Physics Expert

The formula for calculating the total energy of a particle in a relativistic system is given by: E = γmc² where E is the total energy of the particle, m is its rest mass, c is the speed of light, and γ (gamma) is the Lorentz factor, which is defined as: γ = 1 / √(1 - v²/c²) where v is the velocity of the particle. This formula differs from the classical formula for kinetic energy, which is given by: K = 1/2mv² where K is the kinetic energy of the particle, m is its mass, and v is its velocity. The main difference between these two formulas is that the relativistic formula takes into account the increase in mass of a moving object, as well as the fact that its kinetic energy can be converted into other forms of energy, such as rest mass energy or radiation. In the classical formula, the mass is assumed to be constant and the velocity is much less than the speed of light, so the kinetic energy is simply proportional to the square of the velocity. In contrast, the relativistic formula shows that as the velocity of a particle approaches the speed of light, its mass increases, and its kinetic energy can no longer be accurately described by the classical formula. Overall, the relativistic formula for total energy is more accurate and comprehensive than the classical formula for kinetic energy, especially at high speeds or in extreme environments.