Question Video: Finding a Missing Force Given Information About the Resultant Force Mathematics

The angle between forces vector 𝐅₁ and vector 𝐅₂ is 112Β°, and the measure of the angle between their resultant and vector 𝐅₂ is 56Β°. If the magnitude of vector 𝐅₁ is 28 N, what is the magnitude of vector 𝐅₂?

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Video Transcript

The angle between forces vector 𝐅 sub one and vector 𝐅 sub two is 112 degrees, and the measure of the angle between their resultant and vector 𝐅 sub two is 56 degrees. If the magnitude of vector 𝐅 sub one is 28 newtons, what is the magnitude of vector 𝐅 sub two?

Let’s begin by sketching a diagram to model the situation. We are told that the angle between two forces 𝐅 sub one and 𝐅 sub two is 112 degrees. We are also told that the measure of the angle between the resultant force and 𝐅 sub two is 56 degrees. We see that our two forces form a parallelogram, where the resultant is its diagonal. We can calculate the angle πœƒ between 𝐅 sub one and the resultant by subtracting 56 degrees from 112 degrees. This is equal to 56 degrees. We can now add this angle and its alternate interior angle in our diagram as shown.

Next, we can apply the law of sines to either one of our triangles within the parallelogram. We have the magnitude of 𝐅 sub one over sin of 56 degrees is equal to the magnitude of 𝐅 sub two over the sin of 56 degrees. This means that the magnitude of 𝐅 sub one is equal to the magnitude of 𝐅 sub two. And since we are told in the question that the magnitude of 𝐅 sub one is 28 newtons, then the magnitude of 𝐅 sub two must also be 28 newtons.

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