Relativistic Kinetic Energy Calculator
Calculate relativistic kinetic energy: KE = (gamma - 1) * m0 * c^2, which reduces to 0.5mv^2 at low speeds.
Relativistic KE
116,253,787,752,619,490.0000 J
Relativistic KE vs Rest Mass
Formula
## Relativistic Kinetic Energy At high speeds, the classical KE formula (0.5mv^2) underestimates the true kinetic energy. ### Formula **KE = (gamma - 1) * m0 * c^2** This approaches 0.5 m0 v^2 for v much less than c, and grows without bound as v approaches c.
Exemplo Resolvido
1 kg at 0.9c.
- 01gamma = 2.294
- 02KE = (2.294 - 1) * 1 * (2.998e8)^2
- 03KE = 1.294 * 8.988e16
- 04KE = 1.163e17 J
- 05Classical: 0.5 * 1 * (2.698e8)^2 = 3.640e16 J
- 06Relativistic is 3.2x larger
Perguntas Frequentes
Why does classical mechanics fail at high speeds?
Classical mechanics assumes that velocities simply add and that kinetic energy grows as v^2. Relativity shows that the correct energy formula involves the Lorentz factor, which diverges as v approaches c.
At what speed does the relativistic correction matter?
At 10% of c, the relativistic KE is about 0.75% higher than classical. Above 30% of c, the difference exceeds 5%.
What happens to a particle accelerated to 0.99c?
gamma = 7.09, so the relativistic KE is 6.09 times the rest energy (m0 c^2). The classical formula would give only 1/7 of this.
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