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I am reviewing the concept of tension, a force that expresses the internal tensional state in a body (rope, chain, string, solid body). My understanding is that the force of tension "derives" from the stress tensor and relates (it is the product) the diagonal tensor components to an infinitesimal area ##dA## perpendicular to the tension force direction pointing away from the area.

- The stress tensor diagonal components are scalars (they are essentially what we call pressure, I guess, and when positive, they are used to derive tension). If the rope lies along the x-axis, then there is only one of nonzero diagonal components which multiplied by the rope cross-section, results in the tension force, correct?
- In general, a "true" vector is one that is uniquely defined in both magnitude and direction at a point in space. Inside a rope under tension, the tension force is always directed axially and at an arbitrary point ##P## inside the rope seems to point in two opposite directions at the same time...Is that because, considering an imaginary cut at point ##P##, adjacent pieces of the rope have zero relative motion and experience an action-reaction force pair? The piece of rope to the left of the imaginary cut experiences a force pointing to the right and the piece of rope on the right of the cut experience a left directed force...Is that correct?