Answer:
Fe= 2579.68 P
α= 24.8°
Explanation:
Look at the attached graphic
we take the forces acting on the x-y plane and applied at the origin of coordinates
FX = 1260 P , horizontal (-x)
FY = 1530 P , forming 45° with positive x axis
x-y components FY
FYx= - 1530*cos(45)° = - 1081.87 P
FYy= - 1530*sin(45)° = - 1081.87 P
Calculation of the components of net force (Fn)
Fnx= FX + FYx
Fnx= -1260 P -1081.87 P
Fnx= -2341.87 P
Fny=FYy
Fny= -1081.87 P
Calculation of the components of equilibrant force (Fe)
the x-y components of the equilibrant force are equal in magnitude but in the opposite direction to the net force components:
Fnx= -2341.87 P, then, Fex= +2341.87 P
Fny= -1081.87 P P, then, Fex= +1081.87 P
Magnitude of the equilibrant (Fe)
[tex]F_{n} = \sqrt{(F_{nx})^{2} +(F_{ny})^{2} }[/tex]
[tex]F_{e} =\sqrt{(2341.87)^{2}+(1081.87)^{2} }[/tex]
Fe= 2579.68 P
Calculation of the direction of equilibrant force (α)
[tex]\alpha =tan^{-1} (\frac{F_{ny} }{F_{nx} } )[/tex]
[tex]\alpha =tan^{-1} (\frac{1081.87 }{2341.87} )[/tex]
α= 24.8°
Look at the attached graphic
