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class10

# class10 - Announcements Reading for Friday 3.7-3.12 First...

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Announcements Reading for Friday: 3.7-3.12 First Mid-term is next week (Feb. 9 th , 7:30pm). It will cover Chapters 1&2. Room: MUEN E-050 . Allowed materials: see course syllabus. Review: Relativistic mechanics u r p m dt d m propper γ = Relativistic momentum: ( 29 u p F m dt d dt d γ = Relativistic force: E tot = γ mc 2 = K + mc 2 Total energy of a particle with mass ‘m’: We found that these definitions fulfill the momentum and energy conservation laws. And for u<<c the definitions for p, F, and K match the classical definitions. But we found that funny stuff happens to the proper mass ‘m’. E tot = γ 2mc 2 = 2K + 2mc 2 Equivalence of Mass and Energy m v -v m Conservation of the total energy requires that the final energy E tot,final is the same as the energy E tot, before E tot,final = Mc 2 = 2K + 2mc 2 = E tot,initial We find that the total mass M of the final system is bigger than the sum of the masses of the two parts! M>2m. Potential energy inside an object contributes to its mass!!! the collision. Therefore: E=mc 2 Convert mass to energy? Atomic cores are built from neutrons and protons. There are very strong attractive forces between them. The potential energy associated with the force keeping them together in the core is called the binding energy E B. We now know that the total rest energy of the particle equals the sum of the rest energy of all constituents minus the total binding energy E B : Mc 2 = Σ ( m i c 2 ) E B Or in terms of Mass per nucleon

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