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https://texercises.com/exercise/speed-of-a-pion/
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The following quantities appear in the problem: Zeit \(t\) / Geschwindigkeit \(v\) / Strecke \(s\) /
The following formulas must be used to solve the exercise: \(s = vt \quad \) \(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \) \(t = \gamma t_0 \quad \)
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Exercise:
How fast must an average pion be moving to travel m before it decays? The average lifetime at rest is ns.

Solution:
A pion travels in the Earth-System s v gamma t_ where t_ is the half-life measured in the pions System. Solving this for v gets us to: v fracsgamma t_ fracvc fracsct_ sqrt-fracv^c^ fracv^c^ fracs^c^t_^ left-fracv^c^right fracv^c^ left+ fracs^c^t_^right fracs^c^t_^ fracv^c^ leftfracc^t_^ + s^c^t_^right fracs^c^t_^ fracv^c^ c^t_^ + s^ s^ v fracssqrtc^t_^ + s^ c .c Ausrufbox A pion pi^- pi^+ pi^ consists of two quarks. Remember: Protons and Neutrons consist of three quarks. Pions are therefore mesons having a mass between the electrons and the nucleons. Ausrufbox
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Exercise:
How fast must an average pion be moving to travel m before it decays? The average lifetime at rest is ns.

Solution:
A pion travels in the Earth-System s v gamma t_ where t_ is the half-life measured in the pions System. Solving this for v gets us to: v fracsgamma t_ fracvc fracsct_ sqrt-fracv^c^ fracv^c^ fracs^c^t_^ left-fracv^c^right fracv^c^ left+ fracs^c^t_^right fracs^c^t_^ fracv^c^ leftfracc^t_^ + s^c^t_^right fracs^c^t_^ fracv^c^ c^t_^ + s^ s^ v fracssqrtc^t_^ + s^ c .c Ausrufbox A pion pi^- pi^+ pi^ consists of two quarks. Remember: Protons and Neutrons consist of three quarks. Pions are therefore mesons having a mass between the electrons and the nucleons. Ausrufbox
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Tags
contraction, dilation, einstein, length, physics, pion, relativity, srt, time
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(4, default)
Points
4 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
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