Time Dilation Question- NEED HELP (1 Viewer)

[funkless]

The question as follows:
'Muons are very short-lived particles that are created when energetic protons collide with each other. A beam of muons can be produced by very high-energy particle accelerators.

The high-speed muons produced for an experiment by the Fermilab accelerators are measured to have a lifetime of 5.0 microseconds. When these muons are brought to rest, their lifetime is measured to be 2.2 microseconds.

Calculate the velocity of the muons as they leave the accelerator.'

Now diagram thingy of sorts...

It's mainly the whole algebra bit, you know removing the square roots, where to put the numbers, etc. I am not very good at that. I also suspect I might even be using the wrong equation, but since muons were in the time dilation section, I decided to safely assume this was the right equation to use.

 

[insert-username]

Firstly, welcome to BoS!

Now, for the question, first write out the important information, then substitute it correctly into the equation:


T_o = 2.2 microseconds (rest time)

T_v = 5 microseconds (dilated time)

T_v = T_o/√(1 - v²/c²)

√(1 - v²/c²) = T_o/T_v [Multiply both sides by √(1 - v²/c²), then divide by T_v]

√(1 - v²/c²) = 0.44 [Work out 2.2/5]

1 - v²/c² = 0.1936 [Square both sides]

v²/c² = 0.8064 [Subtract 0.1936 from both sides, add v²/c² to both sides]

v/c = 0.898 (3 decimal places) [Take the square root of both sides]

v = 0.898c [Multiply through by c]

I hope that helps.


I_F

 

[funkless]

Firstly, welcome to BoS!

Now, for the question, first write out the important information, then substitute it correctly into the equation:


T_o = 2.2 microseconds (rest time)

T_v = 5 microseconds (dilated time)

T_v = T_o/√(1 - v²/c²)

√(1 - v²/c²) = T_o/T_v [Multiply both sides by √(1 - v²/c²), then divide by T_v]

√(1 - v²/c²) = 0.44 [Work out 2.2/5]

1 - v²/c² = 0.1936 [Square both sides]

v²/c² = 0.8064 [Subtract 0.1936 from both sides, add v²/c² to both sides]

v/c = 0.898 (3 decimal places) [Take the square root of both sides]

v = 0.898c [Multiply through by c]

I hope that helps.


I_F

THANKYOU! It sure does help, I mean if you hadn't of shown me...I'd still have no idea or I would of tried again and got it hideously wrong.