Kinetic energy transformation

• bernhard.rothenstein
In summary: Thanks. There is a poblem. K is a physical quantity for which we do not define a proper value whereas for E we do.I suggest that you will need to calculate K in each frame after transforming E. Kinetic energy is not a component of a 4-tensor, since it is just the additional energy imparted by motion. However, it can be writtenK=mc^2 [(1/sqrt(1-(v/c)^2))-1]Geometrically, the relativistic kinetic energy is difference between the projections of two 4-momenta-related-by-a-boost onto one of those 4-momenta.

bernhard.rothenstein

Please let me know a reference where the transformation of the kinetic energy is performed.
Thanks

Since the kinetic energy is the total energy minus the rest energy, and since the rest energy is invariant, won't any reference suffice that gives the transformation of total energy? That is, K = E - mc^2, m is invariant, and E transforms in the usual way.

kinetic energy

country boy said:
Since the kinetic energy is the total energy minus the rest energy, and since the rest energy is invariant, won't any reference suffice that gives the transformation of total energy? That is, K = E - mc^2, m is invariant, and E transforms in the usual way.
Thanks. There is a poblem. K is a physical quantity for which we do not define a proper value whereas for E we do.

If by "proper" you mean the value in an object's own rest frame, then the "proper kinetic energy" of any object is zero!

bernhard.rothenstein said:
Thanks. There is a poblem. K is a physical quantity for which we do not define a proper value whereas for E we do.

I suggest that you will need to calculate K in each frame after transforming E. Kinetic energy is not a component of a 4-tensor, since it is just the additional energy imparted by motion. However, it can be written

K = mc^2 [(1/sqrt(1-(v/c)^2))-1]

Geometrically, the relativistic kinetic energy is difference between the projections of two 4-momenta-related-by-a-boost onto one of those 4-momenta.

robphy said:
Geometrically, the relativistic kinetic energy is difference between the projections of two 4-momenta-related-by-a-boost onto one of those 4-momenta.
Thanks. For a less sophisticated audience I would present the problem as:
Start with the expression of the kinetic energy in I
K=mcc[(1/g(u))-1] (1)
where g(u) stands for gamma as a function of the speed of the bullet in I,
Express the right side of (1) as a function of u' the speed of the bullet in I' via the composition law of parallel speeds in order to obtain
K=mcc[(1+u'V/cc)/g(V)g(u'))-1] (2)
The transformation equation (2) leads to the following consequences
a. For u'=0
K=mcc[(1/g(V))-1)
b.For V=0 (u'=u)
K=mcc[(1/g(u))-1]
whereas for u'=0 and V=0
K=0
all in good accordance with phyhsical reality!
Is there some thing wrong in my derivation?
Use please soft words and hard arguments:rofl:

What is kinetic energy transformation?

Kinetic energy transformation refers to the process of converting one form of kinetic energy into another form. This can happen through various mechanisms such as transfer of energy, conversion into another type of energy, or dissipation into heat.

Why is understanding kinetic energy transformation important?

Understanding kinetic energy transformation is important for many reasons. It helps us understand how energy is transferred and utilized in different systems, such as in machines and natural phenomena. It also allows us to optimize energy use and efficiency in various processes.

What factors affect kinetic energy transformation?

The factors that affect kinetic energy transformation include the mass and velocity of the object, the type of transformation occurring, and the presence of external forces or resistance. In addition, the type of material the object is made of can also affect the transformation of kinetic energy.

How is kinetic energy transformed into other forms of energy?

Kinetic energy can be transformed into other forms of energy through various mechanisms, such as friction, impact, and conversion into potential energy. For example, when a moving object collides with another object, its kinetic energy is transformed into sound and heat energy.

Can kinetic energy transformation be reversed?

Yes, kinetic energy transformation can be reversed. This can happen through the process of energy conversion, where one type of energy is transformed into another, and then back into kinetic energy. However, there is always some loss of energy during transformation, as it cannot be completely converted without any loss.