equation verification

[seto6]

so we have total energy of partical ->E

p=γp=1/(1-(v/c)2)-1/2

1)E=γpmc2=E0+K=Rest energy+ kinetic energy
=mc2+mv2/2
the second line correct?

2) E2-(pc)2=E0
so P= mv or p=γpmv

im sure that we are suppose to use p=γpmv but not sure some one verify pls

[mathman]

I can't quite understand 2).

However for 1), if you expand p in a power series in (v/c)2, the first two terms are what you are showing. The higher order terms matter when v/c -> 1.

[yuiop]

so we have total energy of partical ->E

p=γp=1/(1-(v/c)2)-1/2

1)E=γpmc2=E0+K=Rest energy+ kinetic energy
=mc2+mv2/2
the second line correct?

Nope, the second line is not correct. mv2 is the newtonian expression for kinetic energy (KE).
You can obtain the correct relativistic expression for KE from:

γ=(1-(v/c)[SUP]2)-1/2

E=γmc2=E0+KE = Rest energy+ kinetic energy

KE = E-E0 = γmc2-mc2 = mc2(γ-1)


2) E2-(pc)2=E0
so P= mv or p=γpmv

im sure that we are suppose to use p=γpmv so but not sure some one verify plsYou should be using p = γmv = mv(1-(v/c)2)-1/2 so that

E2-(pc)2=E02

E2=E02+(pc)2

E2=(mc2)2+(γmvc) 2