Question

Two force vectors are oriented such that the angle between their directions is 46 degrees and they have the same magnitude. If their magnitudes are 2.81 newtons, then what is the magnitude of their sum

Answer 1

F = 5.17 N

Step-by-step explanation:

• If we know the magnitudes of both vectors, and the angle between them, we can find the magnitude of their sum, applying the cosine theorem, as follows:

`F =\sqrt{F_(1) ^(2) +F_(2) ^(2) + 2*F_(1) * F_(2) * cos \theta} (1)`

• Replacing by the givens, F₁ = F₂ = 2.81 N, θ = 46º, we get:

`F =\sqrt{2.81 N ^(2) +2.81 N ^(2) + 2*2.81N* 2.81N* cos 46} = 5.17 N (2)`