How Far Does a Pion Travel in the Lab Frame?

In summary, the conversation is about calculating the mean lifetime and distance traveled of unstable particles called pions in their rest frame and in the laboratory frame. The formula given by the professor is incorrect and the student correctly uses the distance formula to calculate the distance traveled as 5.41 meters.
  • #1
kavamo
45
0

Homework Statement



I have correctly figured out part a but am stuck on part b. Thanks for your help in advance.

An unstable particle called the pion has a mean lifetime of 25 ns in its own rest frame. A beam of pions travels through the laboratory at a speed of 0.587c.
(a) What is the mean lifetime of the pions as measured in the laboratory frame?
30.75 ns

(b) How far does a pion travel (as measured by laboratory observers) during this time?
m


Homework Equations



[ Delta t x c (speed of light) ] / 2

The Attempt at a Solution



using the answer from part a and converting to meters:

[(3.075E-8)(3E8)] / 2 = 4.6125 I've checked for errors and always come up with this number--which according to the web program is incorrect.

What am I not doing/understanding?
 
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  • #2
kavamo said:

Homework Equations



[ Delta t x c (speed of light) ] / 2
:confused: Where in the world did you get this formula?

Hint: How fast is it moving? How long is it moving for? How do you calculate distance traveled?
 
  • #3
I got the formula from my professor.
As far as I can tell it is moving at 0.587c = 176100000 m/s for 25 ns.

Distance = rate x time.

So then I suppose I would do the following:

176100000 m/s x (2.5 x 10^-10) = 0.044025 meters?
 
  • #4
kavamo said:
I got the formula from my professor.
It must be meant for some specific application--but not this one.
As far as I can tell it is moving at 0.587c = 176100000 m/s for 25 ns.
Why 25 ns? Stick to the lab frame.

Distance = rate x time.
That's all you need.
 
  • #5
o.k. then,

176100000m/s x (3.075 x 10^-10) = 0.05415075 ~ 0.0542 and convert to meters = 5.4 m
 
Last edited:
  • #6
kavamo said:
o.k. then,

176100000m/s x (3.075 x 10^-10) = 0.05415075 ~ 0.0542 and convert to meters = 5.4 m
Two things, the first being the most important:
- check your exponents
- use a more accurate value for the time in part a (redo it); only round off at the end.
 
  • #7
thank you I should have typed:

176100000m/s x (3x 10^8)x 30.75 (the answer from part a) = 5415075000

then convert from nano to meters (9 decimal spaces to the left) = 5.41 meters

which is the correct answer. Thank you for your guidance. K
 

FAQ: How Far Does a Pion Travel in the Lab Frame?

1. What is special relativity?

Special relativity is a fundamental theory in physics that explains the relationship between space and time. It was developed by Albert Einstein and is based on two main principles: the laws of physics are the same for all observers in uniform motion, and the speed of light is constant for all observers, regardless of their relative velocities.

2. What are the key concepts of special relativity?

The key concepts of special relativity include time dilation, length contraction, and the relativity of simultaneity. Time dilation refers to the slowing down of time for an object in motion relative to an observer. Length contraction is the shortening of an object's length in the direction of its motion. The relativity of simultaneity states that two events that appear simultaneous to one observer may not appear simultaneous to another observer in a different frame of reference.

3. How does special relativity differ from classical mechanics?

Special relativity differs from classical mechanics in that it takes into account the fact that the laws of physics are the same for all observers, regardless of their relative motion. This means that the concept of "absolute" space and time, which is used in classical mechanics, is no longer applicable. Instead, the laws of physics are described in terms of relative motion and the speed of light is considered to be the same for all observers.

4. Can special relativity be observed in everyday life?

Yes, special relativity can be observed in everyday life. One common example is the Global Positioning System (GPS), which uses special relativity to make accurate calculations of time and location. Special relativity also explains phenomena such as time dilation in high-speed particle accelerators and the observed differences in time between two synchronized clocks on Earth and a clock on a spacecraft.

5. How does special relativity relate to general relativity?

Special relativity is a special case of general relativity, which is a more comprehensive theory that includes gravity. General relativity expands on the concepts of special relativity to explain how gravity affects the fabric of space and time. Special relativity can be thought of as a "building block" of general relativity, providing the foundation for understanding space, time, and motion in the absence of gravity.

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