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Two forces whose magnitudes are in the r...

Two forces whose magnitudes are in the ratio `3:5` give a resultant of 28N. If the angle of their inclination is `60^@`, find the magnitude of each force.

Text Solution

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Let `F_(1) and F_(2)` be the two forces.
Then `F_(1)=3x:F_(2)=5x: R=28 N and theta=60^(@)`
`R= sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2) cos theta)`
`rArr 28= sqrt((3x)^(2)=(5x)^(2)+2(3x)(5x) cos 60^(@))`
`rArr 28=(9x^(2)+25x^(2)+15x^(2))=7x rArr x=(28)/(7) =4`
`:.F_(1)=3=12 N, F_(2)=5xx4=20 N.`
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