# Homework Help: Tension in bar in water

1. Mar 10, 2016

### foo9008

1. The problem statement, all variables and given/known data

calculate the tension in the cable
2. Relevant equations

3. The attempt at a solution
the resultant force act on the each metal bar is equal to the tension of each bar . so FR= tension in bar
but , i have problem of finding the the area in FR , i have only (0.75/2) sin45(1000)(9.81) A . For A , i only know the one of the length , how to do this question ?

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2. Mar 10, 2016

### SteamKing

Staff Emeritus
It's not clear what FR is.

In any event, are you saying you can't work out the dimensions of this trough using trigonometry and the information given in the figure?

3. Mar 10, 2016

### TSny

I'm not sure what you mean here.

To add a little to SteamKing's comment: You are dealing with a trough with two rectangular side panels that are hinged at the bottom and a triangular panel at each end. The cable prevents the rectangular panels from rotating about the hinge. This is a rotational equilibrium problem. (unless I'm misinterpreting the problem)

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4. Mar 10, 2016

### foo9008

FR = resultant force hydrostatic force acting on the metal bar

5. Mar 11, 2016

### foo9008

Is there anything wrong with my working ?

6. Mar 11, 2016

### TSny

I'm not sure what you are calculating here. Can you elaborate? It appears to be a certain weight of water.

Since this is a rotational equilibrium problem, you will need to consider torques rather than just forces.

You might want to consider the torque about the hinge due to fluid pressure on a narrow strip of the trough. See the yellow strip in the figure below.

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7. Mar 11, 2016

### foo9008

I am calculating the resultant hydrostatic pressure acting on the two metal bar ... I'm not sure how to do the calculation for the torque about the hinge due to fluid pressure on a narrow strip of the trough.

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8. Mar 11, 2016

### TSny

The problem doesn't mention any metal bars. My interpretation of the diagram is that it represents a cross-sectional view of the trough.

9. Mar 11, 2016

### foo9008

Ok , i misunderstood it as metal bar . sorry . i changed to trough now , my calculation is still the same . FR , i have only (0.75/2) sin45(1000)(9.81) A , can you show your working ?

10. Mar 11, 2016

### TSny

No. This problem is for you to work.
We are here to give a little guidance, but you must do the work.

11. Mar 11, 2016

### foo9008

FR is the total resultant hydrostatic pressure force acting on the trough

12. Mar 11, 2016

### TSny

Is this the hydrostatic force on just one of the rectangular sides of the trough?

13. Mar 11, 2016

### foo9008

just 1 side

14. Mar 11, 2016

### TSny

OK. I think that's right. But knowing the force on one side is not very helpful for this problem. The side of the trough is free to rotate about the hinged edge. The water pressure tends to make the side rotate about the hinge while the cable prevents the side from rotating.

What is the basic mechanical condition that must be satisfied in order for an object not to rotate about some axis?

15. Mar 11, 2016

### foo9008

ok , can you show which is the direction of tension . I coudn't figure out

16. Mar 11, 2016

### foo9008

moment anticlockwiese= moment clockwise, but how to find the pressuree center ? it's given by the formula of yp= yc +(Ixx) /ycA , while Ixx has the formula of a(b^3)/12 , since we cant find the area of this question , is it possible to find the answer for this question ?

17. Mar 11, 2016

### TSny

Yes.
I'm not familiar with these expressions. When giving formulas that are not "well-known", you should define all symbols.
The area of one side of the trough can be calculated easily from the information given in the statement of the problem and the diagram given in the problem.
Yes. You can figure out the moment due to the fluid pressure by considering the moment on a thin strip (see post #7) and then adding the moments for all such strips. Or, if you were given the formula that you posted above, you could use it. I don't know if the formula is valid since I don't know what the symbols represent.

18. Mar 11, 2016

### foo9008

what is the meaning of the trough is 6m long ? which side ? can you point it out ? i could only see the length of trough is 0.75m long , the 'width' of the trough is unknown , how to do this question ?

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Last edited: Mar 11, 2016
19. Mar 11, 2016

### TSny

The distance from one triangular end to the other triangular end is 6 m.

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20. Mar 11, 2016

### foo9008

the pressure act on the metal trough, right? how to find the area of the metal trough ? i have only 0.75m