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Iwo particles with proper masses m₁, m2 move along the x-axis of an inertial frame velocities u, uz respectively. They collide and coalesce to form a single particle. Assuming the laws conservation of relativistic momentum and energy, prove that the proper mass m3 and velocity u3 0

Iwo particles with proper masses m₁, m2 move along the x-axis of an inertial frame velocities u, uz respectively. They collide and coalesce to form a single particle. Assuming the laws conservation of relativistic momentum and energy, prove that the proper mass m3 and velocity u3 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two particles with proper masses m₁, m2 move along the x-axis of an inertial frame with velocities u, uz respectively. They collide and coalesce to form a single particle. Assuming the laws of conservation of relativistic momentum and energy, prove that the proper mass m3 and velocity u3 of the resulting single particle are given by U₁U2 m² = m² + m² + 2m₁m₂r₁ r₂1- c² and U3 = where m₁r₁u₁ + m₂r2U2 m₁r1 + m2r2 r₁² = 1- - u² (²1 r₂² = 1- c²
Transcribed Image Text:Two particles with proper masses m₁, m2 move along the x-axis of an inertial frame with velocities u, uz respectively. They collide and coalesce to form a single particle. Assuming the laws of conservation of relativistic momentum and energy, prove that the proper mass m3 and velocity u3 of the resulting single particle are given by U₁U2 m² = m² + m² + 2m₁m₂r₁ r₂1- c² and U3 = where m₁r₁u₁ + m₂r2U2 m₁r1 + m2r2 r₁² = 1- - u² (²1 r₂² = 1- c²
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