A trough is filled with a liquid of density $855 \mathrm {~kg} / \mathrm { m } ^ { 3 }$. The ends of the trough are equilateral triangles with sides $7 \mathrm {~m}$ long and vertex at the bottom. Find the hydrostatic force on one end of the
Select the correct answer.
A) $3.5 \times 10 ^ { 5 } \mathrm {~N}$
B) $4.5 \times 10 ^ { 5 } \mathrm {~N}$
C) $6.5 \times 10 ^ { 5 } \mathrm {~N}$
D) $2.5 \times 10 ^ { 5 } \mathrm {~N}$
E) $5.5 \times 10 ^ { 5 } \mathrm {~N}$

Question

Quizplus · Accepted Answer

The hydrostatic force on one end of the trough is given by:$$F = \frac{1}{2} \rho g h A$$where:* $\rho$ is the density of the liquid* $g$ is the acceleration due to gravity* $h$ is the height of the liquid* $A$ is the area of the end of the troughIn this case, the density of the liquid is $855 \mathrm {~kg} / \mathrm { m } ^ { 3 }$, the acceleration due to gravity is $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$, the height of the liquid is $7 \mathrm {~m}$, and the area of the end of the trough is:$$A = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} (7 \mathrm {~m})^2 = 38.97 \mathrm {~m}^2$$Therefore, the hydrostatic force on one end of the trough is:$$F = \frac{1}{2} (855 \mathrm {~kg} / \mathrm { m } ^ { 3 }) (9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }) (7 \mathrm {~m}) (38.97 \mathrm {~m}^2) = 3.5 \times 10 ^ { 5 } \mathrm {~N}$$

A Trough Is Filled with a Liquid of Density 855 kg/m3855 \mathrm {~kg} / \mathrm { m } ^ { 3 }855 kg/m3

A Trough Is Filled with a Liquid of Density $855 \mathrm {~kg} / \mathrm { m } ^ { 3 }$