1. What is Resultant Force?

Definition: The resultant force is the single force that represents the vector sum of two or more forces acting at a point.

Purpose: This calculator determines the magnitude of the resultant force when two forces act at an angle to each other.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( F \) — Resultant force (Newtons)
• \( F_1 \) — First force (Newtons)
• \( F_2 \) — Second force (Newtons)
• \( \theta \) — Angle between the forces (degrees)

Explanation: This formula comes from the Law of Cosines applied to force vectors, accounting for both the magnitudes and directional relationship between the forces.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is fundamental in physics and engineering for analyzing structures, mechanical systems, and motion.

4. Using the Calculator

Tips: Enter both force magnitudes in Newtons and the angle between them in degrees (0-180°). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0° or 180°?
A: At 0° (parallel forces), F = F₁ + F₂. At 180° (opposite forces), F = |F₁ - F₂|.

Q2: What's the maximum possible resultant force?
A: The maximum occurs when θ = 0° (F₁ + F₂), and the minimum when θ = 180° (|F₁ - F₂|).

Q3: How is this different from vector addition?
A: This is the magnitude portion of vector addition - it gives the size but not direction of the resultant.

Q4: Can I use this for more than two forces?
A: No, this calculator is for two forces only. Multiple forces require sequential pairwise addition.

Q5: What if the forces are at right angles?
A: When θ = 90°, the formula simplifies to F = √(F₁² + F₂²) (Pythagorean theorem).