The resultant of two forcews whose magnitudes are in the ratio 3:5 is 28N. If the angle of their inclination is 600, then find the mgnitude of each force.

The resultant of two forcews whose magnitudes are in the ratio 3:5 is

1.	The resultant of two forcews whose magnitudes are in the ratio 3:5 is 28N. If the angle of their inclination is 600, then find the mgnitude of each force.
Answer» Solution :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`.