Question

A swimming pool is in the shape of a rectangular parallelepiped 7 ft deep, 57 ft long, and 24 ft wide. It is filled with water to a depth of 6 ft. How much work is required to pump all the water over

Answer 1

To pump all the water over, approximately 112,273,860.8 ft⋅lb of work is required.

Step-by-step explanation:

To calculate the work required to pump all the water over, we need to find the volume of water in the pool and then multiply it by the weight of water to find the work. First, let's find the volume of the water in the pool:

Volume = length imes width imes depth = 57 ft imes 24 ft imes 6 ft = 8,208 ft³

Now, let's find the weight of the water. The weight of water is equal to its mass multiplied by the acceleration due to gravity:

Weight = mass imes g

To find the mass of water, we can use the density formula:

Density = mass/volume

The density of water is 62.4 lb/ft³, so:

62.4 lb/ft³ = mass/8,208 ft³

Mass = 62.4 lb/ft³ imes 8,208 ft³ = 511,315.2 lb

Now we can calculate the work:

Work = weight imes depth = mass imes g imes depth

Work = 511,315.2 lb imes 32.2 ft/s² imes 7 ft = 112,273,860.8 ft⋅lb

Therefore, approximately 112,273,860.8 ft⋅lb of work is required to pump all the water over.