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

Answer:

total force =   4.704 × $10^5$ N

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 × $\frac{y^2}{2}$    .................2

F = $1000 \times 9.8 \times 8 \times \frac{2^2}{2}$  

F = 1.568 × $10^5$ N

and

now we get here force for depth 4 m

put here value in equation 2

F = $1000 \times 9.8 \times 8 \times \frac{4^2}{2}$  

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