Need help with Lorentz Transformation equations

Find the relative speed between S and S'. (b) Find the location of the two flashes in frame S'. (c) At what time does the red flash occur in the S' frame?In summary, two flashes occur at positions xr = 3.00 m and xb = 5.00 m and times tr = 1.00*10^-9s and tb = 9.00*10^-9s, respectively, in the S reference frame. Reference frame S' has its origin at the same point as S at t = t' = 0 and moves uniformly to the right. The relative speed between S and S' can be found using Lorentz transformation equations. Both flashes are
  • #1
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A red light flashes at position xr = 3.00 m and time tr = 1.00*10^-9s, and a blue light flashes at xb = 5.00 m and tb = 9.00*10^-9s, all measured in the S reference frame. Reference frame S' has its origin at the same point as S at t = t' = 0; frame S' moves uniformly to the right. Both flashes are observed to occur at the same place in S'. (a) Find the relative speed between S and S'. (b) Find the location of the two flashes in frame S'. (c) At what time does the red flash occur in the S' frame?

I don't understand how to start part a. Any help would be great! thx!
 
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  • #2
andrew410 said:
A red light flashes at position xr = 3.00 m and time tr = 1.00*10^-9s, and a blue light flashes at xb = 5.00 m and tb = 9.00*10^-9s, all measured in the S reference frame. Reference frame S' has its origin at the same point as S at t = t' = 0; frame S' moves uniformly to the right. Both flashes are observed to occur at the same place in S'. (a) Find the relative speed between S and S'. (b) Find the location of the two flashes in frame S'. (c) At what time does the red flash occur in the S' frame?

I don't understand how to start part a. Any help would be great! thx!

You have two events, so you have two pairs of Lorentz transformation equations:

[tex]x'_r = \gamma (x_r - v t_r)[/tex]
[tex]t'_r = \gamma \left(t_r - \frac{v x_r}{c^2}\right)[/tex]

[tex]x'_b = \gamma (x_b - v t_b)[/tex]
[tex]t'_b = \gamma \left(t_b - \frac{v x_r}{c^2}\right)[/tex]

where [itex]\gamma = \frac {1} {\sqrt{1 - v^2 / c^2}}[/itex]

You're given the unprimed x's and t's. You're given that [itex]x'_r = x'_b[/itex], so you can replace [itex]x'_r[/itex] with [itex]x'_b[/itex] in the equations above, or you can do it the other way around if you like.

Now, how many unknowns do you have, and how many equations? :wink:
 
  • #3
where in the text am I given that xr = xb?

EDIT: I found where it says xr = xb in the text. It says "Both flashes are observed to occur at the same place in S'." I just missed that...
 
Last edited:
  • #4
Reference frame S' has its origin at the same point as S at t = t' = 0; frame S' moves uniformly to the right. Both flashes are observed to occur at the same place in S'.
 

1. What are the Lorentz Transformation equations?

The Lorentz Transformation equations are a set of equations that describe the relationship between space and time coordinates in two frames of reference that are moving relative to each other at a constant velocity. They were developed by physicist Hendrik Lorentz in the late 19th and early 20th centuries as part of his work on the theory of relativity.

2. Why are Lorentz Transformation equations important?

The Lorentz Transformation equations are important because they allow us to understand how space and time are affected by motion at high speeds. They are a fundamental component of Einstein's theory of special relativity, which revolutionized our understanding of the universe and has been confirmed by countless experiments.

3. How do I use Lorentz Transformation equations?

To use Lorentz Transformation equations, you need to know the velocity of one frame of reference relative to the other. Then, you can plug this velocity into the equations to calculate how distances and time intervals will appear different between the two frames. This can be useful in a variety of situations, such as when studying the behavior of particles at high speeds or when designing spacecraft that need to account for relativistic effects.

4. What are some common misconceptions about Lorentz Transformation equations?

One common misconception about Lorentz Transformation equations is that they only apply to objects moving at near-light speeds. In reality, these equations are relevant for any object moving at a constant velocity relative to another frame of reference. Another misconception is that these equations can only be used in the context of special relativity. While they were first developed for this theory, they can also be applied in other areas of physics, such as electromagnetism.

5. Are there any practical applications for Lorentz Transformation equations?

Yes, there are several practical applications for Lorentz Transformation equations. They are used in particle accelerators to calculate the behavior of particles moving at high speeds, in GPS technology to account for the effects of relativity on satellite signals, and in the design of spacecraft and satellites. They also have implications in the fields of astrophysics and cosmology, helping us understand the behavior of objects moving at extreme speeds in the universe.

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