To be able to calculate the moment of a force about a specified axis. When the moment of a force ...

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To be able to calculate the moment of a force about a specified axis. When the moment of a force is computed about a point, the moment and its axis are always perpendicular to the plane that contains the force and the moment arm. In some instances, it is important to find the component of this moment along a specified axis that passes through the point. In addition to scalar analysis. M_a. the magnitude of the moment of a force about a specified axis, can be found using the triple scalar product M_a = u_a middot (r times F) = |u_a_x r_x F_x u_a_y r_y F_y u_a_z r_z F_z| where u_a is the unit vector that describes the direction of the specified axis and r is the position vector to the point where the force F is applied. 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. (Figure 3) 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 (-2.20, 3.00, 23.5) ft and the point where the cable is attached to the end of the cross member is B (-2.20, -2.00, 26.5) ft. The cable's direction is {1.00 i - 1.00 j - 1.00 k} and it has a tension of 165 lb. What is M_a, the moment that tends to twist the telephone pole due to the tension in the cable applied at point B? Express your answer numerically in pound-feet to three significant figures.