1. What is the Relativistic Velocity Calculator?

Definition: This calculator computes the velocity of an object based on special relativity, using the relationship between rest mass and relativistic mass.

Purpose: It helps physicists, students, and enthusiasts understand how an object's velocity approaches the speed of light as its relativistic mass increases.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( v \) — Relativistic velocity (m/s)
• \( c \) — Speed of light in vacuum (3×10⁸ m/s)
• \( m_0 \) — Rest mass of the object (kg)
• \( m \) — Relativistic mass of the object (kg)

Explanation: As an object's velocity increases toward the speed of light, its relativistic mass increases according to special relativity.

3. Importance of Relativistic Calculations

Details: These calculations are fundamental in high-energy physics, particle accelerators, and understanding the behavior of objects at significant fractions of light speed.

4. Using the Calculator

Tips: Enter the speed of light (default 3×10⁸ m/s), rest mass, and relativistic mass (must be greater than rest mass). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why can't velocity exceed the speed of light?
A: According to special relativity, as velocity approaches c, the relativistic mass approaches infinity, requiring infinite energy to accelerate further.

Q2: What's the difference between rest mass and relativistic mass?
A: Rest mass is the mass measured when the object is at rest, while relativistic mass increases with velocity.

Q3: When is this calculation important?
A: For everyday objects at normal speeds, the difference is negligible. It becomes significant at velocities above about 10% of light speed.

Q4: What happens when m = m₀?
A: This means the object is at rest (v = 0) since there's no relativistic mass increase.

Q5: Can this be used for particles with zero rest mass?
A: No, particles like photons (with m₀ = 0) always travel at exactly c according to relativity.