Reasons for Direction of Tension in Circular Motion?

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Amarantha
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Okay, so me and a friend have been having an ordeal with this question from the AQA Physics A June 2014 Unit 4 paper:

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Originally We got the answer of 17N, which was incorrect. The problem was that we were doing centripetal force plus mg as opposed to minus mg. I identified why it was minus mg - previously we were assuming that tension acts away from the centre, when it actually acts towards it.

So my question is: why is this? Why does the tension acts towards the centre and not away from it? I have been unable to find an explanation for this, just that it is.

Thanks,
Maddie.
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CourtlyCanter
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Is the answer B 13N?
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Amarantha
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(Original post by CourtlyCanter)
Is the answer B 13N?
It is, yes.
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CourtlyCanter
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Tension= (mv^2)/r - mgcosθ
Treat θ as 0.

or alternatively,
T+mg= mv^2/r
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Amarantha
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(Original post by CourtlyCanter)
Tension= (mv^2)/r - mgcosθ
Treat θ as 0.

or alternatively,
T+mg= mv^2/r
Yes I understand this. My question is why does tension act towards the centre and not away from it?
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Isambard Kingdom Brunel
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Who cares?

It's Xmas Eve.

Have some mulled wine.
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CourtlyCanter
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(Original post by Amarantha)
Yes I understand this. My question is why does tension act towards the centre and not away from it?
I guess it's only logical to think that the string itself is providing the 'strength' to hold the ball in that circular motion, hence there is tension to 'pull it' towards the centre.
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Amarantha
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(Original post by CourtlyCanter)
I guess it's only logical to think that the string itself is providing the 'strength' to hold the ball in that circular motion, hence there is tension to 'pull it' towards the centre.
I was thinking along these lines but I found it hard to put it into words. And also a little confusing at the top considering no forces act outwards. I am used to placing the tension in the opposite direction to the main forces if you get what I mean.
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CourtlyCanter
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(Original post by Amarantha)
I was thinking along these lines but I found it hard to put it into words. And also a little confusing at the top considering no forces act outwards. I am used to placing the tension in the opposite direction to the main forces if you get what I mean.
Ye I know what you mean but the way I see it is that when the ball is at the highest point (top), the centripetal force has two constituents — the weight and the tension, hence why the tension is smallest at that point in the circle as the mgcos θ is the largest when θ is 1.
Hope this helps!
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Implication
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(Original post by Amarantha)
Okay, so me and a friend have been having an ordeal with this question from the AQA Physics A June 2014 Unit 4 paper:

Name:  10636670_196039307406701_2196554125428369197_o.jpg
Views: 1242
Size:  85.3 KB

Originally We got the answer of 17N, which was incorrect. The problem was that we were doing centripetal force plus mg as opposed to minus mg. I identified why it was minus mg - previously we were assuming that tension acts away from the centre, when it actually acts towards it.

So my question is: why is this? Why does the tension acts towards the centre and not away from it? I have been unable to find an explanation for this, just that it is.

Thanks,
Maddie.
The answer is that it acts in both directions. The tension pulls the mass towards the fixed point at the center of the circle AND it pulls the fixed point at the center of the circle towards the mass (if you're struggling with that, just imagine what you would feel from a rope if you were being spun around by it, but also what you would feel from a rope if you were spinning something around you with it). However, you are considering the forces acting upon the mass; not those acting upon the circle's center. Hence, the tension in your case is the force pulling the mass towards the center of the circle.

Intuitively, a force acting away from the center would corresponding to the string somehow pushing the mass away, which clearly isn't what's happening!
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Amarantha
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(Original post by Implication)
The answer is that it acts in both directions. The tension pulls the mass towards the fixed point at the center of the circle AND it pulls the fixed point at the center of the circle towards the mass (if you're struggling with that, just imagine what you would feel from a rope if you were being spun around by it, but also what you would feel from a rope if you were spinning something around you with it). However, you are considering the forces acting upon the mass; not those acting upon the circle's center. Hence, the tension in your case is the force pulling the mass towards the center of the circle.

Intuitively, a force acting away from the center would corresponding to the string somehow pushing the mass away, which clearly isn't what's happening!
Thank you this was helpful :3
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Absent Agent
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(Original post by Amarantha)
Okay, so me and a friend have been having an ordeal with this question from the AQA Physics A June 2014 Unit 4 paper:

Name:  10636670_196039307406701_2196554125428369197_o.jpg
Views: 1242
Size:  85.3 KB

Originally We got the answer of 17N, which was incorrect. The problem was that we were doing centripetal force plus mg as opposed to minus mg. I identified why it was minus mg - previously we were assuming that tension acts away from the centre, when it actually acts towards it.

So my question is: why is this? Why does the tension acts towards the centre and not away from it? I have been unable to find an explanation for this, just that it is.

Thanks,
Maddie.
Just in addition to what others have said, you still might be thinking that if the tension in the string is acting towards the center of the circle then why does the mass not fall towards the center. This is because since there are no forces of attraction at work, the tension in the string is a result from the circular orbit of the mass. In other words, the mass has to orbit for there to be a tension in the string (Newton's first law). This is why during the orbit of the mass the tension in the string acting towards the center of the circle is equal to the reaction force acting away from it for which the mass does not fall towards the center of the circle.

Edit: note the above argument applies only when there are no other forces at work, but in the case of your example there is the external weight force.
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atsruser
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(Original post by Mehrdad jafari)
Just in addition to what others have said, you still might be thinking that if the tension in the string is acting towards the center of the circle then why does the mass not fall towards the center.
You seem to be confused here: the mass does indeed fall towards the centre. It *has* to, since by Newton II, a force towards the centre produces an acceleration in the same direction, which over an infinitesimal time produces a velocity, and hence a displacement towards the centre.

However, it doesn't end up any closer to the centre, since it already has a tangential velocity, which moves it from its original position; we therefore have to combine two infinitesimal displacement vectors, one tangential, and one radial. When we add those up, we find that the mass has moved "down" (i.e. closer to the centre) and "left" (assuming anti-clockwise rotation), and the resultant vector puts the mass back on the circumference of the circle, but a little more anti-clockwise.

In the absence of the radial motion, or if the radial speed is too small, the mass would fall towards the centre. You can imagine also a satellite in orbit around the earth. Its "fall" towards the earth each second (of about 5 m (s=0.5gt^2) is combined with its travel around the earth each second (of about 8000 m), to keep it the same distance from the centre of the earth, and the same height above the surface (which is curving away underneath it, of course).

If the satellite starts to lose tangential speed, then the combined displacement vector moves it closer to the earth each second, and eventually it hits the earth.

This is because since there are no forces of attraction at work, the tension in the string is a result from the circular orbit of the mass. In other words, the mass has to orbit for there to be a tension in the string
This is true but irrelevant: the mass feels a force toward the centre, and it doesn't matter how that force arises, physically.

This is why during the orbit of the mass the tension in the string acting towards the center of the circle is equal to the reaction force acting away from it for which the mass does not fall towards the center of the circle.
This is meaningless gobbledygook.
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Absent Agent
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(Original post by atsruser)
You seem to be confused here: the mass does indeed fall towards the centre. It *has* to, since by Newton II, a force towards the centre produces an acceleration in the same direction, which over an infinitesimal time produces a velocity, and hence a displacement towards the centre.
Yeah, that's true, I shouldn't have phrased it that way but I meant it the sense that it doesn't get any closer to it.

However, it doesn't end up any closer to the centre, since it already has a tangential velocity, which moves it from its original position; we therefore have to combine two infinitesimal displacement vectors, one tangential, and one radial. When we add those up, we find that the mass has moved "down" (i.e. closer to the centre) and "left" (assuming anti-clockwise rotation), and the resultant vector puts the mass back on the circumference of the circle, but a little more anti-clockwise.
In the absence of the radial motion, or if the radial speed is too small, the mass would fall towards the centre. You can imagine also a satellite in orbit around the earth. Its "fall" towards the earth each second (of about 5 m (s=0.5gt^2) is combined with its travel around the earth each second (of about 8000 m), to keep it the same distance from the centre of the earth, and the same height above the surface (which is curving away underneath it, of course).

If the satellite starts to lose tangential speed, then the combined displacement vector moves it closer to the earth each second, and eventually it hits the earth.
That's also true but I don't think that would be the reason here. Tangential velocity would only prevent the object getting any closer to the center of the orbit only when the centripetal force is provided by a force of attraction, force of gravity for example, but in the case of the question, even if the tangential velocity decreases the object will not hit the center of the orbit, that's why satellites orbiting a planet must have a specific tangential velocity depending on how far they are from the planet.

This is true but irrelevant: the mass feels a force toward the centre, and it doesn't matter how that force arises, physically.
This is meaningless gobbledygook.
It does matter as I pointed out above but I would love to know why you think I'm wrong.
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atsruser
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(Original post by Mehrdad jafari)
It does matter as I pointed out above but I would love to know why you think I'm wrong.
I won't be able to reply to this fully for a couple of days, but the "mass on an inextensible rope" question isn't the best example with which to discuss this kind of motion (it's not physically realisable - inextensible ropes don't exist) so you can end up with pointless philosophical discussions. That's partly why I started talking about satellites and gravity.
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Absent Agent
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(Original post by atsruser)
I won't be able to reply to this fully for a couple of days, but the "mass on an inextensible rope" question isn't the best example with which to discuss this kind of motion (it's not physically realisable - inextensible ropes don't exist) so you can end up with pointless philosophical discussions. That's partly why I started talking about satellites and gravity.
Well, we are not interested in whether there are inextensible strings in actual reality, we can simply assume there are for the sake of the question. In fact, we have been assuming this to be so from the start. But feel free to respond anytime you want.


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