Joules.
User Krzak
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