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Percent Length Contraction (check solution)

by Quelsita
Tags: check, contraction, length, percent, solution
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Quelsita
#1
Feb1-09, 11:59 PM
P: 50
Question:
What is the percent length contraction of an aircraft traveling at Mach 2?

So, we know that Mach 2= 680.58 m/s
and that L'=L[tex]\sqrt{1-(v/c)^2}[/tex]

If you divide over the L to get:

L'/L=[tex]\sqrt{1-(v/c)^2}[/tex]=% length contraction

Plug-n-chug from here to get:

L'/L=[tex]\sqrt{1-(680.58/c)^2}[/tex]
=[tex]\sqrt{1-(5.15X10^-12)}[/tex]
=[tex]\sqrt{1}[/tex]
=1

Is this correct? It only contracts 1%?
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LowlyPion
#2
Feb2-09, 12:13 AM
HW Helper
P: 5,341
I'd recheck your calculation and be careful in taking your square root.

680/300,000 is what you were intending I trust?
Quelsita
#3
Feb2-09, 12:18 AM
P: 50
Quote Quote by LowlyPion View Post
680/300,000 is what you were intending I trust?
Yep. That's why I thought it was off because it's such a small number that you'll have 1 under the radical...

Or is the percent contraction supposed to be very small since the aircraft, compared to the speed of light, is going extremely slow?

LowlyPion
#4
Feb2-09, 12:27 AM
HW Helper
P: 5,341
Percent Length Contraction (check solution)

Yes it is a small number.

And when you take the square root it gets closer to 1.

Use a calculator, and don't approximate or round until you have an expression for the percentage.
davieddy
#5
Feb2-09, 12:40 AM
P: 181
Quote Quote by LowlyPion View Post
I'd recheck your calculation and be careful in taking your square root.

680/300,000 is what you were intending I trust?
c = 300,000,000 m/s


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