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How do you calculate the speed of a particle given its Total and Kinetic energy? 
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#1
May2711, 10:34 PM

P: 19

Just curious on this method. I seemed to be getting caught up on the method here.
I'm given a K.E. amd Total Energy of a proton, and I was asked to find the speed. So what is the equations and steps for these. This is not a homework question, just me trying to wrap my head around the method and equation. Thanks 


#2
May2711, 10:58 PM

PF Gold
P: 7,120

Either quantity will tell you the speed. The total energy of a particle is:
[tex]E = \gamma mc^2[/tex] where [itex]\gamma = {{1}\over{\sqrt{1{{v^2}\over{c^2}}}}}[/itex] where 'c' is the speed of light so you can solve for the velocity using this formula. The kinetic energy for a particle is simply [itex]E=(\gamma  1)mc^2[/itex] so you can use that as well. 


#3
May2811, 07:39 AM

P: 346

I think you can just solve the mass of the object using E=mc^2, where m is what the mass is at the time but not the rest mass, and you can use E=1/2mv^2. I don't think that rest mass is useful in this case, because in kinetic energy you are not using the rest mass.



#4
May2811, 08:15 AM

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PF Gold
P: 5,027

How do you calculate the speed of a particle given its Total and Kinetic energy?



#5
May2811, 08:20 AM

P: 346




#6
May2811, 08:55 AM

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PF Gold
P: 5,027




#7
May2811, 09:01 AM

P: 346




#8
May2811, 09:07 AM

P: 346

So what is the relativistic kinetic. But does the equation for work still hold? I mean if W=Fx holds, then should W=Fx be added with γ factor?



#9
May2811, 09:11 AM

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PF Gold
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#10
May2811, 09:14 AM

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PF Gold
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#11
May2811, 10:08 AM

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PF Gold
P: 5,027

KE= mc^2 (1  1/gamma) where m is relativistic mass. You won't find this in a book, because no one uses it. 


#12
May2811, 10:14 AM

P: 346




#13
May2811, 08:08 PM

Sci Advisor
PF Gold
P: 5,027

Going from my last formula, given total and kinetic energy you can get speed, not knowing anything else. Solve for v:
1/gamma = 1  KE/E 


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