Time dilation and length contraction help

In summary, the average lifetime of a muon is 2.2 microsec. When observed by a stationary observer with a speed of .60c, the muon would travel an average distance of 2.75 microsec before decaying. The proper time can be found using the equation 2.2/Sqrt[1-(.6c/c)^2]. Length contraction is not a factor in this scenario as the observer is not traveling at any speed. A 1+1 D space-time diagram can also be used to visualize the x-value after shifting to the appropriate point on the hyperbola.
  • #1
dswatson
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0
The average lifetime of a muon is 2.2 microsec. What is the average distance the muon would travel in free space before decaying according to a stationary observer watching the muon travel with a speed of (.60c).

I know how to find the proper time.

2.2/Sqrt[1-(.6c/c)^2] = 2.2/Sqrt[1-.6^2] = 2.2*1.25 =2.75 microsec

thank you in advance for any help.
 
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  • #2
Once you've found the proper time you're basically done. You don't have to worry about length contraction in this case because the observer isn't traveling at any speed. The objects agree on how fast they are traveling with respect to each other.

~Lyuokdea
 
  • #3
It also may be instructive to draw a 1+1 D space-time diagram and see what is the x-value after you shift to the appropriate point on the hyperbola.
 

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for a moving object or observer compared to a stationary one. This is due to the effects of special relativity, which states that the speed of light is constant for all observers.

2. How does time dilation affect our daily lives?

The effects of time dilation are only noticeable at extremely high speeds, such as those reached by objects traveling near the speed of light. In our daily lives, the effects are too small to be noticeable, but they are essential for accurate measurements in fields like GPS technology.

3. What is length contraction?

Length contraction is a phenomenon in which an object appears shorter in the direction of its motion compared to a stationary observer. This is also a result of special relativity and is closely related to time dilation.

4. Can time dilation and length contraction be observed?

Yes, time dilation and length contraction have been observed and verified experimentally through various experiments, including the famous Hafele-Keating experiment and the Muon experiment.

5. How do time dilation and length contraction relate to each other?

Time dilation and length contraction are two sides of the same coin. They are both consequences of the fact that the speed of light is constant for all observers. As an object's speed increases, time slows down, and its length contracts in the direction of motion.

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