- #1
Kunhee
- 51
- 2
Homework Statement
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By expanding Krel / Kcl in powers of (v/c)^2, estimate the value of v/c for which Krel differs from Kcl by 10%.
Homework Equations
Kcl = classical Kinetic Energy = 1/2 m0 v^2
Krel = relative Kinetic Energy = (y-1) (m0 c)^2
The Attempt at a Solution
I did a binomial expansion wherein x = (v/c)^2 and n = -1/2
The result is...
[1 - (v/c)^2]^(-1/2) = 1 + 1/2(v/c)^2
so If I plug this value into the Lorentz factor of Krel,
I can equate K rel to the Kcl equation.
But at which step of this expansion can I apply the 10% difference?
Do I need to set up an equation wherein Krel = 11/10 (Kcl)?
Thanks!