1. What is a Relativistic Velocity Calculator?

Definition: This calculator computes the velocity of an object based on its rest mass and relativistic mass according to special relativity.

Purpose: It helps physicists and students understand the relationship between mass and velocity at relativistic speeds approaching the speed of light.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( v \) — Relativistic velocity (m/s)
• \( c \) — Speed of light (299,792,458 m/s)
• \( m_0 \) — Rest mass (kg)
• \( m \) — Relativistic mass (kg)

Explanation: As an object's velocity approaches the speed of light, its mass increases. This formula calculates the velocity based on the mass increase.

3. Importance of Relativistic Calculations

Details: Understanding relativistic effects is crucial for particle physics, astrophysics, and any systems where objects move at significant fractions of light speed.

4. Using the Calculator

Tips: Enter the speed of light (default 299,792,458 m/s), rest mass, and relativistic mass. The relativistic mass must be greater than the rest mass.

5. Frequently Asked Questions (FAQ)

Q1: What happens when m approaches m₀?
A: The velocity approaches zero, meaning the object is at rest or moving slowly (non-relativistic).

Q2: What happens when m becomes much larger than m₀?
A: The velocity approaches the speed of light (c).

Q3: Can the velocity exceed the speed of light?
A: No, according to special relativity, the speed of light is the ultimate speed limit.

Q4: Where is this calculation important?
A: In particle accelerators, cosmic ray studies, and any high-energy physics applications.

Q5: Why does mass increase with velocity?
A: This is a fundamental consequence of special relativity - energy and mass are equivalent (E=mc²).