Time Dilation particle lifetime

AI Thread Summary
An unstable particle with a mean lifetime of 4 microseconds is moving at 0.6c, prompting questions about its observed lifetime and travel distance in the lab. The initial calculation for the mean lifetime in the lab was incorrect due to a miscalculation involving the Lorentz factor. After correcting the arithmetic, the proper value for the mean lifetime is determined to be 5 microseconds. The discussion highlights the importance of accurately applying the time dilation formula and ensuring all calculations are correctly executed. The participant is now ready to proceed with further calculations after resolving the initial error.
katamaster818
Messages
6
Reaction score
0

Homework Statement


An unstable particle with a mean lifetime of 4 microsecond is formed by a high-energy accelerator and projected through a laboratory with a speed of 0.6c

a. What is the mean lifetime of the particle as determined by an observer in the labratory
b. What is the average distance that the particle travels in the laboratory before decaying
c. How far does an observer at rest with respect to the particle determine its distance to be before it decays

Homework Equations


[/B]
λ = 1 / ((1-V2/c2)1/2)
Δt = λ * Δt
Mean Lifetime = 1 / λ

The Attempt at a Solution



λ = 1 / ( ( 1 - ( (0.6) (299792458) )2 / 2997924582 )1/2 = 1.5625
Δt = λ * Δt = 1.5625 * 4 microseconds = 6.25 microseconds

According to the answers provided to us by the teacher, answer should be 5 microseconds. Where am I going wrong? Am I using the wrong equation?

Edit: This is only part A I've gotten to so far, and I'm hesitant to move on without making sure I get the first part correct.
 
Physics news on Phys.org
Figured out my problem, plugged the numbers in again, and I missed the sqrt :/ Sorry to trouble you guys!
 
You just did the arithmetic wrong. 1/√(1-0.6^2) = 1/√(1-0.36) = 1/√(0.64) = 1/0.8 = 1.25
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Relativity problem involving a muon
Replies
1
Views
2K
Relativistic Distance/Time Problem
Replies
4
Views
2K
How does relativity affect the detection of atmospheric muons?
Replies
11
Views
2K
Relativity question involving time dilation
Replies
1
Views
3K
How Does Time Dilation Affect Pion Decay in Particle Physics?
Replies
3
Views
6K
Length contraction and time dilation in relativity
Replies
30
Views
3K
I Analyzing Time Dilation in a Spaceship-Mars Scenario
Replies
14
Views
2K
I Muon Time Dilation in Accelerating Frames
Replies
2
Views
1K
Another relativistic particle decay question
Replies
2
Views
2K
Length, time and velocity in relativity (special?)
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top