Final answer:
The hydrostatic force on one end of the trough can be found by calculating the pressure exerted by the liquid and multiplying it by the area of the end of the trough. the hydrostatic force on one end of the trough to be 138,564 N.
Step-by-step explanation:
The hydrostatic force on one end of the trough can be found by calculating the pressure exerted by the liquid and multiplying it by the area of the end of the trough. The pressure at a given depth in a liquid can be calculated using the equation P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the depth. In this case, since the vertex of the equilateral triangle is at the bottom, the depth is equal to the height of the triangle.
To find the area of the end of the trough, we can use the formula for the area of an equilateral triangle A = (√3/4)(s^2), where A is the area and s is the side length. In this case, the side length is 8 m.
Plugging the values into the formula, we get P = (810 kg/m^3)(9.8 m/s^2)(8 m), which equals 63,216 N/m^2. Multiplying this by the area of the end of the trough, which is (√3/4)(8 m^2), we get the hydrostatic force on one end of the trough to be 138,564 N.