Concurrent coplanar forces 10N, 15N, 20N, 25N are acting on a body at `0^(@),30^(@),45^(@),120^(@)` w.r.t the x-axis respectively. Calculate the magnitude and direction of their resultant.

Explanation

Give `F_1=10N,theta_1=0^(@),F_2=5,theta_2=30^(@)`
`F_3=20N,theta_3=45^(@),F_4=25N,theta_4=120^(@)`
`X=sigmax=F_1costheta_1+F_2costheta_2+F_3costheta_3+F_4costheta_4`
`=10cos0^(@)+15cos30^(@)+20cos45^(@)+25cos120^(@)`
`=10+15xx0.866+20xx0.707-25xx0.5`
`:.x=24.63N`
`sigma=Y=F_1sintheta_1+F_2sintheta_2+F_3sintheta_3+F_4sintheta_4`
`=10sin0^(@)+15sin30^(@)+20sin45^(@)+25sin120^(@)`
`=0+7.5+14.14+21.65`
`43.29N`
`:.` Magnitude of their resultant `=sqrt(X^2+Y^2)`
`R=sqrt(24.63^2+43.29^2)=sqrt(606.6+1874)" "R=49.8N`
Direction of R`=prop=tan^(-1)(Y/X)=tan^(-1)((43.29)/(24.63))`
`prop=tan^(-1)(1.7576)`
`:." "prop=60^(@)22`' w.r.t x-axis