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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)=3"x",F_(2)=5"x", R=28N and theta = 60^(0)`
`R=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)costheta)`
`rArr28=sqrt((3"x")^(2)+(5"x")^(2)+2(3"x")(5"x")cos60^(0))`
`rArr28=sqrt(9"x"^(2)+25"x"^(2)+15"x"^(2)) =7"x"rArr"x"=(28)/(7)=4`,
`:. F_(1)=3xx4=12N, F_(2)=5xx4=20N`.
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