1. What is Relativistic Kinetic Energy?

Definition: The kinetic energy of an object moving at a significant fraction of the speed of light, accounting for special relativity effects.

Purpose: This calculator helps physicists and students determine the kinetic energy of objects moving at relativistic speeds.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( E_k \) — Kinetic energy (Joules)
• \( γ \) — Lorentz factor (dimensionless)
• \( m_0 \) — Rest mass (kilograms)
• \( c \) — Speed of light (meters/second)

Explanation: The formula accounts for the increase in relativistic mass and energy as velocity approaches the speed of light.

3. Importance of Relativistic Calculations

Details: At velocities approaching the speed of light, classical Newtonian mechanics becomes inaccurate, requiring special relativity corrections.

4. Using the Calculator

Tips: Enter the Lorentz factor (≥1), rest mass in kg, and speed of light (default 3×10⁸ m/s). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Lorentz factor?
A: \( γ = 1/\sqrt{1-(v^2/c^2)} \), where v is the object's velocity. It approaches infinity as v approaches c.

Q2: When do I need relativistic calculations?
A: When velocities exceed about 10% of light speed (30,000 km/s).

Q3: How does this differ from classical KE?
A: Classical KE = ½mv². The relativistic formula reduces to this at low velocities.

Q4: What are typical rest masses?
A: Electron: 9.11×10⁻³¹ kg, Proton: 1.67×10⁻²⁷ kg.

Q5: Can anything reach light speed?
A: Objects with mass would require infinite energy to reach c.