Force at a particular point on a submerged vertical surface (other than Ycp)

[lechatelier]

Homework Statement

https://www.dropbox.com/s/mw1ol8tnrdf0ajb/fm%20prob.JPG?dl=0 [/B]

A 1-m wide by 2-m gate in the vertical wall of a reservoir functions like a door. It is hinged at A and B and latched at C. Determine the forces at A, B, and C when the water surface is 700 mm above the top of the gate.

Hinge A is 0.3 m below the top-left corner of the door
Hinge B is 0.3m above the bottom-left corner of the door
Latch C is in the middle of the right edge of the door.

(Answers:
Force at A 3.57kN
Force at B 13.10kN
Force at C 16.68kN)2. Homework Equations

F = (rho)(g)(hcg)A gives the resultant force on the full door

Ycp = Ycg + (Icg/(Ycg. A)) gives the center of pressure3. The Attempt at a Solution

The resultant force was calculated by the above equations but I am struggling to find forces at the particular points A, B and C

Any help will be greatly appreciated

Thanks

 

[BvU]

The door doesn't move, it doesn't rotate around a horizontal axis and it doesn't rotate around a vertical axis. That gives you three balances to calculate the desired F magnitudes.

 

[lechatelier]

Thanks for the reply. But I still have no idea how to go about calculating the forces at A,B and C
I easily calculated the total force on the full door as 33.354 kN and this is acting at Ycp = 1.896m from the surface.
I don't see how to use "sum of moments = 0" since there are three unknowns.
Thanks for your help

 

[voko]

Consider two axes for the moment calculation: the one where the hinges are located, and the one perpendicular to it and passing through the latch. The resultant moment with regard to either axis must be zero.

 

[lechatelier]

Hi voko Thanks for the help. I was able to calculate Fc (the latch) as you mentioned by taking moments about the hinges (the top view) so that only the Fc and the resultant are considered. This gave me the correct answer for force at C = 16.68kN.

But I am still not able to picture how to take moments about the axis that runs through the latch. I am assuming I look at the side-view of the door. But still there are two unknowns then (Force A and Force B) And the resultant force is acting in the middle of the door and it's in a different plane.
Thanks again for your help

I have the picture of the problem here

https://www.dropbox.com/s/mw1ol8tnrdf0ajb/fm prob.JPG?dl=0

 

[voko]

By considering the moments about the latch axis, you get one equation relating force A and force B. Another equation relating these two unknowns is obtained by equating the total resultant force to zero. Two equations, two unknowns; solve.

 

[lechatelier]

Have been trying to solve this but no luck. The issue that I'm having is that (from what I understand, please correct me if my understanding is wrong) that if there is a force at a particular point on a submerged body, let's say it acts a distance of Ycp. We know that from the surface it is at a distance of Ycp BUT this force acts at all points on that submerged body that are at a distance of Ycp. So how to take a moment arm when we don't have one particular point?

 

[gneill]

Have been trying to solve this but no luck. The issue that I'm having is that (from what I understand, please correct me if my understanding is wrong) that if there is a force at a particular point on a submerged body, let's say it acts a distance of Ycp. We know that from the surface it is at a distance of Ycp BUT this force acts at all points on that submerged body that are at a distance of Ycp. So how to take a moment arm when we don't have one particular point?

It is analogous to how we consider the force of gravity on an extended body to be working through its center of gravity. When you analyze a beam, the force vector for the weight is placed at its center of gravity, right?