An object is in equilibrium under four concurrent forces in the direction shown in figure. Find the magnitudes of `F_(1)` and `F_(2)`

Explanation

The object is in equilibrium. Hence,
(i) `sumF_(x) =0`
:. `8+4 cos 60^(@)-F_(2) cos 30^(@) = 0`
or `8+2-F_(2) sqrt(3)/(2)=0`
or `F_(2) =(20)/sqrt(3)N`
(ii) `sumF_(Y) = 0`
:. `F_(1) + 4 sin 60^(@) - F_(2) sin 30^(@) = 0`
or `F_(1) + 4sqrt(3)/(2) - (F_(2))/(2) = 0`
or `F_(1) = (F_(2))/(2) - 2sqrt3 = (10)/(sqrt(3)-2sqrt3`
or `F_(1) = (4)/sqrt(3)N`