Why Does the Standard Kinetic Energy Formula Fail at High Velocities?

[finchie_88]

Why is it that even if you include a mass correction factor in 0.5mv^2, you get the wrong answer when v is very high? Thanks in advance.

 

[mathman]

Total kinetic energy is mc²-m₀c². When you expand the Lorentz factor, the classical k.e. is just the first term.

 

[Entropia]

The kinetic energy of an object is the energy that it possesses due to its motion. It is calculated by the formula 0.5mv^2, where m is the mass of the object and v is its velocity.

When the velocity of an object is very high, the kinetic energy also becomes very high. This is because the formula takes into account both the mass and the velocity of the object. However, when the velocity is extremely high, the mass correction factor of 0.5mv^2 may not be enough to accurately calculate the kinetic energy.

This is because at high velocities, the effects of relativity and the theory of special relativity come into play. These theories state that as an object approaches the speed of light, its mass increases and the concept of time slows down. Therefore, the mass correction factor in the kinetic energy formula may not accurately reflect the true mass of the object at such high velocities.

In order to calculate the kinetic energy of an object accurately at high velocities, we need to use the relativistic formula for kinetic energy, which takes into account these effects of relativity. This formula is 1/(sqrt(1-v^2/c^2)) * mc^2, where c is the speed of light.

In conclusion, at very high velocities, the mass correction factor in the kinetic energy formula may not give the correct answer due to the effects of relativity. To accurately calculate the kinetic energy, we need to use the relativistic formula that takes into account these effects.