Final answer:
To determine the resultant couple moment acting on a pipe assembly, one must calculate the torque for each force applied and sum these torques. The torque is calculated using the formula (τ = rF sin θ), considering distances and angles at which forces are applied, under static equilibrium conditions.
Step-by-step explanation:
The determinant of the resultant couple moment acting on the pipe assembly involves applying the concepts of static equilibrium and calculating the force effects. We can start by drawing the free-body diagram of the assembly to visually represent the forces in action. Using this diagram, we can apply Newton's laws to set up equilibrium equations, where the sum of the forces in the x and y-directions must be zero (ΣFx = 0 and ΣFy = 0).
To calculate the resultant couple moment, you would typically use the formula for torque (τ = rF sin θ), where 'r' is the distance from the pivot point to the point where the force is applied, 'F' is the magnitude of the force, and 'θ' is the angle between the force vector and the lever arm. In the context of the pipe assembly and assuming the force applied is perpendicular to the radius and that friction is negligible, the applied torque would be the product of the radius and the force applied.
For example, if the force exerted is 250 N and it is applied at a distance of 1.50 m from the pivot point, the resultant torque would be (1.50 m)(250 N) = 375 N·m. Remember, if multiple forces are applied, we would add up all the torques to find the total couple moment affecting the pipe assembly.