Principio de Momentos: Resolución de Problemas

Consider a pole placed in a 3-dimensional system with a cable attached. When the tension of 15 kN is applied to the cable, determine the moment about the z-axis passing through the base.

The moment can be determined using two methods.

In the first method, calculate the projection of the force along the unit vector and multiply it by the force's magnitude to obtain the force vector.

The moment about the origin is the cross-product of the position vector and the force. The moment along the z-axis can be obtained by the dot product of the moment about the origin and the unit vector along the z-axis.

Alternatively, resolve the force vector into its components. The components along the y-axis and z-axis exert no moment as they pass through and are parallel to the z-axis, respectively.

The tension in the x-direction can be obtained by multiplying the tension with the direction cosine with respect to the x-axis.

Recall the moment of force equation, and by substituting the terms, the moment about the z-axis can be determined.