Resultant Of Two Forces Calculator

Resultant Force Formula:

\[ F_r = \sqrt{F1^2 + F2^2 - 2 \times F1 \times F2 \times \cos(180^\circ - \theta)} \]

Resultant Force (F_r):

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1. What is the Resultant of Two Forces?

The resultant of two forces is the single force that has the same effect as the two original forces acting together. It represents the vector sum of the two forces, taking into account both magnitude and direction.

2. How Does the Calculator Work?

The calculator uses the resultant force formula:

\[ F_r = \sqrt{F1^2 + F2^2 - 2 \times F1 \times F2 \times \cos(180^\circ - \theta)} \]

Where:

\( F1 \) — Magnitude of first force (N)
\( F2 \) — Magnitude of second force (N)
\( \theta \) — Angle between the two forces (degrees)
\( F_r \) — Resultant force magnitude (N)

Explanation: The formula calculates the magnitude of the resultant force using the law of cosines, accounting for the angle between the two original forces.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is essential in physics and engineering for analyzing systems with multiple forces, determining net effects, and designing structures that can withstand combined loads.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What happens when the angle is 0°?
A: When forces act in the same direction (θ = 0°), the resultant is simply the sum of the two forces (F1 + F2).

Q2: What happens when the angle is 180°?
A: When forces act in opposite directions (θ = 180°), the resultant is the difference between the two forces (|F1 - F2|).

Q3: What happens when the angle is 90°?
A: When forces are perpendicular (θ = 90°), the resultant is calculated using the Pythagorean theorem: √(F1² + F2²).

Q4: Can this calculator handle more than two forces?
A: No, this calculator is specifically designed for two forces. For multiple forces, you would need to calculate resultants step by step or use vector addition methods.

Q5: Does this calculator provide direction information?
A: No, this calculator only provides the magnitude of the resultant force. To determine direction, you would need additional vector analysis.