Engineering Mechanics - Force System Resultants - Discussion

Moment=force * distance.

By observing the beam we have one force on the left side, apply moment formula.
F1* 4=m(A).
400 * 4==1600.

It is well. But it needs more clarifications.

How can I derive moment?

According to fundamental principles, we can apply a balance force system anywhere along the rigid body.

So if we apply at point A a balance force system of 400lb vertically upward and downward, they will cancel out each other and net effect remains the same but the force F1 will form a couple with the vertical 400lb force at A.

The moment of a couple is nothing but the product of one of the force of couple and its couple arm which is here 4ft, Since the couple is a vector qty, hence we will get the answer as 400*4=1600lb-ft in counterclockwise direction.

Do you have a deeper explanation and solution regarding on this problem?

* {r_{OF}} is the vector from point A to the position where quantity F1 is applied.
* represents the cross product of the vectors.

Therefore,
M1=force(F1)*perpendicular distance(4ft),
M1=400lb*4ft,
M1=1600ft-lb.
And the direction is getting from right hand screw principle as anti-clockwise direction.

Simply we know the M=F*D then 400*horizontal distance (4) =1600 anticlockwise moment.