Couples In Equilibrium
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Couples In Equilibrium

Forces F1, F2, F3, F4 act on a body. Forces F1 and F3 are a couple. Forces F2 and F4 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) S7P7A71 (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 F1 and F3:
Moment = F1 x AC or F3 x AC.
For the couple F2 and F4:
Moment = F2 x BD or F4 x BD.
So, body will be in equilibrium if F1 x AC = F2 x BD
Or
F3 x AC = F4 x BD
Or
F1 x AC = F4 x BD
Or
F3 x AC = F2 x BD
So, body is in equilibrium if AC/BD = F2/F1
Or
AC/BD = F4 /F3
Or
AC/BD = F4 /F1
Or
AC/BD = F2 /F3.

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