Two forces vec{F}_1 and vec{F}_2 are acting o | vedclass

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(A) Let the magnitude of the smaller force be $|\vec{F}_1| = F$.Then the magnitude of the larger force is $|\vec{F}_2| = 3F$.The resultant force $\vec

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Let the magnitude of the smaller force be $|\vec{F}_1| = F$.Then the magnitude of the larger force is $|\vec{F}_2| = 3F$.The resultant force $\vec{F}_R$ has a magnitude equal to the larger force,so $|\vec{F}_R| = 3F$.The formula for the resultant magnitude is $F_R^2 = F_1^2 + F_2^2 + 2F_1F_2 \cos 	heta$,where $	heta$ is the angle between the two forces.Substituting the values: $(3F)^2 = F^2 + (3F)^2 + 2(F)(3F) \cos 	heta$.$9F^2 = F^2 + 9F^2 + 6F^2 \cos 	heta$.$9F^2 = 10F^2 + 6F^2 \cos 	heta$.$-F^2 = 6F^2 \cos 	heta$.$\cos 	heta = -\frac{1}{6}$.Comparing this with $\cos 	heta = \frac{1}{n}$,we get $n = -6$.Therefore,$|n| = |-6| = 6$.

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