Calculate rest mass given relative speed and kinetic energy?

[bai_mi]

The answer is 3.079*10^-26 kg

I tried doing E=mc^2
20*10^9*1.602*10^-19=m*(3*10^8)^2
m=3.56*10^-26 kg
However when I do E=γmc^2 I get the correct answer.

Is the question wrong, because isn't it 20 GeV of kinetic energy, not total energy?

 

[TSny]

Welcome to PF!

Which of the formulas E=mc² and E=(γ-1)mc² represents the kinetic energy?

 

[bai_mi]

Sorry I meant that when I use E=γmc^2 (total energy formula), I get the correct answer. E=(γ-1)mc^2 (kinetic energy formula) gives the wrong answer.
The question should be 20 GeV of total energy, right?

 

[TSny]

When I use E = (γ-1)mc² I get the answer that is given (3.079 x 10^-26 kg). If you are not getting this, then show more details of your calculation.

 

[bai_mi]

20*10^9*1.602*10^-19= ((1/(root(1-0.5^2)))-1) m*(3*10^8)^2
m=2.30*10^-25 kg

 

[TSny]

20*10^9*1.602*10^-19= ((1/(root(1-0.5^2)))-1) m*(3*10^8)^2

OK

m=2.30*10^-25 kg

I don't get this value. The mistake must be in the manipulations to solve for m.

 

[bai_mi]

What do you get with E=γmc^2 then?

 

[TSny]

Yikes. MY FAULT!

You are correct. E=γmc² produces the given answer. Very Sorry. I kept forgetting to subract the 1 in (γ-1). So, yes, it appears that they took the 20 GeV to be the total energy.