Exploring Algebra 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

 

[sardar]

This is a very interesting exploration of algebra in the energy-momentum-mass relations. It is clear that you have a strong understanding of the concepts and equations involved. However, as your professor pointed out, there is something wrong with your final result. It is important to always check your work and make sure that your equations are consistent and accurate.

One possible issue with your calculation is that you have used the equation E=mc^2, which is only valid for objects at rest. In the context of the energy-momentum-mass relations, the mass (m0) refers to the rest mass, not the total mass. When an object is in motion, its total mass increases due to its kinetic energy, so the correct equation to use would be E=√(m0c^2)^2+(pc)^2.

Another potential problem is that you have equated kinetic energy (Ek) with the total energy (E). While this may be true in some cases, it is not always the case. It is important to clearly define your variables and make sure they are consistent throughout your calculations.

Overall, exploring algebra in energy-momentum-mass relations is a fascinating topic and can lead to important insights in the field of physics. Keep questioning and exploring, and always double-check your work for accuracy.