A newly planted tree is supported against the wind by a rope tied to a stake in
ID: 2143796 • Letter: A
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 and d = 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 d = 1.28 m.)Explanation / Answer
Force of the wind, F = 117 N
let Tension in the rope be 'T'
anticlockwise torque about the base is equals to clockwise torque about the base
F * D = T Sin(theta) * d
T = ( 117 *2.3 ) / ( Sin 37 * 1.28 )
= 349.3444 N
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