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
Expert's answer
2020-05-01T10:14:12-0400

Solution.

τ=1.501016s;\tau =1.50\sdot10^{-16}s;

τ0=0.901016s;\tau_0 =0.90\sdot10^{-16}s;

c=3108m/s;c = 3\sdot10^8m/s;

τ=τ01υ2c2;    \tau= \dfrac{\tau_0}{\sqrt{1-\dfrac{\upsilon^2}{c^2}}}; \implies υ=c1τ02τ2;\upsilon = c\sqrt{1-\dfrac{\tau_0^2}{\tau^2}};

υ=c1(0.901016)2(1.51016)2=1.92108m/s;\upsilon = c\sqrt{1-\dfrac{(0.90\sdot10^{-16})^2}{(1.5\sdot10^{-16})^2}}=1.92\sdot10^8m/s;

E=mc21υ2c2E = \dfrac{mc^2}{\sqrt{1-\dfrac{\upsilon^2}{c^2}}} ;

E=139.6MeV1(1.92108m/s)2(3108m/s)2=232.7MeV;E =\dfrac{139.6MeV}{\sqrt{1-\dfrac{(1.92\sdot10^8m/s)^2}{(3\sdot10^8m/s)^2}}}=232.7MeV;

Answer:υ=1.92108m/s;\upsilon = 1.92\sdot10^8m/s;

E=232.7MeV.E = 232.7MeV.




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