Resultant Force And Angle Calculator

Resultant Force Formulas:

\[ F_r = \sqrt{F1^2 + F2^2 + 2 F1 F2 \cos(\theta)} \] \[ \theta_r = \arctan\left(\frac{F2 \sin(\theta)}{F1 + F2 \cos(\theta)}\right) \]

Resultant Force (F_r):

Resultant Angle (θ_r):

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1. What is a Resultant Force And Angle Calculator?

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

Purpose: It helps engineers, physicists, and students analyze force systems and understand vector addition.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ F_r = \sqrt{F1^2 + F2^2 + 2 F1 F2 \cos(\theta)} \] \[ \theta_r = \arctan\left(\frac{F2 \sin(\theta)}{F1 + F2 \cos(\theta)}\right) \]

Where:

\( F_r \) — Resultant force magnitude (N)
\( F1 \) — First force magnitude (N)
\( F2 \) — Second force magnitude (N)
\( \theta \) — Angle between the two forces (degrees)
\( \theta_r \) — Angle of resultant force relative to F1 (degrees)

Explanation: The formulas come from the law of cosines and law of sines for vector addition.

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 the magnitudes of both forces (must be ≥ 0) and the angle between them (0° to 180°). The calculator will compute both the resultant force magnitude and its direction relative to F1.

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0° or 180°?
A: At 0° (parallel forces), Fr = F1 + F2. At 180° (opposite forces), Fr = |F1 - F2|.

Q2: What's the maximum possible resultant force?
A: The maximum occurs when θ = 0° (Fr = F1 + F2). The minimum occurs when θ = 180° (Fr = |F1 - F2|).

Q3: How is the resultant angle measured?
A: θr is measured relative to F1 in the direction toward F2.

Q4: What if one force is zero?
A: If F2 = 0, then Fr = F1 and θr = 0°.

Q5: 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 add them sequentially.