* Relativistic Mass: In Einstein's theory of special relativity, the mass of an object increases as its speed approaches the speed of light. This increase is due to the object's increased energy. The formula for relativistic mass is:
```
m = m₀ / √(1 - v²/c²)
```
* m = relativistic mass
* m₀ = rest mass (mass at rest)
* v = speed of the object
* c = speed of light
* The Problem with "Relativistic Mass": While the formula above is valid, the concept of "relativistic mass" has fallen out of favor in modern physics. It's more accurate to say that the object's energy increases as its speed approaches the speed of light, and this energy contributes to its inertia (resistance to change in motion).
* Calculating Speed for Double the Mass: To find the speed at which an electron's mass *appears* to double, we can set up the following equation:
```
2m₀ = m₀ / √(1 - v²/c²)
```
Solving for 'v' (speed):
1. 2 = 1 / √(1 - v²/c²)
2. √(1 - v²/c²) = 1/2
3. 1 - v²/c² = 1/4
4. v²/c² = 3/4
5. v² = (3/4)c²
6. v = √(3/4)c ≈ 0.866c
Therefore, the speed at which the electron's relativistic mass would appear to double is approximately 86.6% of the speed of light.
Important Note: While this calculation demonstrates the concept of relativistic mass, remember that modern physics emphasizes the energy-momentum relationship, and not the concept of "relativistic mass" as a separate quantity.
