Resultant force

Calculate mathematically and graphically the resultant of a three forces with a common centre if:

F1 = 50 kN α1 = 30°
F2 = 40 kN α2 = 45°
F3 = 40 kN α3 = 25°

Correct result:

F =  113.1225 kN
f =  65.613 °

Solution:

F1=50 kN F2=40 kN F3=40 kN a1=30 a2=a1+45=30+45=75 a3=a2+25=75+25=100 x=F1 cosa1+F2 cosa2+F3 cosa3=F1 cos30 +F2 cos75 +F3 cos100 =50 cos30 +40 cos75 +40 cos100 =50 0.866025+40 0.258819+40 (0.173648)=46.7081 y=F1 sina1+F2 sina2+F3 sina3=F1 sin30 +F2 sin75 +F3 sin100 =50 sin30 +40 sin75 +40 sin100 =50 0.5+40 0.965926+40 0.984808=103.02934  F=x2+y2=46.70812+103.02932=113.1225 kN
f=180πarctan(y/x)=180πarctan(103.0293/46.7081)=65.613=653647"



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For Basic calculations in analytic geometry is a helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Our vector sum calculator can add two vectors given by its magnitudes and by included angle.
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See also our trigonometric triangle calculator.

 
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