Resultant Forces
The resultant is a single force that has the same effect as all the original forces combined. Finding resultants is fundamental to statics.
Finding the Resultant
Resultant of Two Forces
Easy
Find the resultant of F1 = 80N at 0° and F2 = 60N at 90°.
1
Components
F1: Fx=80, Fy=0
F2: Fx=0, Fy=60
2
Sum components
Rx = 80 + 0 = 80 N
Ry = 0 + 60 = 60 N
3
Magnitude
R = √(80² + 60²) = √10000 = 100 N
4
Direction
θ = tan⁻¹(60/80) = 36.87°
Answer:
R = 100 N at 36.87°
Key Takeaways
Resultant = single equivalent force
Add component-wise: Rx = ΣFx, Ry = ΣFy
R = √(Rx² + Ry²), θ = tan⁻¹(Ry/Rx)