An old wooden telephone pole with a single cross member was blown off center dur
ID: 1900284 • Letter: A
Question
An old wooden telephone pole with a single cross member was blown off center during a recent storm. To temporarily stabilize the telephone pole, a repair crew has attached a cable from the end of the cross member to an eye-ring stake anchored in the ground. If the origin O of a coordinate system is placed where the pole meets the ground, the point where the cross member is attached to the pole is A(-1.50,1.70,23.5) ft and the point where the cable is attached to the end of the cross member is B(-1.50,-3.30,26.5) ft. The cable's direction is {1.00i - 1.00j - 1.00k) and it has a tension of 185 lb. What is Ma, the moment that tends to twist the telephone pole due to the tension in the cable applied at point B?
Ma = ux(ryFz - rzFy) - uy(rxFz - rzFx) + uz(rxFy - ryFx)
Explanation / Answer
r = B - A = (-1.50,-3.30,26.5) - (-1.50,1.70,23.5) = (0, -5, 3) ft
F = 185 (1.00i - 1.00j - 1.00k) = (185, -185, -185)
r×F = (0, -5, 3) × (185, -185, -185)
r×F = (1480, 555, 925) ft.lb
r×F = (1480, 555, 925) * (0.3048*4.448)
r×F = (1480*(0.3048*4.448), 555*(0.3048*4.448), 925*(0.3048*4.448))
r×F = (2007, 752, 1254) N.m