Calculate rest mass given relative speed and kinetic energy?

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Homework Help Overview

The discussion revolves around calculating the rest mass of a particle given its kinetic energy and relative speed, specifically in the context of relativistic physics. Participants are examining the application of different energy equations, including the total energy and kinetic energy formulas.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of the equations E=mc² and E=(γ-1)mc² to determine the rest mass from kinetic energy. There is debate over whether the given energy should be interpreted as total energy or kinetic energy, with some questioning the correctness of the problem setup.

Discussion Status

The discussion is active, with participants providing calculations and seeking clarification on the correct application of formulas. Some have acknowledged errors in their reasoning, while others are attempting to reconcile different interpretations of the energy values involved.

Contextual Notes

There is a noted confusion regarding whether the energy provided (20 GeV) refers to total energy or kinetic energy, which affects the calculations and interpretations of the problem.

bai_mi
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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?
 
Last edited:
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Welcome to PF!

Which of the formulas E=mc2 and E=(γ-1)mc2 represents the kinetic energy?
 
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?
 
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.
 
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
 
bai_mi said:
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.
 
What do you get with E=γmc^2 then?
 
Yikes. MY FAULT! o:)

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.
 

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