Question Video: Using the Triangle of Forces Rule to find the Magnitude of a Force Mathematics

Use the triangle force rule to Find the magnitude of force 𝐹 that is in equilibrium with two perpendicular forces of magnitudes 2 and 3 newtons.

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Video Transcript

Use the triangle force rule to find the magnitude of force 𝐹 that is in equilibrium with two perpendicular forces of magnitudes two and three newtons.

The triangle force rule states that when three coplanar forces acting at a point are in equilibrium, they can be represented in magnitude and direction by the adjacent sides of a triangle taken in order. In this question, we are told that we have two perpendicular forces of magnitudes two and three newtons. Let’s imagine they are drawn vertically and horizontally as shown. We are trying to find the magnitude of a third force 𝐹 that maintains equilibrium amongst these three forces. We can do this using the Pythagorean theorem, which states that 𝑎 squared plus 𝑏 squared is equal to 𝑐 squared, where 𝑐 is the length of the hypotenuse in any right triangle.

Substituting in our values, we have two squared plus three squared is equal to 𝐹 squared. Two squared is equal to four, and three squared is equal to nine. As the sum of these is 13, we have 𝐹 squared equals 13. We can then square root both sides of this equation. And since the magnitude must be positive, we have 𝐹 is equal to root 13. The magnitude of force 𝐹 is root 13 newtons.