Some statics confusion - Vectors & Polygon of forces

[EntropicGhost]

Hi all, I am a little confused with a supposedly simple statics concept. The topic was on vector forces and the polygon of forces with respect to a static mechanics problem.

The text i was reading was a little confusing:

If three or more forces act at the same point and are in equilibrium, they may be represented in magnitude and direction by the sides of a polygon taken in order. Taken in order refers to the order of drawing the sides of the polygon and not the order in which the forces are taken from the space diagram.

The text also shows a diagram both spatial and a 2D polygon of vectors diagram.

The text offers no explanation of why they must betaken in a specific order, or what that order is.

For example, the spatial diagram (which shows 4 tie-bars coincident at a point) has the forces numbered (1-4) in a clockwise direction about the common point. Then the polygon of forces 2D diagram shows the forces arranged (1-4) in a counter-clockwise direction showing how they form a polygon end-to-end.

Yet no justification or explanation of why the forces are drawn this way (other than it works, which isn't good enough for me :P).

Can anyone offer an explanation why the stated order works over any other possible combination of arrangements of forces?

 

[robphy]

I think "taken in order" means that the orientation of the arrows on each force must be retained...and these arrows are connected tail to head. (If they sum to zero, then the last head will meet the first tail.) However, the sum of the vectors A,B,C can be expressed in any order [using commutativity and associativity]: A+B+C or A+C+B or C+B+A, etc...

 

[TVP45]

It's a graphical technique. If you do the same problem using vector components, the order doesn't matter.