Question Video: Identifying the Property of the Triangle of Forces Rule | Nagwa Question Video: Identifying the Property of the Triangle of Forces Rule | Nagwa

Question Video: Identifying the Property of the Triangle of Forces Rule Mathematics • Second Year of Secondary School

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Complete the following: If three coplanar and equilibrium forces are represented by the sides of a triangle taken in one cyclic order, then the lengths of the sides of the triangle are proportional to _.

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Video Transcript

Complete the following: If three coplanar and equilibrium forces are represented by the sides of a triangle taken in one cyclic order, then the lengths of the sides of the triangle are proportional to what.

The correct answer here is the magnitude of the forces. If we consider three forces 𝐅 sub one, 𝐅 sub two, 𝐅 sub three that act at a point and they’re in equilibrium, then they can be redrawn as a triangle, providing we consider the order and direction of the forces. We begin by drawing the force 𝐅 sub one as shown. Then we move on to 𝐅 sub two. This begins at the terminal or endpoint of the force 𝐅 sub one. Finally, we repeat this process with the third force 𝐅 sub three. This begins at the terminal point of 𝐅 sub two and travels in the same direction as in our first diagram. Its terminal point will correspond to the initial point of 𝐅 sub one. And we have therefore created a triangle of forces.

The magnitude of these forces is proportional to the lengths of the sides of the triangle drawn. This is true of any three coplanar forces in equilibrium.

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