Question

To prevent incursions by nocturnal ursine marauders, you hang your food from a tree. To do so, you have thrown a rope over two parallel branches, attached a bag containing 45.3 kg of food to their center with a bungee cord, and hoisted it up into the air. This gives the entire contraption a Y-shape, with two rope strands hanging down from the branches with angles 35⁰ and 65⁰ down from the horizontal, respectively.*

Find the tension in each rope or cord:

(a) The bungee cord supports a weight:

(b) The strand making the 35⁰ angle supports a weight:
  
(c) The strand making the 65⁰ angle supports a weight:

* Think of them as two angles of a triangle, with the third angle being at the point you hang the bungee cord.

Answer 1

Suppose tension in left strand = T1

Tension in right strand = T2

Weight of Box = W = m*g = 45.3*9.8 = 443.94 N

Now Using force balance in ropes

In horizontal direction:

T1*cos 65 deg = T2*cos 35 deg

T1 = T2*cos 35 deg/(cos 65 deg) = 1.938*T2

Force balance in vertical direction

T1*sin 65 deg + T2*sin 35 deg = T3 = W

1.938*T2*sin 65 deg + T2*sin 35 deg = 443.94

T2 = 443.94/(1.938*sin 65 deg + sin 35 deg)

T2 = 190.53 N

Part (b): T2 = 190.53 N (Magnitude of tension in strand making the 35 deg angle)

Part (c): T1 = 1.938*T2 = 1.938*190.53 = 369.25 N (Magnitude of tension in strand making the 65 deg angle)

Part (a): Tension in bungee cord = T3 = W = 443.94 N

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