[spr] Re: Tension, scalar or vector?

In answer to:

> Hi. I am in a big argument regarding tension, like in a cord or
> string. Some knowledgeable people tell me it is a vector; others say
> it is a scalar. The implications are important. I think it is a
> scalar, because it has no unique direction and I cannot imagine the
> meaning of negative tension. Who is right? Could someone please help
> me?

The answer is that Tension is a vector.  Given a piece of string between
two points and weighted by gravity the string sags.  This leads to a
tension vector T(x) at each point in the string.  Obviously the tension
vector near the bottom is longitudinal and near the edges it points
slightly downward. Any elementary textbook that derives the catenary
shape or wave equation will show this.  The magnitude of the tension
vector at a point x can also be called the "tension" and this leads to
the difficulty of interpretation. Just keep in mind that tension is a
force, force is a vector quantity, therefore tension is a vector
quantity. 

Doug

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