# Algebra in energy-momentum-mass relations

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 Ek=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!

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phinds
Gold Member
2021 Award
This might actually be readable if you put in some parentheses.

Bandersnatch