A newly planted tree is supported against the wind by a rope tied to a stake in

Question

A newly planted tree is supported against the wind by a rope tied to a stake in the ground, as shown in the figure below. The force of the wind, though distributed over the tree, is equivalent to a single force F, as shown in the figure. Find the tension in the rope. Assume that neither the tree's weight nor the force of the ground on the tree's roots produces any significant torque about point O. (Let F = 117 N, D = 2.30 m andd = 1.28 m.)

A newly planted tree is supported against the wind by a rope tied to a stake in the ground, as shown in the figure below. The force of the wind, though distributed over the tree, is equivalent to a single force F, as shown in the figure. Find the tension in the rope. Assume that neither the tree's weight nor the force of the ground on the tree's roots produces any significant torque about point O. (Let F = 117 N, D = 2.30 m and = 1.28 m.)

Explanation / Answer

On taking torque at O:-
=>F x D = T x sin37* x d
=>T = FD/dsin37* = (117 x 2.30)/(1.28 x 0.60)
=>T = 350.39N

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