Moment of a Couple: Problem Solving

Consider a pipe attached to a coupling at point O on the x-axis in a three-dimensional coordinate system.

Two wrenches of length 0.12 meters apply an equal and opposite force of 120 newton along the z-axis. The wrenches are at a distance of 0.5 meters and 0.7 meters from point O along the x-axis.

Determine the couple moment of the system.

The couple moment about point O is determined as the sum of the cross-products of the position vectors and the applied forces.

r_A and r_B represent the position vectors originating from point O to points A and B, respectively.

The difference between the position vectors r_A and r_B is the vector r, which is the distance between the opposing forces.

The couple moment can be expressed in the determinant form as the cross-product of the position and force vectors.

The magnitude of the couple moment is determined by taking the square root of the sum of the squares of the components of the resulting vector.