A physics problem regarding a rope with mass M, attached to two poles. Tension at ends of rope, lowest point.?

Question

A clothesline has a mass M, and each end makes an angle X with the horizontal. What is a) the tension at the ends of the clothesline? b) the tension at the lowest point? The curve is hanging under it's own weight (catenary curve).

Answer 1

F1(vert) = F2(vert) = Mg/2
Tension @ A = Tension @ B = (Mg/2)/sinX = Mg/(2sinX)
Tension(lowest point) = F(A horz) = F(B horz) = (Mg/2)/tanX = Mg/(2tanX)

Answer 2

Hey - just out of curiosity, the tension in the vertical direction at the bottom should be 0, right (because all of the forces in the vertical direction are being pulled at the catenary's edges, right?)

Answer 3

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