Answer :
Answer:
total force = 4.704 × [tex]10^5[/tex] 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 × [tex]\frac{y^2}{2}[/tex] .................2
F = [tex]1000 \times 9.8 \times 8 \times \frac{2^2}{2}[/tex]
F = 1.568 × [tex]10^5[/tex] N
and
now we get here force for depth 4 m
put here value in equation 2
F = [tex]1000 \times 9.8 \times 8 \times \frac{4^2}{2}[/tex]
F = 6.272 × [tex]10^5[/tex] N
so that here
total force will be
total force = 6.272 × [tex]10^5[/tex] N - 1.568 × [tex]10^5[/tex] N
total force = 4.704 × [tex]10^5[/tex] N
Final answer:
The increase in the total force on the aquarium wall when the water depth is increased from 2.00 m to 4.00 m is calculated using the expression ΔF = (1000 kg/m³)(9.81 m/s²)(h₂² - h₁²)(L)/2. Inserting the given values for h₁, h₂, and L, allows us to find the answer in newtons (N).
Explanation:
The question asks about the increase in the total force on the wall of an aquarium when the water depth is changed. According to physics, the force exerted by a static fluid in a container on its wall can be found by using the equation F = ρgh²L/2, where:
- ρ (rho) is the density of the fluid (water in this case), which is 1000 kg/m³,
- g is the acceleration due to gravity, which is 9.81 m/s²,
- h is the depth of the water,
- L is the width of the wall in contact with the water.
To find the increase in force when the depth of water is increased from 2.00 m to 4.00 m, we use the equation twice for each depth and subtract the smaller force from the larger force:
- Calculate the force at 2.00 m depth: F₁ = ρgh₁²L/2
- Calculate the force at 4.00 m depth: F₂ = ρgh₂²L/2
- Find the difference in force: ΔF = F₂ - F₁
Substituting the given values, the width (L) is stated as 8.00 m:
ΔF = (1000 kg/m³)(9.81 m/s²)(4.00 m)²(8.00 m)/2 - (1000 kg/m³)(9.81 m/s²)(2.00 m)²(8.00 m)/2
Simplifying these expressions will give the answer in newtons (N), which is the increase in total force on the wall.
