Formula For Calculating Resultant Force

Resultant Force Formula:

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

Resultant Force (F_r):

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1. What is Resultant Force?

Definition: The resultant force is the single force that represents the vector sum of two or more forces acting on an object.

Purpose: It helps in determining the net effect of multiple forces acting on an object at different angles.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the magnitude of the resultant force when two forces act at an angle to each other.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is essential in engineering, physics, and construction to understand how multiple forces will affect an object's motion or stability.

4. Using the Calculator

Tips: Enter the magnitudes of both forces in Newtons and the angle between them in degrees (0-180°).

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0° or 180°?
A: At 0° (forces in same direction), F_r = F1 + F2. At 180° (opposite directions), F_r = |F1 - F2|.

Q2: What's the unit of measurement?
A: The calculator uses Newtons (N), the SI unit of force. 1 N = 1 kg·m/s².

Q3: Can I use this for more than two forces?
A: No, this calculates the resultant of exactly two forces. For more forces, you'd need to combine them pairwise.

Q4: What if the angle is 90 degrees?
A: The formula simplifies to F_r = √(F1² + F2²) since cos(90°) = 0.

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