Resultant Force Calculation Worksheet

Resultant Force Formula:

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

Resultant Force (F_r):

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1. What is a Resultant Force Calculator?

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

Purpose: It helps engineers, physicists, and students solve problems in statics and dynamics involving vector addition.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This is derived from the Law of Cosines in vector mathematics, accounting for both the magnitudes of the forces and the angle between them.

3. Importance of Resultant Force Calculation

Details: Calculating resultant forces is fundamental in structural analysis, mechanical design, and understanding force systems in physics.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: The forces act in the same direction, and F_r = F1 + F2 (maximum resultant).

Q2: What happens when θ = 90°?
A: The formula simplifies to F_r = √(F1² + F2²) (Pythagorean theorem).

Q3: What happens when θ = 180°?
A: The forces act in opposite directions, and F_r = |F1 - F2| (minimum resultant).

Q4: Can this be used for more than two forces?
A: No, this calculator is for two forces only. For multiple forces, you'd need to combine them pairwise.

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