Relativity Problem: Muons Traveling at .99c Towards Earth

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SUMMARY

The discussion centers on a relativity problem involving muons traveling at 0.99c towards Earth. The user, Bob, calculated the time dilation effect, resulting in a half-life of 10.633 microseconds for ground observers, but struggled with the classical calculation of travel time for muons over a distance of 2000 meters. The expected number of detected muons at Earth is 420, while Bob's calculations yield over 600, indicating a misunderstanding in the application of relativistic effects in time calculation.

PREREQUISITES
  • Understanding of special relativity principles, particularly time dilation.
  • Familiarity with muon behavior and half-life calculations.
  • Knowledge of classical mechanics for calculating travel time.
  • Basic grasp of the speed of light as a constant (c).
NEXT STEPS
  • Study the implications of time dilation in special relativity with a focus on muons.
  • Learn about relativistic velocity addition to understand how speeds close to c affect calculations.
  • Explore the concept of proper time versus coordinate time in relativistic contexts.
  • Review classical mechanics principles for calculating distance, speed, and time.
USEFUL FOR

Physics students, educators, and anyone interested in understanding the effects of relativity on particle behavior, particularly in high-speed scenarios involving muons.

Wannabeagenius
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Hi All,

I'm trying to do a Relativity problem and I'm having trouble.

There is a detector on a balloon at 2000 meters above the Earth that in one hour has detected 650 muons that normally have a half life of 1.5 microseconds. They are traveling at .99c towards the earth. How many are detected at the Earth in one hour.

Now due to time dilation, I get 10.633 microseconds for the half life relative to ground observers. That seems pretty reasonable.

Now I figure that all I need to know is how long it takes for them to travel 2000 meters and that seems to be a classical calculation. Time =2000 meters/.99c but my answer is way off.

Am I approaching this correctly? I am wondering about calculating the time it takes the muons to reach the ground in a classical manner?

The book answer is 420 but I get over 600.

Thank you,
Bob
 
Physics news on Phys.org
I don't see that you've done anything wrong so far. How did you finally get to 'over 600'?
 

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