An old wooden telephone pole with a single cross member was

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(3.00,2.00,25.9)ft and the point where the cable is attached to the end of the cross member is B(3.00,3.00,28.9)ft. The cable\'s direction is {1.00i1.00j1.00k} and it has a tension of 145 lb . What is Ma, the moment that tends to twist the telephone pole due to the tension in the cable applied at point B?

Solution

You did it correctly by M = u dot (r X F), except your have to know the right u, r, and F.

Let G be the point where the cable is attached to the ground

OA = [-3, 2.7, 24.9] <---This is a vector

u = unit vector of OA

r = any vector from OA to BG (line of action of F). So, pick OB as r, therefore,

r = [-3, -2.30, 27.9]<---This is a vector

F = 155[1i - 1j - 1k] = 155i - 155j - 155k

So, now plug these values in the formula below and take the determinant as in the link below:

M = u*(r X F)