Relativistic Energy Visualisation
The well known formula
are catheters in a triangle.
By recognizing that
it is plain to see that as the velocity (v) approaches c, the alpha angle approaches vertical and thus
which indeed equals E.
Calculating alpha may be done by
Now we can do some parameter eliminations like
simplifying this expression we get
and finally we get
where it is quite easy to calculate pc with regard to number of rest energies, knowing only rest mass and velocity.
Visualisation of relativistic kinetic energy
Using vectors we may write total energy as
which gives the magnitude of E as
and while using
we may write
Ek is then
where n<1 thus
where m_k0<m_0 and m_k<m
The length of the E_0 vector is
this means that
where it is obvious that E_0 has less energy than the total energy, E.
The rather fascinating consequence of this is that Ek seams to have a "rest energy" of less than the actual rest energy, looking at pc the same happens here where it comes to the mass, this must happen because kinetic energy is calculateted by subtracting rest energy from E and the only way this can be done is by keeping the E-vector direction (but reversed) so that the pc-mass has the same proportion as the rest mass, otherwise substraction is impossible.
- Physics Part II, Intitution of Physics, Chalmers University of Technology, Max Fagerstroem, Bengt Sebler, Sven Larsson, 1985