Why Does the Kinetic Energy Equation Change at Speeds Close to the Speed of Light?

[julianwitkowski]

I'm curious as to the reasons why K_E = ½ m ⋅ v² only works at speeds much less than c?

Also, how does the equation change?

Thank you!

 

[ShayanJ]

This thread may help.

 

[julianwitkowski]

This thread may help.

Is it because you have to compensate for the increasing mass of the object which is proportional to the Lorentz factor, and then the integrals give you the the accurate change in mass over the entire distance with acceleration/deceleration and other factors compensated for?

 

[ShayanJ]

Is it because you have to compensate for the increasing mass of the object which is proportional to the Lorentz factor, and then the integrals give you the the accurate change in mass over the entire distance with acceleration/deceleration and other factors compensated for?

I prefer not to use relativistic mass at all and in fact its not needed. Physicists don't use it too. Its just that in both Newtonian and Relativistic mechanics, linear momentum and kinetic energy depend on the reference frame, but with different forms. In relativity we have $KE=(\gamma-1)mc^2$ and $\vec p=\gamma m \vec v$. By m, I mean rest mass and this is the only concept of mass I use.
These forms are dictated by consistency with special relativity and actually they can be derived. See e.g. this paper!

 

[PJC01]

The equation KE = ½ m ⋅ v2, where KE is kinetic energy, m is mass, and v is velocity, is derived from classical mechanics and is applicable for objects moving at speeds much less than the speed of light, c. This is because at such speeds, the effects of special relativity must be taken into account.

At speeds close to c, the mass of an object increases significantly according to the equation m = m0/√(1-(v2/c2)), where m0 is the rest mass and c is the speed of light. This means that the mass term in the equation for kinetic energy also changes, resulting in a different equation for KE. It becomes KE = (m0c2)/(√(1-(v2/c2)) - m0c2, where m0c2 is the rest energy of the object.

This change in the equation for KE at high speeds is necessary to accurately calculate the energy of an object moving at relativistic speeds. As an object approaches the speed of light, its kinetic energy also approaches infinity, making it impossible to reach the speed of light. This is due to the fact that an infinite amount of energy would be required to accelerate an object with mass to the speed of light.

In conclusion, the equation KE = ½ m ⋅ v2 only applies to objects moving at speeds much less than the speed of light. At high speeds, the equation must be modified to take into account the effects of special relativity. This is a fundamental concept in physics and is crucial for understanding the behavior of objects at extreme speeds.