Question

multiple choice question 4.19. part a determine the magnitude and direction of the couple moment. m = 3120 lb - ft cw m = 2496 lb - ft cw m = 3900 lb - ft cw m = 2496 lb - ft ccw

Explanation:

Step1: Recall couple - moment formula

The magnitude of a couple moment $M = Fd$, where $F$ is the force and $d$ is the perpendicular distance between the lines of action of the two equal and opposite forces forming the couple.

Step2: Identify force and distance

Here, $F = 120$ lb. The perpendicular distance between the two 120 - lb forces can be found by considering the horizontal and vertical components. The horizontal distance between the two forces is $6 + 6=12$ ft and the vertical distance is $8 + 8 = 16$ ft. Using the Pythagorean theorem for the right - angled triangle formed by the components of the distance, $d=\sqrt{(12)^{2}+(16)^{2}}=\sqrt{144 + 256}=\sqrt{400}=20$ ft.

Step3: Calculate the couple moment

$M = Fd=120\times20 = 2400$ lb - ft. To determine the direction, we use the right - hand rule. By observing the orientation of the forces, the couple moment is clock - wise (CW).

Answer:

The closest answer from the given options is $M = 2496$ lb - ft CW. So the answer is: $M = 2496$ lb - ft CW.