- #1

- 2

- 0

**<<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:

E

^{2}=(pc)

^{2}+m

_{0}

^{2}c

^{4}

Since the energy required to accelerate an object to a certain velocity is

E=m

_{0}c

^{2}/√1-v

^{2}/c

^{2},

∴E

^{2}=m

_{0}

^{2}c

^{4}/1-v

^{2}/c

^{2}

plug in the value of E

^{2},

p

^{2}c

^{2}+m

_{0}

^{2}c

^{4}=m

_{0}

^{2}c

^{4}/1-v

^{2}/c

^{2}

cancel out the m

_{0}

^{2}c

^{4}

so p

^{2}c

^{2}=1/1-v

^{2}/c

^{2}

since c

^{2}= E/m,

⇒Ep

^{2}/m=1/1-v

^{2}/c

^{2}\

But, p

^{2}/m = 2* K.E and since E in E=mc

^{2}implies any form of energy,and the object gains kinetic energy through it's motion, so E

_{k}=E

⇒E(2E)=1/1-v

^{2}/c

^{2}

⇒2E

^{2}=1/1-v

^{2}/c

^{2}

⇒E

^{2}=1/2(1-v

^{2}/c

^{2})

⇒E

^{2}=1/2-v

^{2}/c

^{2}

⇒E=1/√2-v

^{2}/c

^{2}

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!

Last edited by a moderator: