4.14:
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.
rA and rB represent the position vectors originating from point O to points A and B, respectively.
The difference between the position vectors rA and rB 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.
4.14:
Moment of a Couple: Problem Solving
The moment of couple is an essential concept in physics and engineering, used to calculate the rotational force, or torque, that is created when a couple —two equal and opposite forces—acts on an object.
The moment of a couple is found by multiplying the magnitude of one of the forces by the perpendicular distance between the line of action of the two forces. This creates a twisting force, which can be used to rotate an object. The moment of a couple is used to solve problems involving balanced and unbalanced forces.
The process of the moment of couple problem-solving involves several key steps. Initially, the relevant forces acting on the object must be identified and drawn in a clear and simple diagram. This can help to visualize the problem and make it easier to understand.
Next, find the vector associated with the perpendicular distance between the lines of action of the two forces. The cross product of the force vector and the perpendicular vector will give us the moment of the couple. The direction of the moment can be determined using the right-hand rule, which states that the direction of the torque is perpendicular to both the force and the distance vector.
Finally, the moment can be used to solve the problem at hand. This may involve calculating the overall torque on an object, determining the angular velocity or acceleration of a rotating object, or calculating the work done by the couple.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. pp 154-156, 165.