Resultant Force Calculation Formula

Resultant Force Formula:

\[ F_r = \sqrt{F1^2 + F2^2 + 2 F1 F2 \cos(\theta)} \]

Resultant Force (Fr): N

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1. What is Resultant Force Calculation?

Definition: This calculator determines the magnitude of the resultant force when two forces act on an object at an angle.

Purpose: It helps engineers, physicists, and students understand the combined effect of two vector forces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_r = \sqrt{F1^2 + F2^2 + 2 F1 F2 \cos(\theta)} \]

Where:

\( F_r \) — Resultant force (Newtons)
\( F1 \) — First force (Newtons)
\( F2 \) — Second force (Newtons)
\( \theta \) — Angle between forces (degrees)

Explanation: The formula combines the vector components of both forces using the Law of Cosines.

3. Importance of Resultant Force Calculation

Details: Understanding resultant forces is crucial for structural analysis, mechanical design, and solving physics problems involving multiple forces.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: The forces act in the same direction, and Fr = F1 + F2 (maximum resultant).

Q2: What happens when θ = 90°?
A: The formula simplifies to Fr = √(F1² + F2²) (Pythagorean theorem).

Q3: What happens when θ = 180°?
A: The forces act in opposite directions, and Fr = |F1 - F2| (minimum resultant).

Q4: Can I use this for more than two forces?
A: No, this calculator is for two forces only. For multiple forces, you'd need to combine them pairwise.

Q5: Does this give the direction of the resultant?
A: No, this only calculates the magnitude. Direction requires additional calculations.