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
f=180πarctan(y/x)=180πarctan(103.0293/46.7081)=65.613=653647"



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