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 = 105 N, D = 2.32 m and d = 1.30 m.)

Explanation / Answer

On taking torque at O:- =>F x D = T x sin37* x d =>T = FD/dsin37* = (129 x 2.02)/(1.28 x 0.60) =>T = 3.39 N or separate the tension into its x and y components, T in the x direction would be Tsin(37) and in the y it would be Tcos(37) since the force we must cancel out is specifically in the x direction we will only look at the x component of the tension for the tree to remain at tranlastional equilibrium we must have the equations F-Tx=0 so Tsin(37)=F T=F/sin37=124/sin37 EDIT: try making the force to be canceled 1.18F/1.96=74.65N which ends up giving you a 124N tension in the rope but it would give a torque, it will only be in translational equilibrium

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