Lorentz Velocity Transformations Question

In summary, the conversation is about finding the speed of a positron when observed in the electron's rest frame. The solution involves deriving the velocity addition formula, which the poster prefers to do in order to fully understand the concept. The result seems to be correct according to the attached document. The poster also mentions their previous experience with a professor who emphasized deriving formulas rather than just memorizing them.
  • #1
zellwwf
34
0

Homework Statement



An electron and a positron are observed from the lab to move in opposite
directions with a speed of 0.5c and 0.7c, respectively. Find the speed of the
positron when observed in the electron's rest frame.


Homework Equations


in attached PDF


The Attempt at a Solution


in attached PDF
---------------------%------------------
I would like you to check my solution, if it is wrong, show me where i went wrong, and give me a hint, if it's right, gimme a cookie!
this forum has been helping me immensely with Modern Physics.

Please refer to the attached Document
 

Attachments

  • Electron Positron P1.pdf
    192.3 KB · Views: 221
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  • #2
You ended up deriving the velocity addition formula. I wonder why you could not just have used it directly. The result seems correct.
 
  • #3
if i don't derive it a couple of times myself, i won't memorize it, and i won't know "what" it means, ...
i was taught physics 1 by a great professor who didn't use except two formulas (f=ma, and a=+- 9.8) we had to derive everything else..
i remember he said once when we told him it was hard to derive the displacement from the acceleration... he looked at us with such a stare and said "Wow... are you all really that stupid! It's not that hard"...
 

1. What are Lorentz velocity transformations?

Lorentz velocity transformations are a set of equations that describe how velocities and other physical quantities appear to change when observed from different reference frames in special relativity.

2. Why are Lorentz velocity transformations important?

Lorentz velocity transformations are important because they allow us to understand how the laws of physics behave in different reference frames, and they are essential for accurately describing time, length, and velocity in special relativity.

3. How do Lorentz velocity transformations differ from Galilean transformations?

Lorentz velocity transformations take into account the principles of special relativity, including the constancy of the speed of light, while Galilean transformations do not. This means that Lorentz transformations are required for accurate predictions in high-speed and high-energy situations.

4. What is the formula for Lorentz velocity transformations?

The formula for Lorentz velocity transformations is:
v' = (v + u) / (1 + (vu / c^2))
where v' is the observed velocity, v is the velocity of the object in its own frame of reference, u is the velocity of the reference frame, and c is the speed of light.

5. How are Lorentz velocity transformations used in real-world applications?

Lorentz velocity transformations are used in many fields, such as particle physics and astrophysics, to accurately describe the behavior of particles and objects moving at high speeds. They are also used in the design of technologies such as GPS systems and particle accelerators.

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