Systems of coplanar forces — A/L Combined Mathematics

How do I practise Systems of coplanar forces?

1 question with a worked solution

1. Three coplanar forces of magnitudes 6 N, 8 N, and 10 N act at a point in equilibrium. What is the angle between the 6 N and 8 N forces?
   1. A) 60°
   2. B) 180°
   3. C) 120°
   4. D) 90°
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   Correct answer: D) 90°

   For three forces in equilibrium, any one force must be equal in magnitude and opposite in direction to the resultant of the other two: R² = F₁² + F₂² + 2F₁F₂ cos θ. Here, 10² = 6² + 8² + 2(6)(8) cos θ => 100 = 36 + 64 + 96 cos θ => 100 = 100 + 96 cos θ => 96 cos θ = 0 => cos θ = 0 => θ = 90°.

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   Step 1: Vector equilibrium: F₃² = F₁² + F₂² + 2F₁F₂ cos θ. Step 2: 100 = 36 + 64 + 96 cos θ => 96 cos θ = 0 => θ = 90°. Answer: 90°.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Systems of coplanar forces fit in the syllabus?

Year 2 · Term 2