Time Dilation particle lifetime

Your mistake was leaving the 0.6^2 as 0.6*299792458 and then dividing by 2997924582, but that's wrong. You can just divide 0.6^2 by 2997924582 or you can leave it as 0.6^2 and divide 2997924582 by 2997924582. Either way you want to do it, you get the same thing. So you should have 1 - 0.6^2 = 1 - (0.6*299792458)^2/2997924582 = 1 - 0.36/2997924582 = 1 - 0.36*
  • #1
katamaster818
6
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.
 
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  • #2
Figured out my problem, plugged the numbers in again, and I missed the sqrt :/ Sorry to trouble you guys!
 
  • #3
You just did the arithmetic wrong. 1/√(1-0.6^2) = 1/√(1-0.36) = 1/√(0.64) = 1/0.8 = 1.25
 

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for a moving object than for a stationary observer. This is a result of the theory of relativity, which states that the laws of physics are the same for all observers, regardless of their relative motion.

2. How does time dilation occur?

Time dilation occurs due to the effect of velocity on the perception of time. As an object moves faster, its time appears to slow down from the perspective of a stationary observer. This is because the speed of light is constant and time must adjust to compensate for the change in velocity.

3. What is a "Time Dilation particle lifetime"?

A time dilation particle lifetime refers to the amount of time a particle exists before it decays or disappears. This can be affected by the speed at which the particle is moving, as well as other factors such as its mass and energy.

4. How does time dilation affect particle lifetimes?

Time dilation can affect particle lifetimes by slowing down or speeding up the decay process. The faster a particle travels, the longer it appears to exist from the perspective of a stationary observer. This can also affect the observed mass and energy of the particle.

5. What are some real-world applications of time dilation?

Time dilation has been observed and measured in experiments with subatomic particles and high-speed particles, such as those in particle accelerators. It also plays a crucial role in technologies such as GPS, where the precise timing of signals is essential for accurate navigation.

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