Problem dealing with a chapter on relativity

[jrd007]

I think I know how to do this problem, but need to make sure... so...

1) In an Earth reference frame, a star is 82 light years away. How fast would you have to travel so that to you the distance would only be 35 light years?

First I have two simple questions:

1. Light years is in a unit of time or length?

2. How to convert light years?

So I would use either:

a) L = Lo x sqroot(1-v^2/c^2) ~~~> 82 light years = 35 light years x sqr(1-v^2/(3.0 x 10^8)^2)

or

b) to = t x sqroot(1-v^2/c^2) ~~~> 35 light years = 85 light years x sqr(1-v^2/(3.0 x 10^8)^2)

 

[Hootenanny]

Light years is a unit of length, therefore, you would use Lorentz length contraction. A light year is the distance light can travel in the period of one year.

~H

 

[mrjeffy321]

A light year is a unit of length/distance.

If the distance between the Earth and the star (as seen from Earth) is 82 ly, how much of a contraction would be needed to make the distance only seem like 35 ly in the frame of someone traveling at relativistic velocities?

Lenth = Proper Length / gamma

where gamme is the lorentz factor,
gamma = 1/ sqrt(1 - v^2/c^2)

If we call "proper length" the length in the Earth's frame of reference, then we solve for gamma to be 82 ly / 35 ly = 2.3429

Now how fast must an object be flying fast Earth in order to have a lorentz factor this height?

2.3429 = 1/ sqrt(1 - v^2/c^2)
solve for v.

 

[jrd007]

(also so you cannot use L = Lo x sqroot(1-v^2/c^2)?) Look below.

could you also have said --> 85 = 35 x sqroot(1-v^2/c^2) and then solve for V?

 

[Hootenanny]

(also so you cannot use L = Lo x sqroot(1-v^2/c^2)?) Look below.

could you also have said --> 85 = 35 x sqroot(1-v^2/c^2) and then solve for V?

You have applied L = Lo x sqroot(1-v^2/c^2) here, which is the correct thing to do. However, I am confused as to why you have used 85 lightyears.

~H

 

[jrd007]

I mis typed it the first time.

 

[Hootenanny]

Then you are correct, apply lorentz's length contraction and solve for v.

~H