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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

Verified by Experts

Let`F_(1)"and " F_(2)` be the two forces.
Then `F_(1)=3x, F_(2)=5x, R=28N"and"theta= 60^(0)`
`R=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos theta)`
`rArr28=sqrt((3x)^(2)+(5x)^(2)+2(3x)(5x)cos60^(@))`
`rArr 28=sqrt(9x^(2)+25x^(2)+15x^(2))=7x`
`rArrx=(28)/7=4, :. F_(1)=3xx4=12N,F_(2)=5xx4=20N`.
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