Calculating Tension in a Telephone Wire with Mass and Angle

[SillyYak]

Homework Statement

A telephone wire of mass m is strung between two poles, making an angle θ with the horizontal at each end find the tension at the center. in terms of Theta Mass and G

The attempt at a solution
i assumed it was T= mg/2sintheta using the same logic as the tight rope walker problem. i think I am messing up in accounting for the mass of the wire as if someone were standing in the middle. could someone point me n the right direction

 

[andrewkirk]

What you wrote looks correct for the tension in the wire at a post. You then need to find the horizontal component of that tension in order to get the tension at the midpoint between the two posts.

Or you can collapse those two steps into one and go directly from the vertical component of the tension (which is what supports the weight of half the wire) to the horizontal component, by using a different trig function of the angle.

 

[SillyYak]

Thanks for the reply!, I thought the tension is the same throughout the wire since it is inelastic. The horizontal components of T would be -Tcostheta+Tcostheta=0 correct? I am not sure how I should use this to find the midpoint tension.

 

[SillyYak]

so i played around with it and got the correct answer of MgCostheta/2sintheta but am not sure how to interpret this, why would the tension at the center be equaled to the horizontal component of the tension at the post?

 

[andrewkirk]

why would the tension at the center be equaled to the horizontal component of the tension at the post?

Because the horizontal tension is the same all the way along the wire. It must be, or the wire would move.

By contrast, the vertical tension decreases as the height of the wire decreases. At any point in the wire, the vertical tension is what's necessary to support all the wire below that point on this side of the centre point. At the centre point itself, there is no wire below it, so the vertical tension is nil.

The reason for the difference is that there's no external force acting horizontally on the wire, other than the pull from the two poles at either end. But every part of the wire has a vertical force acting on it from gravity.

 

[SillyYak]

I think i get it, in all my other problems the ropes/wires were massless so i didnt understand this one, Thanks for breaking it down for me!