Force-Couple System: Find Resultant, Pitch & Point of Wrench

[physicsss]

Two bolts A and B are tightened by applying the forces and couple shown. replace the two wrenches with a single equivalent wrench and determine (a) the resultant, (b) the pitch of the single equivalent wrench (c), the point where the axis of the wrench intersects the xz plane.

 

[physicsss]

Does anyone know how to add two wrenches pictured above?

 

[quicknote]

I would approach this problem by first understanding the concept of a force-couple system. A force-couple system is a combination of forces and a couple acting on a body, where the forces act in the same plane and the couple acts perpendicular to that plane. In this scenario, the two bolts A and B are being tightened by applying a force and a couple.

To find the resultant of the force-couple system, we can use the principle of moments. The resultant is the magnitude and direction of the single force that would produce the same effect as the original force-couple system. By equating the moments of the original system to the moment of the resultant force, we can solve for the magnitude and direction of the resultant force.

Next, we can determine the pitch of the single equivalent wrench by finding the distance between the axis of rotation and the line of action of the resultant force. This distance represents the perpendicular distance between the force and the axis of rotation and is known as the pitch.

Finally, to find the point where the axis of the wrench intersects the xz plane, we can use the concept of torque equilibrium. Since the wrench is in equilibrium, the sum of the torques acting on it must be equal to zero. By setting up an equation with the known forces and distances, we can solve for the unknown point where the axis of the wrench intersects the xz plane.

In conclusion, as a scientist, I would use principles of mechanics and equations of equilibrium to find the resultant, pitch, and point of the single equivalent wrench in this force-couple system. This approach allows for an accurate and precise solution to the problem at hand.