Answer to Question #259872 in Analytic Geometry for Hamad

Question #259872

Two forces act a point The magnitude of the Two forces are F, 2 newton and the measure of the angle between them is 60, if their resultant equal 2√3 newton,then F =newton


1
Expert's answer
2021-11-02T14:12:19-0400

Given: Two forces as 2 N and F N, angle between them is "60\\degree"and their resultant is "2\\sqrt{3}" N.

We know that,

"R=\\sqrt{R_1^2+R_2^2+2R_1R_2\\cos\\theta}"

"\\Rightarrow 2\\sqrt{3}=\\sqrt{2^2+F^2+2\\times2\\times F\\cos 60\\degree}\n\\\\\\Rightarrow 2\\sqrt{3}=\\sqrt{4+F^2+2F} \\ [\\because \\cos 60\\degree=\\frac 1 2]\n\\\\\\Rightarrow 12=4+F^2+2F\n\\\\\\Rightarrow F^2+2F-8=0\n\\\\\\Rightarrow (F-2)(F+4)=0\n\\\\\\Rightarrow F=2,-4\n\\\\\\text{As the magnitude of force can't be negative }\n\\\\So, F=2N"


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