1. What is 3D Force Equilibrium?

3D force equilibrium refers to the state where the sum of all forces acting on an object in all three dimensions (x, y, and z) equals zero. This principle is fundamental in statics and structural analysis.

2. How Does the Calculator Work?

The calculator uses the force equilibrium equations:

Where:

• \( F_x \) — Force component in x-direction (Newtons)
• \( F_y \) — Force component in y-direction (Newtons)
• \( F_z \) — Force component in z-direction (Newtons)

Explanation: The calculator determines the resultant force magnitude and its direction angles relative to each coordinate axis.

3. Importance of Force Equilibrium

Details: Understanding force equilibrium is crucial for analyzing structures, designing mechanical systems, and ensuring stability in engineering applications.

4. Using the Calculator

Tips: Enter force components in Newtons for each coordinate direction. The calculator will compute the resultant force magnitude and its direction angles.

5. Frequently Asked Questions (FAQ)

Q1: What is force equilibrium?
A: Force equilibrium occurs when the vector sum of all forces acting on an object equals zero, resulting in no acceleration.

Q2: How are direction angles calculated?
A: Direction angles are calculated using the cosine of the angle between the force component and the resultant force vector.

Q3: Can this calculator handle negative force values?
A: Yes, negative values indicate forces acting in the negative direction of the coordinate axis.

Q4: What units should I use?
A: The calculator uses Newtons (N) for force inputs and degrees (°) for angle outputs.

Q5: What if the resultant force is zero?
A: If all force components are zero, the resultant will be zero, and direction angles will be undefined.