# Force exterted on triangles

1. Jun 27, 2015

### Ikastun

The question is part of a mechanical aptitude test. The correct answer is 2, but there is no explanation.

I do not understand why is 2, and not "equal on both". Can anyone give me some clues?.

2. Jun 27, 2015

### theodoros.mihos

The only way that can see is to not allow liquid access on (2) body base.

3. Jun 27, 2015

### 256bits

The author of the question deserves a big FAIL. It could be another one of those copy and paste with parts left out and thus becomes ambigious, or non-sensical.

Anyways,do you know anything about hydrostatic forces, bouyancy, pressure? which is probably waht the question was supposed to get at.

What is your reasoning, or calculations, that the answer should "be equal"?

4. Jun 28, 2015

### Ikastun

I have a scant knowledge of hydrostatics, to say the least.

My answer is just a guess, given that they are identical triangles and they are at the same depth. The only difference is their position, but the basic formulas of pressure and force do not consider the position:

p=dgh
F=PA

Am I wrong?, what else should I consider?.

5. Jun 28, 2015

### stedwards

Yes. A big fail for the author of the question, or cut-and-paste squad. Pressure on a "triangle", something with zero thickness?

6. Jun 28, 2015

### Staff: Mentor

Perhaps the best (most interesting, most educational) question to ask is: What is the force exerted by the bottom of the pool on the triangle? It's different for the two triangles, and when you can see why you'll have nailed this class of problems.

7. Jun 29, 2015

### CWatters

Are they? The centroid of a triangle is 1/3rd of the way up from the base. So isn't 2 slightly deeper than 1 ?

8. Jun 29, 2015

### Staff: Mentor

Could you guys who think it is a bad question explain why you think so?

9. Jun 29, 2015

### Staff: Mentor

It's not clear which force the question is asking for. The net force on the triangle? The hydrostatic force on the triangles? Or the force exerted by the bottom the container on the triangles?

10. Jun 29, 2015

### PWiz

I think the hydrostatic force is being implied. Secondly, the question does not ask for a numerical answer - there is no need to know the 3rd spatial dimension features of the triangles or the pool to answer this question. No offense to anyone, but I think the question is obviously talking about prisms of equal depth into the page (so one only needs to concentrate upon the 2 dimensional view), since the answer cannot otherwise be determined with the given information (unless there were some omissions while posting the question).

11. Jun 29, 2015

### 256bits

My objection is that the author seems to not have considered the following simple analysis:
Since the triangles are fixed in position, there is no acceleration, and according to Fnet = ma, with acceleration a being 0, the net force Fnet = 0.
In which case, " On which triangle will a greater force be exerted?" has the answer "equal on both".

Of course,
Fnet = Fmg + Fbouyancy + Fbottom = 0
which he/she thought would be a nice tricky question.
But really, Is it?

12. Jun 29, 2015

### 256bits

Normally the 3rd dimesnion is taken as a thickess of unit 1.

13. Jun 29, 2015

### Staff: Mentor

In the absence of qualification, isn't "all" implied (all forces we can see in the diagram)? I don't think we have a grammar issue like in the last thread.

Also, in question's like this, lack of information requires the student to use the process of elimination. Is it just the hydrostatic force or also the normal force? Is triangle 2 sealed to the bottom? Turns out, with a bit of logic, those two issues cancel each other out.

14. Jun 29, 2015

### DTM

Agree the question is worded too vaguely. But I think the intent of the question is hydrostatic forces. Although as correctly pointed out, the net force must be 0 since acc = 0. The magnitude of the hydrostatic forces on the individual faces is relevant. The question could have been worded, as you fill the container with more and more water, which triangle will crush first? The answer would certainly be 2. The centroid of the 2 triangle is lower than 1's, thus 2's hydrostatic pressure will be greater. One thought experiment you can do is imagine the tank is only filled to a depth just equal to the height of the triangles. Triangle 1 would have virtually no force on one entire sides. While triangle 2 would have no force only at a vertex.

15. Jun 29, 2015

### stedwards

The question could have used "triangular prisms" or is this too much to ask of middle school(?) science students?

16. Jun 29, 2015

### jerromyjon

I took the small black triangle pointing down at the 2 horizontal lines just below the surface as a pictorial indication of hydrostatic force.

17. Jun 29, 2015

### jbriggs444

My interpretation is that the question asks for a comparison of the sum of the magnitudes of the forces on the three sides on each triangle.

Since it is rarely meaningful to add the magnitudes of forces while ignoring their directions, the question seems a poor one.

18. Jun 29, 2015

### MrAnchovy

OK its not a perfectly worded question, but:
1. this is a mechanical aptitude test, and to my mind making sense of imperfect information is a relevant part of assessing mechanical aptitude;
2. the question states that the "triangles" are identical, so their 3rd dimension is irrelevant - in fact you can even assume they ARE triangles with zero thickness;
3. one possible answer is "the net force on each triangle is zero because they are fixed in position", but that is not the best answer because it doesn't make use of all the information provided in the question; a better answer is "the force of water pressure on triangle 2 is greater because the mean depth of its surface area is greater".

19. Jun 29, 2015

### Staff: Mentor

So don't - it doesn't change the answer if you include the directions. In fact, solving that (if we had the numbers) provides the buoyant force (if not sealed to bottom).

20. Jun 29, 2015

### jbriggs444

If it's not sealed to the bottom, the buoyant forces are clearly equal. As is the weight of the triangles and the force required to fix them in place. No reasonable vector sum fits the "correct" answer.

If it is sealed to the bottom, one can still find a state of affairs where both triangles have zero net force. So that still fails to produce the "correct" answer.

21. Jun 29, 2015

### MrAnchovy

Why?

22. Jun 29, 2015

### jbriggs444

Equal volumes submerged in fluid of equal density. Unless you are going for second order effects where the fluid is more dense when deeper.

23. Jun 29, 2015

### MrAnchovy

Why are you ignoring the magnitude of the force on the faces of the triangles? If they are triangles (with zero thickness) the force on the sides is zero.

24. Jun 29, 2015

### jbriggs444

Reaching back to the problem definition to rationalize an answer... Because the triangles are "fixed in place". If the triangles are of zero thickness and we are looking at pressure on their faces, that specification is pointless.

25. Jun 29, 2015

### 256bits

Good point. It may have been an overwhelming state of affairs for both the student, AND the administrators.