Force on two cables holding a liquid-filled container against a wall

[A13235378]

Homework Statement

A plate is in the shape of a quarter cylinder of radius R and length L. This plate is hinged at C to a vertical wall and can rotate freely about C. The end A of the plate is tied to the wall using two horizontal cables the other cables is parallel to OA and the two cables are placed symmetrically). the space between the wall and the plate is filled completely with water (density=rho) Neglect the weight of the plate and calculate the tension in each cable .

Relevant Equations

p = rho . g . h (pression)

Before, sorry for my English, it is not my native language

I already have the solution to the issue, I just didn't understand a step.

1) Calculation of weight force (vertical):

$$ F_v = \frac{\rho \pi R^2 . L .g}{4}$$

2) Calculation of force due to water pressure on the plate (horizontal)

Mean pressure . effective area = $$ \frac{\rho . g . R}{2} . RL = \frac {\rho g R^2 .g} {2} $$

From this, the resulting force between the two forces is calculated and its direction must pass through point O.

My doubt is exactly this: why do you need to go through the O point?

 

[andrewkirk]

From this, the resulting force between the two forces is calculated and its direction must pass through point O.

Four forces act in this diagram: the tension of the two cables, the weight of the water and the force through the hinge C. I don't know which two forces you refer to here. Nor do I understand what you mean by "need to go through the O point".

I would find it simplest to approach this problem as a need to balance two torques around the hinge C. One torque is provided by the weight of the water. Find the location of the centre of mass of the water and assume the weight force is applied there in order to calculate a torque around C. Then calculate the torque around C provided by the cables in terms of the tension T in each cable.

 

[haruspex]

Why do you need to go through the O point?

Consider a small patch of the curved plate. The water pressure exerts on it a force normal to the plate. This force has zero moment about O, so the net force of the water on the whole plate has no moment about O.