Bang the box

There is a cuboidal box which is filled with liquid of density 800 kg m 3 800 \text{ kg m}^{-3} . Let F 1 F_{1} & F 2 F_{2} be the force applied by the liquid on Δ A B C \Delta ABC and Δ A C D \Delta ACD , respectively.

Find F 1 F 2 \frac{F_{1}}{F_{2}} .

Bonus: Solve this problem without using calculus.


The answer is 0.5.

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2 solutions

Aniket Verma
Feb 28, 2015

There is a property that the total force on an area inside any fluid is equal to the pressure applied by that fluid at the center of the area \text{pressure applied by that fluid at the center of the area} × \times total area \text{total area}

now let a r e a o f Δ A B C = a r e a Δ A D C = Δ area of \Delta ABC = area \Delta ADC = \Delta

and when we calculate the depth of the center of both the triangle we will sea that the depth of the center of Δ A D C \Delta ADC is twice the depth of the center of Δ A B C \Delta ABC

so F 1 F 2 \dfrac{F_1}{F_2} = = δ × g × h × Δ δ × g × 2 h × Δ \dfrac{\delta\times g\times h \times \Delta}{\delta\times g\times 2h\times \Delta} = = 0.5 0.5

where δ = d e n s i t y g i v e n l i q u i d \delta = density~ given~ liquid

h = d e p t h o f c e n t e r o f Δ A B C h = depth ~of~ center~ of \Delta ABC

g = a c c e l e r a t i o n d u e t o g r a v i t y g = acceleration ~due ~to ~gravity

Being triangular sections center of pressure of the upper wedge is located at 1/3 from the surface meanwhile the center of the lower wedge is at 2/3, so the ratio is 0.5

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