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Which of the following represents the triangle of forces rule?
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Is it (A) πΉ sub one over π΄πΆ equals πΉ sub two over ππΆ equals πΉ sub three over π΄π?
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Option (B) πΉ sub one over ππ΄ equals πΉ sub two over π΄πΆ equals πΉ sub three over ππΆ.
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Option (C) πΉ sub one over angle π΄ equals πΉ sub two over angle πΆ equals πΉ sub three over angle π.
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Option (D) πΉ sub one over angle πΆ equals πΉ sub two over angle π, which is equal to πΉ sub three over angle π΄.
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Or finally, option (E) πΉ sub one over sin π΄ is equal to πΉ sub two over sin πΆ, which is equal to πΉ sub three over sin π.
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The triangle law of forces states that if a body is in equilibrium under the action of three forces at a point, then the three forces can be represented by the three sides of a triangle in order.
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This can be seen in our diagram, where the force πΉ sub one acts along ππ΄, the force πΉ sub two acts along π΄πΆ, and the force πΉ sub three acts along the third side of our triangle, πΆπ.
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The magnitude of these forces will therefore be proportional to the length of their corresponding sides.
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Options (A) and (B) both have the three forces written as proportions to the lengths of the three sides.
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Option (A) has πΉ sub one proportional to side length π΄πΆ.
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However, this is not its corresponding side.
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Option (B), on the other hand, has the correct forces matched to the correct sides.
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It is worth noting that the force πΉ sub three acts in the direction πΆπ.
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However, as this is the side length of the triangle, πΆπ is equal to ππΆ.
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This confirms that the correct answer is option (B).
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πΉ sub one over ππ΄ equals πΉ sub two over π΄πΆ equals πΉ sub three over ππΆ represents the triangle of forces rule.
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Options (C) and (D) match the three forces to angles in the triangle.
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Whilst option (D) has matched the forces to the angles opposite them, this is not the triangle of forces rule.
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The forces are not proportional to the angles in the triangle.
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Option (E) looks like it could be Lamiβs theorem.
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This states that when three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
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For this to be true, πΉ sub one would have to be matched with sin πΆ, πΉ sub two with sin π, and πΉ sub three with sin π΄.
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Option (E) is therefore not the correct form of Lamiβs theorem.
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However, even if this was the case, this would not be the correct answer for this question as we were looking for the equation that represents the triangle of forces rule.