Resultant Force Formula Calculator

Resultant Force Formula:

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

Resultant Force (F_r):

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1. What is the Resultant Force Formula?

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

Purpose: It helps in physics and engineering to determine the net effect of two forces acting at an angle.

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, N)
\( F1 \) — First force (N)
\( F2 \) — Second force (N)
\( \theta \) — Angle between the forces (degrees)

Explanation: The formula calculates the vector sum of two 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 values in Newtons (N) and the angle between them in degrees (0-180°). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What happens when θ = 180°?
A: When forces act in opposite directions, 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 apply the formula sequentially.

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