Physics Emergency: Two Trains Moving Away at 51% Light Speed

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In summary, the conversation discusses a statement made in another forum and a question about two trains moving away from each other at 51% the speed of light. The correct answer is that in one train's frame, the other train will appear to be moving at 80.946% the speed of light. The importance of specifying the frame of reference when discussing such problems is also emphasized.
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Rico Bamchug
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Okay, I made a statement in another forum completely unrelated to physics and I believe it to be wrong even though I made the statement in good faith. (Which is to say, I THOUGHT I knew what I was talking about.)

So please, if you can, bail me out.

Two trains are moving away from each other, both traveling at 51% the speed of light. In one train, viewing the other, would it appear to be traveling at 102% the speed of light?

Okay, that's it! Any help will be greatly appreciated!
 
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  • #2
Rico Bamchug said:
Okay, I made a statement in another forum completely unrelated to physics and I believe it to be wrong even though I made the statement in good faith. (Which is to say, I THOUGHT I knew what I was talking about.)

So please, if you can, bail me out.

Two trains are moving away from each other, both traveling at 51% the speed of light. In one train, viewing the other, would it appear to be traveling at 102% the speed of light?
Nope, you have to use the relativistic velocity addition formula here--in one train's frame, the other train will be moving at (0.51c + 0.51c)/(1 + 0.51^2) = 0.80946c, i.e. 80.946% the speed of light.
 
  • #3
Awesome! And thank you Jesse!
 
  • #4
Whenever you talk about this kind of problem, it helps to always add "as measured ..." When you say a train is moving at 0.51c, state relative to what or measured relative to what. That helps keep things straight.
 

Related to Physics Emergency: Two Trains Moving Away at 51% Light Speed

1. How is the speed of light relevant in this scenario?

The speed of light is a fundamental constant in physics. It is the fastest speed at which any object or information can travel in the universe. In this scenario, the two trains are moving away from each other at 51% of the speed of light, which is an extremely high velocity and has significant implications for the behavior of the trains.

2. How do you calculate the speed of the trains?

The speed of the trains can be calculated using the formula for relative velocity, which takes into account the speed of both trains and their direction of motion. In this scenario, the trains are moving away from each other, so their relative velocity would be the sum of their individual speeds. However, at such high speeds, the equations of classical mechanics are no longer accurate and would need to be adjusted using Einstein's theory of relativity.

3. What happens to the length of the trains at such high speeds?

According to Einstein's theory of relativity, objects moving at high speeds experience a phenomenon known as length contraction. This means that the length of the trains would appear shorter to an observer on the ground compared to an observer on one of the trains. This effect becomes more pronounced as the speed of the trains approaches the speed of light.

4. How does time dilation affect this scenario?

Time dilation is another consequence of Einstein's theory of relativity and occurs when an object is moving at high speeds. In this scenario, time would appear to pass slower for an observer on the ground compared to an observer on one of the trains. This means that the two trains would experience a difference in the passage of time, which could have significant effects on their schedules and arrival times.

5. What are the potential dangers or challenges in this physics emergency scenario?

At such high speeds, the trains would experience an enormous amount of energy and would need to be constructed with incredibly strong materials to withstand the forces. Any sudden changes in speed or direction could lead to catastrophic consequences, making it crucial for the trains to have advanced safety measures in place. Additionally, the relativity effects mentioned earlier could also pose challenges for accurate navigation and communication between the trains and the ground.

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