Two Forces 3n And 2n Are At An Angle Theta

Resultant Force Formula:

\[ F_r = \sqrt{9 + 4 + 12 \cos(\theta)} \]

Resultant Force F_r (N):

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1. What is the Resultant Force Calculator?

Definition: This calculator computes the magnitude of the resultant force when two forces (3N and 2N) act at an angle θ to each other.

Purpose: It helps physics students and engineers determine the combined effect of two vector forces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_r = \sqrt{9 + 4 + 12 \cos(\theta)} \]

Where:

\( F_r \) — Resultant force magnitude (Newtons)
\( \theta \) — Angle between the two forces (degrees)

Explanation: This formula comes from the law of cosines applied to vector addition, where 3N and 2N are the magnitudes of the two forces.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is fundamental in physics and engineering for understanding how multiple forces interact in a system.

4. Using the Calculator

Tips: Enter the angle between the forces in degrees (0° to 180°). The calculator will compute the resultant force magnitude.

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: The forces act in the same direction, so F_r = 3N + 2N = 5N (maximum resultant).

Q2: What happens when θ = 90°?
A: The forces are perpendicular, so F_r = √(3² + 2²) = √13 ≈ 3.606N.

Q3: What happens when θ = 180°?
A: The forces act in opposite directions, so F_r = 3N - 2N = 1N (minimum resultant).

Q4: Can I use this for forces other than 3N and 2N?
A: No, this calculator is specifically for 3N and 2N forces. For other magnitudes, the formula would need adjustment.

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