problem 1.10 - determine the magnitude and sense of the resultant couple moment acting on the rectangular…

problem 1.10 - determine the magnitude and sense of the resultant couple moment acting on the rectangular plate.

problem 1.10 - determine the magnitude and sense of the resultant couple moment acting on the rectangular plate.

Answer

Explanation:

Step1: Resolve the 20 - N forces into components

The vertical component of the 20 - N force is $F_y = 20\sin30^{\circ}=10$ N and the horizontal component is $F_x = 20\cos30^{\circ}=10\sqrt{3}$ N.

Step2: Calculate the moment due to each couple

The couple formed by the 30 - N forces: $M_1=30\times8 = 240$ N·m (counter - clockwise). The couple formed by the vertical components of the 20 - N forces: $M_2 = 10\times4=40$ N·m (counter - clockwise). The horizontal components of the 20 - N forces do not create a couple moment about an axis perpendicular to the plane of the plate.

Step3: Find the resultant couple moment

$M = M_1+M_2$. $M=240 + 40=280$ N·m (counter - clockwise).

Answer:

The magnitude of the resultant couple moment is 280 N·m and the sense is counter - clockwise.