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

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SUMMARY

The discussion centers on the application of Newton's second law in the context of relativistic mechanics, specifically the equation F = γ³ma. The term γ (gamma) represents the Lorentz factor, which accounts for relativistic effects as an object's speed approaches the speed of light. The participants clarify that the force vector F and momentum vector p are parallel, allowing for simplification in calculations. The speed v is defined as the velocity of the particle relative to the lab frame, leading to the expression p = γmv.

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  • Understanding of Newton's second law and its mathematical representation.
  • Familiarity with relativistic mechanics and the Lorentz factor (γ).
  • Knowledge of calculus, specifically differentiation using the product and chain rules.
  • Concept of momentum in physics, particularly in relativistic contexts.
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This discussion is beneficial for physics students, educators, and professionals interested in advanced mechanics, particularly those focusing on the intersection of classical and relativistic physics.

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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