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Lesson: Chapter 12 — Equilibrium of Forces

12.4. Equilibrium under three non-parallel forces 5 of 6

More than three forces

What we have discussed so far are systems in equilibrium under two or three forces. A body can be in equilibrium under a larger number of forces as well.

Figure to be added

Figure 12.14 — a body in equilibrium under five forces: a plank hung by four ropes knotted to its four corners, with its weight w acting downward.

Figure 12.14 shows a plank hung by four ropes knotted to its four corners. The plank stays still because its weight, acting vertically downward, is balanced by the tensions in the four ropes.

Count them up

That is five forces — four tensions in the ropes and the weight of the plank. Yet the requirement has not changed: the forces acting upward add up to the force acting downward.

The rule never changes

Two forces, three, or five — the requirement is the same one: the resultant must be zero. What grows with the number of forces is the work of checking it, not the rule.

Beyond three forces

Even under more than three forces a system can be kept in equilibrium by applying forces as required.