Question

A large aquarium of height 5.00 m is filled with fresh water to a depth of 2.00 m. One wall of the aquarium consists of thick plastic 8.00 m wide. By how much does the total force on that wall increase if the aquarium is next filled to a depth of 4.00 m?

Answer 1

total force = 4.704 ×
`10^5` N

Step-by-step explanation:

given data

height = 5 m

depth = 2 m

thick plastic = 8.00 m

depth = 4.00 m

solution

first we get here force in which aquarium fill with depth 2 m

dF = PdA ......1

F = ∫PdA

F = ∫ϼgy(wdy)

F = ϼgw ∫ y dy

F = ϼgw ×
`(y^2)/(2)` .................2

F =
`1000 * 9.8 * 8 * (2^2)/(2)`

F = 1.568 ×
`10^5` N

and

now we get here force for depth 4 m

put here value in equation 2

F =
`1000 * 9.8 * 8 * (4^2)/(2)`

F = 6.272 ×
`10^5` N

so that here

total force will be

total force = 6.272 ×
`10^5` N - 1.568 ×
`10^5` N

total force = 4.704 ×
`10^5` N