Massive particles are relativistic particles if their speed....

[amyy]

Homework Statement

Massive particles are relativistic when their kinetic energy is comparable to or greater than the energy

corresponding to their rest mass. (This condition implies that their speed is close to the speed of light.)
But what does the comparable mean? Is it that the particle whose speed is more than 0.1c must take the relativistic effect into account?

Homework Equations

The Attempt at a Solution

Thank you!

 

[Ray Vickson]

Homework Statement

Massive particles are relativistic when their kinetic energy is comparable to or greater than the energy

corresponding to their rest mass. (This condition implies that their speed is close to the speed of light.)
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Says who?
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But what does the comparable mean? Is it that the particle whose speed is more than 0.1c must take the relativistic effect into account?

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Depends on accuracy. If all you want are, say, 1 significant figure, relativistic effects at speeds of 0.1 c won't affect the answer. However, if you want to keep more accuracy, relativistic effects, even at speeds around 0.1 c, can alter the answer. Certainly, if you work with 5 or 6 significant figures the relativistic effects will matter.

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Homework Equations

The Attempt at a Solution

Thank you!

 

[amyy]

Hi, Ray Vickson, thank you very much for your reply!

Massive particles are relativistic when their kinetic energy is comparable to or greater than the energy

corresponding to their rest mass. (This condition implies that their speed is close to the speed of light.)

This is from the Wikipedia https://en.wikipedia.org/wiki/Relativistic_particle

You said it depends on accuracy, could you give me an example please? If the ³⁶Ar¹⁸⁺ is accelerated up to some certain speed, we will consider relativistic momentum when we calculate the magnetic rigidity:$B\rho=p/q=mv\gamma/q.$

 

[Physics-Tutor]

HI Amy, Ray is correct. All depends on the error you are willing to consider

It might be relevant to neglect the Rel. effect or not depending on what you are trying to achieve.

For example, you can calculate the fraction of the speed of light for which you have to take into account relativistic effects, given a certain experimental framework.

You can set the threshold of difference you need. Say, I consider 1% as being the threshold above which I will consider relativistic effects for KE. I can calculate

by solving this:

With

and

and

(where m is the rest mass).

The value you find for

, allows you for instance to determine from what speed you need to be considering relativistic effects based on the threshold you chose from the error in your experimental data.

 

[amyy]

HI Amy, Ray is correct. All depends on the error you are willing to consider

It might be relevant to neglect the Rel. effect or not depending on what you are trying to achieve.

For example, you can calculate the fraction of the speed of light for which you have to take into account relativistic effects, given a certain experimental framework.

You can set the threshold of difference you need. Say, I consider 1% as being the threshold above which I will consider relativistic effects for KE. I can calculate View attachment 97873 by solving this:

View attachment 97867

With
View attachment 97868 and View attachment 97869 and View attachment 97870

(where m is the rest mass).

The value you find for View attachment 97874 , allows you for instance to determine from what speed you need to be considering relativistic effects based on the threshold you chose from the error in your experimental data.

Physiscs-Tutor, hello
I see your point, thank you very much for explaining it to me

 

[ProfuselyQuarky]

HI Amy, Ray is correct. All depends on the error you are willing to consider

It might be relevant to neglect the Rel. effect or not depending on what you are trying to achieve.

For example, you can calculate the fraction of the speed of light for which you have to take into account relativistic effects, given a certain experimental framework.

You can set the threshold of difference you need. Say, I consider 1% as being the threshold above which I will consider relativistic effects for KE. I can calculate View attachment 97873 by solving this:

View attachment 97867

With
View attachment 97868 and View attachment 97869 and View attachment 97870

(where m is the rest mass).

The value you find for View attachment 97874 , allows you for instance to determine from what speed you need to be considering relativistic effects based on the threshold you chose from the error in your experimental data.

You can use the LaTeX editor, you know. Just thought I'd tell you in case you didn't know, and was getting annoyed with attaching images

$KE_{rel} =(\gamma-1)mc^2$

KE_{rel} =(\gamma-1)mc^2

 

[Physics-Tutor]

You can use the LaTeX editor, you know. Just thought I'd tell you in case you didn't know, and was getting annoyed with attaching images

KErel=(γ−1)mc2KErel=(γ−1)mc2KE_{rel} =(\gamma-1)mc^2

Thank you ProfuselyQuarky, I'll definitely check it out... :-) Could be a less painful than typing the equation in word, capturing pictures and posting them in my posts!

 

[ProfuselyQuarky]

Thank you ProfuselyQuarky, I'll definitely check it out... :-) Could be a less painful than typing the equation in word, capturing pictures and posting them in my posts!

Totally! Give it a try!