What is the direction of tension force in a rope?

[personage]

Hi everyone,

What I understand is that tension only exists if there are two forces pulling on a rope in opposite directions. What I have also read is that due to Newton's third law, the rope actually pulls back with a force equal but opposite to the two applied forces, so the forces look a bit like this:

<F---------(-->T)------(<--T)-------F>

So there are actually two opposite tension forces on the rope. Now if both the applied forces are equal (i.e. object is in equilbrium), how can we say that the tension forces have any particular direction? An example of this is in my lecture notes, on page 19, here: http://www.physics.usyd.edu.au/~helenj/Mechanics/PDF/mechanics01.pdf
Somehow there's a tension force away from the sled, and yet they talked about 'both ends of the string pull back with a force called tension'.

If anyone could help me out with this, I'd really appreciate it

 

[Tom_K]

Your understanding is correct. Maybe the illustration in your notes only intended to show the Tension force from one end?

 

[ZelfZA]

If I understand correctly.
When you look at every Force independently you have a Force and an "Opposite equal reaction"(Tension).
When you add the two together the Tension in the rope is going to be equal to the combination of the two opposite forces.
Also I believe that the Tension is applied over the whole rope. Thus a break will happen at the weakest spot, not able to handle the Tension.

So to answer your question. I believe that the tension is the energy applied to the rope(or what ever) unconditional to direction.
Even the definition of Tension is : "the state of being stretched tight".
Force is a whole different thing.

But like I said.. It's my opinion

 

[personage]

So would it be correct if I thought of the overall 'tension force' as the net result of all these individual, smaller tension forces? For example, if the tension forces in the left direction were smaller than that in the right, then the net tension force would be to the right?

 

[PhanthomJay]

So would it be correct if I thought of the overall 'tension force' as the net result of all these individual, smaller tension forces? For example, if the tension forces in the left direction were smaller than that in the right, then the net tension force would be to the right?

No to your first question, yes to your second question only if the rope has mass and acceleration is involved..

The tension in a massless rope is the same everywhere, and its direction is such that it always pulls away from the object on which it acts. In the figure shown in post 2, draw free body diagrams. The tension force pulls away from the block, to the right. The tension force pulls away from the hand, to the left. And if you look at a section of the rope in the middle, the left part of the rope pulls away from the middle piece, tension pointing to the left, and the right part of the rope pulls away from it, tension pointing to the right.
In the real world, ropes are not massless, so the tension in the rope would vary slightly for the accelerating condition, but negligible mass is often assumed if the cable isn't large. If the mass of the rope must be considered, only then will there be a net force on the rope if there is acceleration of the object (and rope).