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