Couples In Equilibrium

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{7}A_{71} Base Sequence = 12735 String Sequence = 12735 - 7 - 71 **

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Forces F_{1}, F_{2}, F_{3}, F_{4} act on a body. Forces F_{1} and F_{3} are a couple. Forces F_{2} and F_{4} are a couple (figure 4.7). Determine the ratio AC/BD in terms of the forces so that the body will be in equilibrium.

**The string**:

(a) S_{7}P_{7}A_{71} (Static - Equilibrium).
**The math**:

Pj Problem of Interest (PPI) is of the type *equilibrium*.

A couple consists of two equal and parallel forces acting on a body in opposite directions.

A couple is balanced by another couple when their moments are equal and tend to rotate the body in opposite directions.

For the couple F_{1} and F_{3}:

Moment = F_{1} x AC or F_{3} x AC.

For the couple F_{2} and F_{4}:

Moment = F_{2} x BD or F_{4} x BD.

So, body will be in equilibrium if F_{1} x AC = F_{2} x BD

Or

F_{3} x AC = F_{4} x BD

Or

F_{1} x AC = F_{4} x BD

Or

F_{3} x AC = F_{2} x BD

So, body is in equilibrium if AC/BD = F_{2}/F_{1}

Or

AC/BD = F_{4} /F_{3}

Or

AC/BD = F_{4} /F_{1}

Or

AC/BD = F_{2} /F_{3}.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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