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 28.5 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 42⁰ and 58⁰ 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 42⁰ angle supports a weight: (c) The strand making the 58⁰ angle supports a weight:

Answer 1

Suppose tension in AB rope = T1

Tension in AC rope = T2

Weight of Box = W = m*g = 28.5*9.8 = 279.3 N

Now Using force balance in ropes

In horizontal direction:

T1*cos 42 deg = T2*cos 58 deg

T1 = T2*cos 58 deg/(cos 42 deg) = 0.713*T2

Force balance in vertical direction

T1*sin 42 deg + T2*sin 58 deg = W

0.713*T2*sin 42 deg + T2*sin 58 deg = 279.3

T2 = 279.3/(0.713*sin 42 deg + sin 58 deg)

Part (c): T2 = 210.8 N (Magnitude of tension in rope AC)

Part (b): T1 = 0.713*T2 = 0.713*210.8 = 150.3 N (Magnitude of tension in rope AB)

Part (a): Tension in rope AD = W = 279.3 N

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