Relativistic Density - Check My Work & Learn Methods

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Homework Help Overview

The discussion revolves around calculating the relativistic density of a cube with an initial density of 2.0 kg/m³ at a velocity of 0.95c. Participants are exploring the implications of relativistic effects on mass and volume, particularly focusing on length contraction and its impact on density calculations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to apply the formulas for relativistic mass and length contraction but are questioning their understanding of how these concepts affect the density of the cube. There are discussions about whether all dimensions of the cube are affected by length contraction and how to correctly calculate the new volume and mass.

Discussion Status

The discussion is active, with participants providing guidance on the correct application of formulas and clarifying misconceptions about length contraction. Some participants express confusion about the calculations and the relationship between mass, volume, and density, while others offer insights into the geometric implications of relativistic effects.

Contextual Notes

There is a noted concern about the accuracy of calculations and the interpretation of the formulas provided. Participants are also addressing potential errors in unit representation and the significance of rounding in their final answers.

  • #31
I think @PeroK and myself are on the same page here. If you perceive a conflict, either of us can probably clarify it away.
 
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  • #32
Okay thank you!
 
  • #33
jbriggs444 said:
I think @PeroK and myself are on the same page here. If you perceive a conflict, either of us can probably clarify it away.

Yes, I agree.

I was distracted trying to find a way to show that it's true in general, even when motion is not in the same direction as one side of the cube. Which I've just spotted!
 
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  • #34
PeroK said:
I was distracted trying to find a clever way to show that it's true in general, even when motion is not in the same direction as one side of the cube. Which I've just spotted!
I was taking it as an obvious geometric property -- scale down one dimension by a factor of ##\gamma## and the volume clearly goes down proportionately.

I gave a moment's though to Terrell rotation, but it does not apply.
 
  • #35
jbriggs444 said:
I was taking it as an obvious geometric property -- scale down one dimension by a factor of ##\gamma## and the volume clearly goes down proportionately.

Yes, I was only thinking about cubes, parallelopipeds and the triple scalar product! Then, I realized ...

o:)
 

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