Large trees manage to support some very heavy branches with nothing more than wo

Question

Large trees manage to support some very heavy branches with nothing more than wood fibers inside the tree trunk. The tree in part (a) of the figure is supporting a 70.0 kg (about 130 lb) horizontal branch whose center of mass is 1.75 m from the vertical centerline of the trunk.The trunk is 65.0 cm in diameter at the level of the branch. The only place the forces (and torques) necessary to hold up this heavy branch can come from is inside the trunk. To get an idea of how large these forces need to be, we can model this tree as a horizontal bar supported by a cable (the wood fibers), as in part (b) of the figure. Find the tension in the fiber (in N).

Explanation / Answer

The weight of the horizontal branch is w = m * g where m = 70.0 kg and g = 9.8 m/s^2 The tension in the fiber (in N) is T = (Tx^2 + Ty^2)^1/2 where Tx = T * cos? and Ty = T * sin? where T = w and ? = 45o
The tree in part (a) of the figure is supporting a 70.0 kg (about 130 lb) horizontal branch whose center of mass is 1.75 m from the vertical centerline of the trunk.The trunk is 65.0 cm in diameter at the level of the branch. The only place the forces (and torques) necessary to hold up this heavy branch can come from is inside the trunk. To get an idea of how large these forces need to be, we can model this tree as a horizontal bar supported by a cable (the wood fibers), as in part (b) of the figure.

Find the tension in the fiber (in N).

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