Visual Net Force Resultant & Static Equilibrium Equilibrant Solver
By Newton's Second Law, concurrent forces $\vec{F}_1, \vec{F}_2$ acting on a body equivalate to a single resultant force $\vec{F}_{net} = (\sum F_x, \sum F_y)$; static equilibrium ($\sum \vec{F} = 0$) requires a third equilibrant force $\vec{F}_{eq} = -\vec{F}_{net}$ at $\theta_{net} + 180^\circ$.
|F_net| = √[(∑F_x)² + (∑F_y)²], θ_eq = θ_net + 180°Inputs & Parameters (4)
20-Row Comparison Table
| # | Force F₁ Magnitude (N) | Resultant Magnitude |R⃗| | Dot Product | Direction θ_R |
|---|---|---|---|---|
| 01 | 1 N | 19.765 N | -5.18 | 137.2° |
| 02 | 4 N | 19.354 N | -20.71 | 128.5° |
| 03 | 6 N | 19.336 N | -31.06 | 122.6° |
| 04 | 9 N | 19.693 N | -46.59 | 113.8° |
| 05 | 11 N | 20.177 N | -56.94 | 108.2° |
| 06 | 14 N | 21.238 N | -72.47 | 100.5° |
| 07 | 16 N | 22.144 N | -82.82 | 95.7° |
| 08 | 19 N | 23.755 N | -98.35 | 89.4° |
| 09 | 22 N | 25.617 N | -113.88 | 83.9° |
| 10 | 24 N | 26.973 N | -124.23 | 80.7° |
| 11 | 27 N | 29.146 N | -139.76 | 76.5° |
| 12 | 29 N | 30.672 N | -150.12 | 74° |
| 13 | 32 N | 33.056 N | -165.64 | 70.8° |
| 14 | 35 N | 35.534 N | -181.17 | 67.9° |
| 15 | 37 N | 37.228 N | -191.53 | 66.3° |
| 16 | 40 N | 39.823 N | -207.06 | 64° |
| 17 | 42 N | 41.583 N | -217.41 | 62.7° |
| 18 | 45 N | 44.262 N | -232.94 | 60.9° |
| 19 | 47 N | 46.07 N | -243.29 | 59.8° |
| 20 | 50 N | 48.809 N | -258.82 | 58.3° |
Key Analytical Takeaways
- 01Never add force magnitudes directly unless their angles are identical—always resolve into $F_x = F\cos\theta$ and $F_y = F\sin\theta$ first.
- 02Triangle inequality bounds the net force between $||F_1| - |F_2|| \le |F_{net}| \le |F_1| + |F_2|$.
- 03The equilibrant force has the exact same magnitude as $\vec{F}_{net}$ but points $180^\circ$ opposite.
Frequently Asked Questions
What is the difference between a resultant force and an equilibrant force?+
The resultant force is the single force that produces the same net acceleration as all applied forces combined. The equilibrant force is equal in magnitude and opposite in direction (−F_net), canceling the resultant to keep the object at rest.
When do two equal forces produce a resultant equal to each individual force?+
When two equal forces F are separated by 120°, their resultant has magnitude 2F·cos(60°) = F.
How does an equilibrant force differ from the resultant force?+
The resultant vector represents the single net force equivalent to all applied forces combined, whereas the equilibrant has the exact same magnitude pointed 180° opposite to bring ∑F⃗ = 0.