The resultant of two forces,one double the ot | vedclass

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(B) Let the two forces be $F$ and $2F$. Let the angle between them be $	heta$.Let the resultant $R$ be perpendicular to the smaller force $F$. The an

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$120$

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(B) Let the two forces be $F$ and $2F$. Let the angle between them be $	heta$.Let the resultant $R$ be perpendicular to the smaller force $F$. The angle $\alpha$ between the resultant $R$ and the force $F$ is $90^\circ$.The formula for the direction of the resultant is $	an \alpha = \frac{2F \sin 	heta}{F + 2F \cos 	heta}$.Since $\alpha = 90^\circ$,$	an 90^\circ = \infty$,which implies the denominator must be zero:$F + 2F \cos 	heta = 0$$F(1 + 2 \cos 	heta) = 0$$1 + 2 \cos 	heta = 0$$\cos 	heta = -\frac{1}{2}$$	heta = 120^\circ$.

The resultant of two forces,one double the other in magnitude,is perpendicular to the smaller of the two forces. The angle between the two forces is ........ $^o$

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