Understanding Relativity's F=y^3ma: How Does it Apply and What is Gamma?

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Homework Help Overview

The discussion revolves around applying Newton's second law in the context of relativistic mechanics, specifically exploring the relationship between force, momentum, and acceleration as expressed by the equation F = γ³ma. Participants are trying to understand the implications of the gamma factor and how it relates to the change in momentum in different reference frames.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to start the problem, with one suggesting to differentiate momentum in terms of velocity. Questions arise regarding the definition of 'v' and its relation to different frames of reference.

Discussion Status

The discussion is active, with participants providing insights on how to approach the problem. Some guidance has been offered regarding the differentiation of momentum, and there is an ongoing exploration of the definitions and implications of the variables involved.

Contextual Notes

There is some ambiguity regarding the reference frames being used, particularly in relation to the speed of the particle and how it is defined in the context of the problem.

Pengwuino
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The question I'm given is:

Newton's second law is given by \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} <br /> \over F} = \frac{{d\vec p}}{{dt}}. If the force is always parallel to the velocity, show that \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} <br /> \over F} = \gamma ^3 m\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} <br /> \over a}.

Now, how do I get started on this thing?

Also, what I'm really wondering is how this is actually applied. When they say \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} <br /> \over F} = \gamma ^3 m\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} <br /> \over a}… what gamma is being used? Also, are we looking at the change in momentum from wrt to the K frame?
 
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Since \vec{F} and \vec{p} are always parallel, you can remove the arrows, and just work with magnitudes. Write p in terms of v, and differentiate using the product rule and the chain rule. After differentiating, find a common denominator

Regards,
George
 
What is the 'v'. Is v the speed of the moving frame?
 
Pengwuino said:
What is the 'v'. Is v the speed of the moving frame?

v is the speed of the particle with respect to the lab frame, so that p = \gamma m v.

Regards,
George
 

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