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# Challenging question - forces

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1. if both have same cross sec area and some length and according to P=F/A they have same force down. Which one goes down?

Any help/tips would be appreciated, and I am excited to see your thoughts

2. Is one closer to the centre of gravity?
3. I would say this is mostly challenging because the problem isn't clear. Both what?
4. (Original post by mik1a)
I would say this is mostly challenging because the problem isn't clear. Both what?
yes sorry

both containers have their bases of equal cross sectional area and the height (level of water) is same. So pressure is same and force = pressure x area.
5. (Original post by Daniel Atieh)
yes sorry

both containers have their bases of equal cross sectional area and the height (level of water) is same. So pressure is same and force = pressure x area.
If the containers are the same distance from the middle, then the left hand one will go down as it contains more water.
6. (Original post by TimGB)
If the containers are the same distance from the middle, then the left hand one will go down as it contains more water.
that's what I thought. The left one is right, as you said, but the explanation required is different, because force downwards is same according to F = P x A.
7. If we assume both containers have the same volume of water, and their centre of masses are exactly the same distance away from the pivot, then the left hand side goes down. This is because the water exerts a force against the walls of the containers which we can assume to be perpendicular to the wall. As the right hand container is conical, then the force due to the pressure of the water on the side walls is directed diagonally upwards, whereas the force on the left hand side container's side walls is exactly horizontal. This means that there is a very slight vertical resultant force directed upwards on the right hand side so the left side goes down.
8. (Original post by dancepiratedance)
If we assume both containers have the same volume of water, and their centre of masses are exactly the same distance away from the pivot, then the left hand side goes down. This is because the water exerts a force against the walls of the containers which we can assume to be perpendicular to the wall. As the right hand container is conical, then the force due to the pressure of the water on the side walls is directed diagonally upwards, whereas the force on the left hand side container's side walls is exactly horizontal. This means that there is a very slight vertical resultant force directed upwards on the right hand side so the left side goes down.
But what about the centre of mass of the conical container being lower than that of the other container? Would that make a difference?
9. (Original post by dancepiratedance)
If we assume both containers have the same volume of water, and their centre of masses are exactly the same distance away from the pivot, then the left hand side goes down. This is because the water exerts a force against the walls of the containers which we can assume to be perpendicular to the wall. As the right hand container is conical, then the force due to the pressure of the water on the side walls is directed diagonally upwards, whereas the force on the left hand side container's side walls is exactly horizontal. This means that there is a very slight vertical resultant force directed upwards on the right hand side so the left side goes down.
Yes! perfect

I got what you said, thank you. Just my last question: if we want to look at it in terms of weight of water, then the left one should have more weight. How can I think about this one?

EDIT: or we use different densities somehow maybe to achieve the criteria?
10. Sorry, the pressure argument is wrong. If there is the same volume of water then you have the same weight. If the base is the same area, then you have identical forces acting down. I don't see any reason why the scale wouldn't balance.
11. (Original post by mik1a)
Sorry, the pressure argument is wrong. If there is the same volume of water then you have the same weight. If the base is the same area, then you have identical forces acting down. I don't see any reason why the scale wouldn't balance.
hmm I agree, but it's still confusing. I think since this is an interview question, the main goal is to say that both have same weight somehow (assumption), and expect us to say how the left one goes down. As said above, due to the vertical component of the normal force of water acting on the wall (right container).

What do you say?
12. There's an explanation on the answer in Simon Clark's Oxford physics interview video here: https://youtu.be/kSEM91KR0cg?t=2m53s

Is this where you found the question from?
13. (Original post by Daniel Atieh)
hmm I agree, but it's still confusing. I think since this is an interview question, the main goal is to say that both have same weight somehow (assumption), and expect us to say how the left one goes down. As said above, due to the vertical component of the normal force of water acting on the wall (right container).

What do you say?
I thought you said they had the same weight. The question is still not clearly specified.

If they have the same volume and is the same liquid at the same height then the weight is the same.
14. (Original post by dancepiratedance)
There's an explanation on the answer in Simon Clark's Oxford physics interview video here: https://youtu.be/kSEM91KR0cg?t=2m53s

Is this where you found the question from?
yes, long time back. i kept it and returned to it yesterday because i remember it didn't make sense to me.

Regarding the vertical force, it's clear. But I can't see how both have the same weight. Is it correct to say FA = mg giving same weight in both? That doesn't seem right. I think I miss understood te pressure relationship. Otherwise, their main aim is to say assume somehow both have same downward force

That's what I think
15. (Original post by mik1a)
I thought you said they had the same weight. The question is still not clearly specified.

If they have the same volume and is the same liquid at the same height then the weight is the same.
check if what i say here is right:

if we add water of equal height in both and of same density rho
F= P x A
and P = rho . g . h
F = mg

is it right to say: mg = rho . g . h . A ?

logically it should not be right.
16. Again, really confusing because of unspecified symbols. What is P, the water pressure or the pressure acting on the plank sure to the container? These are not the same.
17. (Original post by mik1a)
Again, really confusing because of unspecified symbols. What is P, the water pressure or the pressure acting on the plank sure to the container? These are not the same.
from water
18. Why would the water pressure affect the scales?
19. (Original post by mik1a)
Why would the water pressure affect the scales?
this problem seems confusing, sorry if it might take a bit more.

i try to say that if we have two containers of different shapes (like ones i drew), and we fill both with water to the same height. I must say that the bases have same area also.

by looking at the containers, the one on the left must contain more volume,

we know W = mg so both should have different W.
But if we use F = P (of water on base) x A then both will have same force down.

This is what confuses me now.
20. Ah. If you have different container shapes then different volumes then different masses then different weights therefore different forces.

The pressure of the water according to rho*g*h is a hydrostatic pressure of the water exerted on the inside of the container. That's an internal force that doesn't affect the total weight.

The pressure of the container on the scale is F/A, where F is the weight. Since they have the same area at the base, the pressure is higher for the cubic container since the weight is higher.

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