Forces as Vectors
Welcome to Statics!
The study of forces in equilibrium
Statics is the study of bodies at rest or moving with constant velocity. For that to happen, forces must be in equilibrium - they balance out.
Forces are vectors: they have both magnitude and direction. Understanding vector operations is essential for analyzing forces.
Force Vector
Vector Components
Resolving a Force
Easy
A 100 N force acts at 30° above the horizontal. Find its x and y components.
1
Find x-component
Fx = F cos(θ) = 100 cos(30°) = 100 × 0.866 = 86.6 N
2
Find y-component
Fy = F sin(θ) = 100 sin(30°) = 100 × 0.5 = 50 N
Answer:
Fx = 86.6 N, Fy = 50 N
Key Takeaways
Forces are vectors (magnitude + direction)
Resolve into components: Fx = F cos(θ), Fy = F sin(θ)
Add vectors by adding components