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Help with length contraction and relativistic momentum please!

  • Thread starter shamille
  • Start date
  • #1
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Homework Statement


A woman is 2.0 m tall and has a mass of 60 kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of 2.30x1010 kg·m/s. What does the observer measure for her height?


Homework Equations


L=Lo √1 - (v2/c2)
p=mv/√1 - (v2/c2)

The Attempt at a Solution


I'm pretty sure that these are what the variables are
Lo= 2.0m proper length
p=2.3x1010
m=60kg
we want to solve for L

my problem is I don't know what v is, if I did i could find it.

I saw that L/Lo = mv/p
so L= Lomv/p right?

but i have no idea how to get v. i haven't had math in a while! any ideas or can you help me? i've tried an online equation solver for didn't work...
 

Answers and Replies

  • #2
Cyosis
Homework Helper
1,495
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You have p and m so you can solve the momentum equation for v.
 
  • #3
4
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well i got the answer as 1.24 but i had to use a function grapher and play around with the x and y mins and maxes to find what speed gives a momentum of 2.3E10! which was 0.79C

but i still want to know how to do this because there will be a test and i won't have the internet to help me

thanks in advance
 
  • #4
4
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You have p and m so you can solve the momentum equation for v.
yes but this is relativistic momentum not p=mv but
p=mv/√(1 - (v2/c2))
and i couldn't solve it for v.... is it because i'm crap at math?
can you walk me through how to solve for it? maybe it's more algebra than physics but...
 
  • #5
Cyosis
Homework Helper
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shamille said:
yes but this is relativistic momentum not p=mv but
p=mv/√(1 - (v2/c2))
There are still only three variables of which you know two.


You know how to solve quadratic equations I assume?

[tex]
\begin{align}
p=mv \gamma=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}
\\
p\sqrt{1-\frac{v^2}{c^2}}=mv
\\
p^2(1-\frac{v^2}{c^2})=m^2v^2
\end{align}
[/tex]

Can you solve it from here on?
 
  • #6
4
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yes! wow as soon as i wrote that last message i figured it out. I don't know where my head was before... and then I used a - instead of +... gahhh

i'm sorry!

but thank you so much
 
  • #7
Cyosis
Homework Helper
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You're welcome.
 

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