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Relativistic Density

  • #1

Homework Statement:

Consider a cube to have a density of 2.0kg/m^3. What is its relativistic density at 0.95c?

Homework Equations:

Lm = Ls/(1-v^2/c^2)^ - 1/2
mm = ms/(1-v^2/c^2)^ - 1/2
Density = mass/volume
We never learned how to use these formulas, so I'm pretty much grasping for straws. I got 2.04 kg/m^3. Can anyone check my work/teach me proper methods if I'm wrong? Thanks.
 

Answers and Replies

  • #2
Wait that's definitely wrong... Now I'm getting 42.3. Is that right?
 
  • #3
PeroK
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Wait that's definitely wrong... Now I'm getting 42.3. Is that right?
Can you explain what you're doing?
 
  • #4
Yes. I'll attach a picture.
 

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  • #5
I wrote the last division statement wrong (switch numerator and denominator) but yes I get 42.3 or 45 if I don't round.
 
  • #6
jbriggs444
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Homework Statement: Consider a cube to have a density of 2.0kg/m^3. What is its relativistic density at 0.95c?
Homework Equations: Lm = Ls/(1-v^2/c^2)^ - 1/2
mm = ms/(1-v^2/c^2)^ - 1/2
Density = mass/volume
Typesetting those equations for you. See this link to see how it was done.

$$L_m = \frac{L_s}{\sqrt{1-v^2/c^2}}$$
$$m_m = \frac{m_s}{\sqrt{1-v^2/c^2}}$$

One assumes that ##L_m## is the length of the moving cube and ##L_s## is its length as measured from a frame where it is stationary. Similarly, ##m_m## would be the relativistic mass of the moving cube and ##m_s## is its mass as measured from a frame where it is stationary.

Did you forget to square something?
 
  • #7
PeroK
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If I can understand what you're doing, you are length contracting all three dimensions of of the cube.
 
  • #8
If I can understand what you're doing, you are length contracting all three dimensions of of the cube.
Yes I think that's what I'm doing. Am I not supposed to? Is this the wrong formula?
 
  • #9
jbriggs444
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Length contraction is only in the direction of relative motion.
 
  • #10
So what formula should I be using to get the new volume?
 
  • #11
jbriggs444
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So what formula should I be using to get the new volume?
Same one they taught you in grade school. Volume = length * width * height.
 
  • #12
Okay, so I don't need to change anything about length? Just mass changes?
 
  • #13
jbriggs444
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Okay, so I don't need to change anything about length? Just mass changes?
What makes you think that length contraction does not apply?
 
  • #14
Length contraction is only in the direction of relative motion.
I confuse easily, sorry. I thought this meant not to use it.

Can you please walk me through the correct process of calculating the new mass and lengths?
 
  • #15
jbriggs444
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I confuse easily, sorry. I thought this meant not to use it.

Can you please walk me through the correct process of calculating the new mass and lengths?
You already quoted the correct formula for length contraction. By what factor has the length of the cube contracted?

This factor is also known as gamma (##\gamma##).
 
  • #16
Okay here's the problem. The square root of 1 - (0.95c)^2 / c^2 should be 0.312. I calculated this wrong.

I'm gonna try again with this new value; I'll let you know what I get
 
  • #17
PeroK
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Okay here's the problem. The square root of 1 - (0.95c)^2 / c^2 should be 0.312. I calculated this wrong.

I'm gonna try again with this new value; I'll let you know what I get
Put your calculator away and start thinking instead!
 
  • #18
Is only one side length affected by length contraction or all three?
 
  • #19
PeroK
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Is only one side length affected by length contraction or all three?
Who says the cube is moving parallel to one of its edges? But, let's assume it is, what do you think?
 
  • #20
Yes?
 
  • #21
PeroK
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Yes?
There is no length contraction in directions perpendicular to the motion.
 
  • #22
There is no length contraction in directions perpendicular to the motion.
So does that mean I'm right? Sorry I'm not great at this!
 
  • #23
jbriggs444
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So does that mean I'm right? Sorry I'm not great at this!
Right about what?
 
  • #24
PeroK
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So does that mean I'm right? Sorry I'm not great at this!
Yes, only one side is contracted.
 
  • #25
Yes, only one side is contracted.
Okay thank you!

Now one more thing I don't understand.

mm = 2 / 0.312 = 6.4 m
Lm = 1 / 0.312 = 3.2 kg

6.4 / 3.2(1)(1) = 2

Why am I still getting 2 as the answer? Does the density not change?
 

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