What is the angle between two forces of equal magnitude, $F_{a}$ $F_a$ and $F_{b}$ $F_b$ , when the magnitude of their resultant is also equal to the magnitude of either of these forces?

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What is the angle between two forces of equal magnitude, $F_{a}$ $F_a$ and $F_{b}$ $F_b$ , when the magnitude of their resultant is also equal to the magnitude of either of these forces?

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Answer 1 · 2016-07-28T13:13:20

$θ = \frac{2 π}{3}$ $theta=(2pi)/3$

Explanation:

Let the angle between $F_{a} and F_{b}$ $F_a and F_b$ be $θ$ $theta$ and their resultant is $F_{r}$ $F_r$ So

$F_{r}^{2} = F_{a}^{2} + F_{b}^{2} + 2 F_{a} F_{b} cos θ$ $F_r^2=F_a^2+F_b^2+2F_aF_bcostheta$
Now by the given condition
let $F_{a} = F_{b} = F_{r} = F$ $F_a=F_b=F_r=F$

So

$F^{2} = F^{2} + F^{2} + 2 F^{2} cos θ$ $F^2=F^2+F^2+2F^2costheta$

$\Rightarrow cos θ = - \frac{1}{2} = cos (2 \frac{π}{3})$ $=>costheta=-1/2=cos(2pi/3)$

$:.theta=(2pi)/3$

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What is the angle between two forces of equal magnitude, $F_{a}$ $F_a$ and $F_{b}$ $F_b$ , when the magnitude of their resultant is also equal to the magnitude of either of these forces?

1 Answer

Explanation:

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