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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 what.
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The correct answer here is the magnitude of the forces.
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If we consider three forces ๐น sub one, ๐น sub two, ๐น sub three that act at a point and theyโre in equilibrium, then they can be redrawn as a triangle, providing we consider the order and direction of the forces.
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We begin by drawing the force ๐น sub one as shown.
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Then we move on to ๐น sub two.
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This begins at the terminal or endpoint of the force ๐น sub one.
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Finally, we repeat this process with the third force ๐น sub three.
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This begins at the terminal point of ๐น sub two and travels in the same direction as in our first diagram.
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Its terminal point will correspond to the initial point of ๐น sub one.
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And we have therefore created a triangle of forces.
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The magnitude of these forces is proportional to the lengths of the sides of the triangle drawn.
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This is true of any three coplanar forces in equilibrium.