107 750
Assignments Done
100%
Successfully Done
In May 2024

Answer to Question #113264 in Mechanics | Relativity for Moel Tariburu

Question #113264
A pion lives 1.50 x 10-16 s as measured in the laboratory, and 0.90 x 10-16 s when at rest
relative to an observer.
i) Determine the speed of the pion.
[2.5]
ii) Calculate the kinetic energy in MeV of the particle, given its rest mass energy is
139.6 MeV?
1
2020-05-01T10:14:12-0400

Solution.

"\\tau =1.50\\sdot10^{-16}s;"

"\\tau_0 =0.90\\sdot10^{-16}s;"

"c = 3\\sdot10^8m\/s;"

"\\tau= \\dfrac{\\tau_0}{\\sqrt{1-\\dfrac{\\upsilon^2}{c^2}}}; \\implies" "\\upsilon = c\\sqrt{1-\\dfrac{\\tau_0^2}{\\tau^2}};"

"\\upsilon = c\\sqrt{1-\\dfrac{(0.90\\sdot10^{-16})^2}{(1.5\\sdot10^{-16})^2}}=1.92\\sdot10^8m\/s;"

"E = \\dfrac{mc^2}{\\sqrt{1-\\dfrac{\\upsilon^2}{c^2}}}" ;

"E =\\dfrac{139.6MeV}{\\sqrt{1-\\dfrac{(1.92\\sdot10^8m\/s)^2}{(3\\sdot10^8m\/s)^2}}}=232.7MeV;"

"E = 232.7MeV."

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

No comments. Be the first!

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS