Answer to Question #86595 in Mechanics | Relativity for Lawrence

Question #86595
The resistance of two forces which are of 130N and 90N is 150N. Calculate the angle between the two forces
1
Expert's answer
2019-03-19T12:19:02-0400


Using the cosine rule,


F1F22=F12+F222F1F2cosθ|{\bf F_1}-{\bf F_2}|^2=F_1^2+F_2^2-2F_1F_2\cos \theta

we obtain

cosθ=F12+F22F1F222F1F2\cos \theta=\frac{F_1^2+F_2^2-|{\bf F_1}-{\bf F_2}|^2}{2F_1F_2}

cosθ=1302+90215022×130×90=0.1068\cos \theta=\frac{130^2+90^2-150^2}{2\times130\times90}=0.1068

θ=84\theta=84^{\circ}


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