Question

If a 12m high tree is being pulled by the tractor, by a rope tied over the top. With the tractor at a linear distance of 12m and 4m away perpendicularly from the tree. If the force applied by the tractor is 2KN then what is the moment caused by the roots of the tree?

(a) -16.5i+7.51j KNm

(b) -16.5i+5.51j KNm

(c) -16.5i+5.51j KNmm

(d) -16.5i+7.51j KNm

This question was addressed to me in examination.

Query is from Moment of a Force topic in portion Force System Resultants of Engineering Mechanics

Answer 1

Right answer is (b) -16.5i+5.51j KNm

The explanation is: The force developed is 2KN, and the roots are having the coordinate (0, 0, 0). Coordinates of the top of the tree is (0, 0, 12). The tractor’s coordinates are (4, 12, 0). Thus applying the cross product on the force and the distance of the tractor from the roots we get the answer as -16.5i+5.51j KNm.