1. What is the Resultant Force Formula?

The resultant force formula calculates the magnitude of the combined effect of two forces acting at an angle. It's derived from the law of cosines and provides the single force that would produce the same effect as the two original forces.

2. How Does the Calculator Work?

The calculator uses the resultant force formula:

Where:

• \( R \) — Resultant force magnitude (newtons)
• \( A \) — Magnitude of first force (newtons)
• \( B \) — Magnitude of second force (newtons)
• \( \theta \) — Angle between the two forces (degrees)

Explanation: The formula calculates the vector sum of two forces using the cosine rule, accounting for both the magnitudes of the forces and the angle between them.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is essential in physics and engineering for determining net forces, analyzing structural stability, and predicting motion in mechanical systems.

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 numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: When forces act in the same direction (θ = 0°), cos(0) = 1, so R = A + B (maximum resultant).

Q2: What happens when θ = 90°?
A: When forces are perpendicular (θ = 90°), cos(90) = 0, so R = √(A² + B²) (Pythagorean theorem).

Q3: What happens when θ = 180°?
A: When forces act in opposite directions (θ = 180°), cos(180) = -1, so R = |A - B| (minimum resultant).

Q4: Can this formula be used for more than two forces?
A: For more than two forces, you need to resolve all forces into components and sum them vectorially.

Q5: What are typical applications of this calculation?
A: Used in structural engineering, mechanical design, physics problems, and any situation involving multiple force vectors.