What is My Speed When Running on Top of a Moving Train?

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Discussion Overview

The discussion revolves around the speed of a person running on top of a moving train, specifically when the train is traveling at 10 km/hr and the person is running at 2 km/hr. It explores both classical physics and relativistic perspectives on the problem.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that if running toward the front of the train, the speed relative to the ground is 12 km/hr, while running toward the back results in a speed of 8 km/hr.
  • Another participant introduces a relativistic approach, suggesting that the speed calculations remain effectively the same (12 km/hr and 8 km/hr) due to the low speeds involved, which do not yield measurable relativistic effects.
  • A participant provides a specific speed in meters per second (3.33 m/s) for a stationary observer on the ground.
  • One participant humorously comments on the precision of speed calculations, referencing a calculator's output and noting the slow running speed compared to typical walking speeds.
  • Another participant emphasizes the concept of being at rest relative to oneself, suggesting a philosophical perspective on motion.

Areas of Agreement / Disagreement

There are multiple competing views regarding the interpretation of speed in this scenario, with some participants favoring classical physics explanations and others introducing relativistic considerations. The discussion remains unresolved regarding the implications of these different frameworks.

Contextual Notes

The discussion does not resolve the assumptions underlying the relativistic calculations or the definitions of speed in different reference frames.

Sriram.S
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What speed am I traveling at when I am run at the top a moving train.(Assuming train is going at 10 km/hr and I am running at 2km/hr)

Sriram
 
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Classical Physics:
If you are on a train going 10 km/hr, relative to the ground, and you are running at 2 km/hr relative to the train, toward the front of the train, then your speed relative to the ground is 10+2= 12 km/hr. If you are running toward the back of the train, your speed relative to the ground is 10-2= 8 km/hr.

Relativity:
If you are on a train going 10 km/hr, relative to the ground, and you are running at 2 km/hr relative to the train, toward the front of the train, then your speed relative to the ground is [itex](10+2)/(1+ (10)(2)/c^2[/itex]= [itex](10+2)/(1+ 20/( 299,792,458)^2[/itex] which, even to 12 decimal place accuracy, the limit of my calculator, 12.000000000000 km/hr. Similarly, if you are running toward the back of the train, your speed is still 8 km/hr to with 12 decimal places.

Those speeds are simply to low for relativistic effects to be measurable.
 
3.33 m/s [for stationary observer in ground]
 
HallsofIvy said:
even to 12 decimal place accuracy, the limit of my calculator, 12.000000000000 km/hr.
Microsoft PowerToy Calculator for Windows XP says 11.999999999999999258233295964254424402093624772443805600625656194569150201085437567008465314216160709462212415964961122075175062 :smile:

By the way, that has to be the slowest runner ever, considering that normal walking speed is about 6 km/h. :wink:
 
Hey, YOU try running on top of a moving train!
 
You're at rest. You are always at rest relative to yourself.
 

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