The child on the swing
A child sitting on a swing is another example of a system held in equilibrium under three parallel forces.
Figure to be added
The child sits in equilibrium on the swing because the sum of the forces F1 and F2 acting upward along the two ropes equals the child's weight (W).
The metre rule result again
For the metre rule: F1 + F2 = weight of the rule
For the swing: F1 + F2 = weight of the child
The apparatus has changed; the relationship has not.
Must the two forces be equal?
If the child sits exactly in the middle of the swing, F1 and F2 are equal. But shifted a little towards one side, the force in the nearer rope grows and the force in the other falls — while the sum stays exactly equal to the weight.
What decides how the sum divides between them is the principle of moments from chapter 11.