Understanding the Concepts
* Special Relativity: At speeds close to the speed of light, the principles of special relativity come into play. One of the key consequences is that the mass of an object increases as its speed approaches the speed of light.
* Rest Mass: The mass of a proton at rest is approximately 1.6726 × 10^-27 kg.
* Lorentz Factor (γ): This factor accounts for the relativistic increase in mass and is calculated as: γ = 1 / √(1 - (v²/c²)) where 'v' is the object's velocity and 'c' is the speed of light.
Calculation
1. Calculate the Lorentz Factor:
* v = 0.999c (99.9% of the speed of light)
* γ = 1 / √(1 - (0.999c)²/c²) ≈ 22.366
2. Calculate the Relativistic Mass:
* Relativistic mass (m) = γ * rest mass
* m = 22.366 * 1.6726 × 10^-27 kg ≈ 3.74 × 10^-26 kg
Conclusion
The mass of a proton traveling at 99.9% the speed of light is approximately 3.74 × 10^-26 kg. This is about 22 times greater than its rest mass due to the effects of special relativity.
