Final answer:
The question seems related to physics problems, involving momentum conservation, Ohm's law, electrical circuits and kinematics. Understanding of basic physics principles and equations is needed to provide a solution to this problem.
Step-by-step explanation:
The question provided seems to be deriving from a series of physics problems, potentially involving concepts like resistances in circuits, momentum, velocity, and the conservation of charge and energy. The equation mv' 1 v'2 cos(0₁-0₂) = 0 suggests a situation involving momentum where either mass (m), velocity (v), or the cosine of the angle difference is zero for momentum to be conserved in a system. An understanding of physics concepts such as Ohm's law applied to resistive circuits, forces and electric fields (as suggested by E₂), and the principles of conservation are crucial to comprehensively answer the question and provide a correct solution.
It's also noted that the student is asked to consider cases where the instantaneous velocity is greatest, indicating a question related to kinematics or dynamics. The mention of junctions and loops within a circuit falls under the study of electricity and equations involving current (I) and resistance (R) denote a direct application of Ohm's law. Additionally, the mention of a stable element in a mass sequence might involve nuclear physics and the study of radioactive decay.