What Are the Algebraic Mysteries in Energy-Momentum-Mass Relations?

[Bazinga101]

<<Mentor note: Please always use descriptive thread titles.>>

First of all, the title is such that it attracts most views.You see, in class our professor did some goofing around numbers and variables in the relativistic energy momentum relation:
E²=(pc)²+m₀²c⁴
Since the energy required to accelerate an object to a certain velocity is
E=m₀c²/√1-v²/c²,
∴E²=m₀²c⁴/1-v²/c²
plug in the value of E²,
p²c²+m₀²c⁴=m₀²c⁴/1-v²/c²
cancel out the m₀²c⁴
so p²c²=1/1-v²/c²
since c²= E/m,
⇒Ep²/m=1/1-v²/c²\
But, p²/m = 2* K.E and since E in E=mc² implies any form of energy,and the object gains kinetic energy through it's motion, so E_k=E
⇒E(2E)=1/1-v²/c²
⇒2E²=1/1-v²/c²
⇒E²=1/2(1-v²/c²)
⇒E²=1/2-v²/c²
⇒E=1/√2-v²/c²
and that's it.No one in the room could figure out what's wrong, but our prof. said that something is wrong, but it is our job to find it out, plus, immediately one notices that if v=c, E=1 J. WTH!

 

[phinds]

This might actually be readable if you put in some parentheses.

 

[Bandersnatch]

p2c2+m02c4=m02c4/1-v2/c2
cancel out the m02c4
so p2c2=1/1-v2/c2

That's... an interesting piece of algebra you did there.

 

[Bazinga101]

That's... an interesting piece of algebra you did there.

Thanks Bandersnatch, i finally find out the mistake he did, and sorry for sounding stupid