Reasons for Direction of Tension in Circular Motion?

Is the answer B 13N?

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?

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.

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



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!

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



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.

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 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.

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 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.

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.