Statics — Forces & Equilibrium

Forces have direction — resolve them into components

ELI5: a force pulling at an angle does some of its work sideways and some upward. Split it into a horizontal part F·cos θ and a vertical part F·sin θ, handle each axis on its own, and recombine at the end. That split is the move you make in every statics problem.

F_{pull} := 200 N

= 200 N a rope tension

\theta := 30 deg

= 30 deg angle above horizontal

Fx = F_{pull} \cdot \mathrm{cos}\left(\theta\right)

= 173.21 N horizontal component ≈ 173 N

Fy = F_{pull} \cdot \mathrm{sin}\left(\theta\right)

= 100 N vertical component = 100 N

✓ pass

abs(sqrt(Fx^2 + Fy^2) - F_{pull}) < 1e-6 N

the components recombine to the original force

Real-world hook: this is how a crane operator knows how much of a cable's pull actually lifts the load versus drags it sideways — and why a shallow sling angle is dangerous.

10 / sin(x)

cable tension (kN) to hold a 10 kN load at angle x (radians) — it explodes as the cable goes flat