Homework question on special relativity

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Homework Help Overview

The problem involves special relativity, specifically focusing on time dilation experienced by a triplet, Samantha, who works as an airline pilot. The scenario compares her aging process to that of her brother Tom over a period of 30 years.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the time dilation formula and question the calculations related to the time difference in aging between Samantha and Tom. There is a focus on verifying the accuracy of the calculations and the units used.

Discussion Status

The discussion is ongoing, with participants identifying potential errors in the calculations and clarifying the correct units of measurement. There is no explicit consensus yet, but guidance has been offered regarding the interpretation of the results.

Contextual Notes

Participants are addressing the implications of using the time dilation formula and are checking assumptions related to the calculations, including the correct application of relativistic effects over the specified time frame.

spaghetti3451
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Homework Statement



Samantha, Tom, and Roberta are triplets.

(i) Samantha is an airline pilot who flies along a straight flight path at 300 ms-1 for 80 hours per month (in her rest frame). How much younger will she be than her brother Tom (who handles baggage at the airport) when she retires after 30 years?

Homework Equations



Time dilation formula

The Attempt at a Solution



Use the time dilation formula t = γt0, where t is the time in the moving frame (that of Tom) and t0 is the time in the rest frame (that of Samantha).

t0 = (3600*80*12*30) = 103680000 s
v = 300 ms-1

Therefore, t = t0 + (51.84 ms), using the binomial expansion in the calculation.

So, Samantha will be 51.84 ms younger when she retires after thirty years.

Could you please confirm if I am right?
 
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Seems like you're off by a few powers of 10. (Unless I messed up the calculation.)

What did you get for γ-1?
 
I think I have spotted the error. Is your answer in microseconds rather than milliseconds?
 
i.e. 51.84 microseconds.
 
That's it. μs, not ms.
 

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