1. What is the Resultant Force Formula?

Definition: This formula calculates 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 Formula Work?

The formula is derived from the law of cosines:

Where:

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

Explanation: The formula combines the magnitudes of both forces and accounts for their directional relationship through the cosine of the angle between them.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is essential for understanding equilibrium, designing structures, and analyzing motion in physics and engineering applications.

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° (forces in same direction)?
A: The resultant force is simply the sum of F1 and F2 (maximum possible resultant).

Q2: What happens when θ = 90° (perpendicular forces)?
A: The formula reduces to the Pythagorean theorem: \( F_r = \sqrt{F1^2 + F2^2} \).

Q3: What happens when θ = 180° (opposite forces)?
A: The resultant is the absolute difference between F1 and F2 (minimum possible resultant).

Q4: Can this be used for more than two forces?
A: No, this formula is specifically for two forces. For multiple forces, you would need to use vector addition methods.

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