Question

If the two ends of a rope in eqilibrium are pulled with forces of equal magnitude and opposite direction, why is the total tension in the rope not zero?

Answer 1

If you break it into its component form you would see that the x components will cancel as they point in opposite direction, but when you look at the y components they will both point upwards (i.e. in the same direction) therefore the net tension is not zero.

Answer 2

Basically tension in a rope at a point means the force exerted by the elementary part of string at that point but not net force acting on that part.Here net force acting on elementary part is zero but force exerted by that part is not equal to zero but it is equal to either force which you can obtain by simple free body diagram

Answer 3

A rope in equilibrium is not mutually exclusive to there being tension in the rope. In fact if there were no tension, then the two opposite forces would cause an acceleration in the rope both ways, like what happens in elastic. Newton's third law of force/reaction force pairs is what causes the tension. Tension is the reaction forces transmitted through the rope.

Answer 4

Tension is not the same as total force acting at a point. Tension in a rope can be measured by a thought experiment. Imagine that you cut the rope at some point. Then what force would you need to apply at the cut end so that a cut piece, that was free to move, doesn't move? The fact that you had to apply this force to keep the cut piece from moving, shows that when the rope was not cut, this force must have been there to prevent the rope from breaking up into pieces and flying apart. So, the tension is not zero and is equal to the equal and opposite forces you mention in your question.