Resultant force

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

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

Correct answer:

F =  113.1225 kN
f =  65.613 °

Step-by-step explanation:

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

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Tips to related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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