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torisob [31]
3 years ago
7

Two forces whose resultant is 100N are at right angle to eachother. if one of them makes an angle of 30° with the resultant, det

ermine its magnitude​
Physics
1 answer:
mihalych1998 [28]3 years ago
8 0

Let <em>F₁ </em>and <em>F₂</em> denote the two forces, and <em>R</em> the resultant force.

<em>F₁ </em>and <em>F₂</em> point perpendicularly to one another, so their dot product is

<em>F₁ </em>• <em>F₂</em> = 0

<em />

We're given that one of these vectors, say <em>F₁</em>, makes an angle with <em>R</em> of 30°, so that

<em>F₁</em> • <em>R</em> = ||<em>F₁</em>|| ||<em>R</em>|| cos(30°)

But we also have

<em>F₁</em> • <em>R</em> = <em>F₁ </em>• (<em>F₁ </em>+ <em>F₂</em>) = (<em>F₁ </em>• <em>F₁</em>) + (<em>F₁ </em>• <em>F₂</em>) = <em>F₁ </em>• <em>F₁ </em>=<em> </em>||<em>F₁</em>||²

So, knowing that ||<em>R</em>|| = 100 N, we get that

(100 N) ||<em>F₁</em>|| cos(30°) = ||<em>F₁</em>||²

(100 N) cos(30°) = ||<em>F₁</em>||

||<em>F₁</em>|| ≈ 86.6 N

(And the same would be true for <em>F₂</em>.)

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