A tree contractor has been hired by a homeowner to remove a damaged tree from a

Question

A tree contractor has been hired by a homeowner to remove a damaged tree from a previous storm. The top of the tree broke off leaving the trunk left in the ground. The two arborists will remove the tree by attaching a rope near the top and cutting the base close to the ground. The scenario is shown in the figure below. If the arborist pulls on the rope with a force of magnitude F = 38.5 N calculate the components of the torque ? with respect to the base P of the tree. The distances in the figure are: d = 13.8 m, h = 1.45 m, s = 6.49 m and r = 10.64 m.

Explanation / Answer

r = PI= d k = 13.8 k

vector parrallel to force = (1.45 - 13.8)k + 10.64i + 6.49 j

force vector = 38.5 x (10.64i + 6.49j - 12.35 k )/ sqrt(10.64^2 + 6.49^2 +12.35^2)

F =2.19 (10.64i + 6.49j - 12.35 k ) N

torque =r x F = 13.8 k x 2.19 (10.64i + 6.49j - 12.35 k )

= 321.56j - 196.14i

= -196.14i + 321.56 j + 0 k

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