Question

Compare and contrast the relativistic and classical expressions for the kinetic energy of an object.

How does the relativistic expression explain the impossibility of an object to reach the speed of light?

Answer 1

The relativistic kinetic energy is given by the total energy minus the rest mass energy of the object, it is given by,

The classical expression for kinetic energy is,

From the above expressions we can see that, for the case of relativistic kinetic energy the Kinetic energy increases at a much faster rate as compared to the classical kinetic energy, this is due to 1/square root term, which makes the increase much faster as it approaches the speed of light. This increase is also due to the fact that the mass of the object increases as speed increases.

From the above expression of relativistic Kinetic energy, we can say that if the velocity of the particle is greater than or equal to the speed of light, then the denominator becomes 0 or imaginary. Therefore the kinetic energy will go to infinity when the denominator is 0, which is not possible. Therefore, the object can never reach the speed of light.