13.1 Rope Hanging Between Trees

A diagram of two trees with a rope hanging between them.

A rope of mass \(\displaystyle m \) hangs between two trees, making an angle \(\displaystyle \theta \) with the vertical at each end. (It is attached to to each tree at the same height.) Your goal in this problem will be to find the magnitude of the tension force in the rope at the ends and midpoint of the rope. Begin by drawing a free-body diagram just for the left half of the rope.

Calculate \(\displaystyle T_{mid}\), the tension in the rope at the midpoint. Express your answer in terms of \(\displaystyle m\), \(\displaystyle g\), and \(\displaystyle \theta\).

 

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