Few questions related to Tension I am struggling with the concept of tension in a rope. Below specific questions. 


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*I am understanding tension to be an elastic force between rope molecules. If so, is it fair to say the net tension on each rope molecule is zero (if rope is in rest) but there is a net tension for the rope whose direction is opposite to applied force?

*What is the direction of the tension. I am reading conflicting answers for it. If a mass attached to rope is hanging. I think tension in rope is equal and opposite of weight. is that true?

*Kleppner seems to mention that tension has no direction which is confusing me. 

*Also, does the tension vary. Mass attached to rope and hanging. does value of tension vary throughout the rope?
 A: Tension is a force transmitted by a rope. At an individual point in the rope, if the rope is stationary, there can be no net force so all forces cancel out. In a sense this means there is equal "tension" to the left and to the right; in that interpretation there is no direction (although I would normally say the tension is "along the length).
When you have a massive rope haying down, the tension varies with position since at any point the tension must balance the force of gravity on the part of the rope below it. Similarly when a longitudinal wave is traveling along a rope there will be variations in tension.
A: Tension is a concept which is introduced in physics. The molecular interpretation of the concept is not requited. Because it is complicated. Your preposition that the tension in the rope the summation of tension in the individual molecule is not correct an the molecular structure may not be linear.
Direction of the tension force is always acting away from the object. As it is a rope the compression is not there.
the Diagram will show it better

The tension force in the rope is acting away from the mass.
This is THE ONLY DIRECTION TENSION IN A ROPE
The tension in a string will not vary as long as it is made up of same material and is having the same thickness throught. If the young's modulus is changing then the tension may vary throught the string.
