Theory of relativity -- Car and Garage Paradox

[Groovy2]

Homework Statement

Theory of relativity

Relevant Equations

Delta(t)=tA-tB

Hey everyone!

Im new here so im not really familiar with this forum. But nice to meet yal! Btw im not really sure if this problem fits in the "Advanced Phyics Homework Help". But heres my problem:

Assume that the car and the garage in the garage paradox have the same rest length L0
and that they move at a speed of 0.53c relative to each other. Call the event when the front of the car reaches the end of the garage A and the event when the end of the car reaches the beginning of the garage B. What is the time difference delta(t)=tA-tB
between these events in the garage rest system?

Tried to solve it a couple of times and gotten nowhere. I appreciate all the help!

 

[phinds]

Please show your work in your attempt

 

[Groovy2]

Please show your work in your attempt

Alright so heres what i did:

stept 1: Lorentz abbreviation

L=L0*sqrt(1−(0.53)^2)=L0*(1−0.2809)=L0sqrt(0.7191)≈L0⋅0.847

Step 2:
Δt=L/v
Δt=L0*0.847/0.53c

Therefore
(0.847/0.53)*(Lo/c)= approx 1.598

 

[PeroK]

What happened to $L_0$?

Is that supposed to be approximately $1.6$ seconds? It's considered very ungroovy to omit units after a numerical quantity.

 

[Groovy2]

What happened to $L_0$?

Is that supposed to be approximately $1.6$ seconds? It's considered very ungroovy to omit units after a numerical quantity.

Sorry, forgot to mention. They want the answere to be in L0/c. So therefor my answere is 1.6*Lo/c

 

[PeroK]

More importantly, which event happens first: A or B?

 

[Groovy2]

More importantly, which event happens first: A or B?

According to the question? I assume A

 

[PeroK]

According to the question? I assume A

Better to check that with a diagram. 1.6 doesn't look right.

 

[Groovy2]

Better to check that with a diagram. 1.6 doesn't look right.

I honestly dont know how to solve this more than this. The answere needs to be as a multiple of L0/c

 

[PeroK]

I honestly dont know how to solve this more than this. The answere needs to be as a multiple of L0/c

In the rest frame of the garage, the car is shorter than the garage.

 

[Groovy2]

In the rest frame of the garage, the car is shorter than the garage.

Im very new to this whole theory of relativity, so what does that really mean?

 

[PeroK]

Im very new to this whole theory of relativity, so what does that really mean?

Shorter simply means its length is less. I.e. it fits inside the garage.

 

[Groovy2]

Shorter simply means its length is less. I.e. it fits inside the garage.

Yeah i got that. Am I suppose to draw anything to see the big picture? Im just using formulas at the moment, so thats why i dont really understand what that means

 

[Steve4Physics]

Am I suppose to draw anything to see the big picture? Im just using formulas at the moment, so thats why i dont really understand what that means

Let O be an observer in the garage frame.

A couple of diagrams showing the car’s positions (as seen by O) at events A and B should help.

From the description, it sounds like O should see event B before event A. And that you are being asked to find the time for the car (of contracted length $L’$) to travel a distance $L_0 – L’$. This corresponds to the time the car is entirely inside the garage (as measured by O).