Fisica Moderna

 

  󰁔󰁅󰁍󰁁 1. 󰁒󰁅󰁌󰁁󰁔󰁉󰁖󰁉󰁄󰁁󰁄

1905 ↔ E󰁩󰁮󰁳󰁴󰁥󰁩󰁮 ↔ T󰁥󰁯󰁲󰃭󰁡 󰁥󰁳󰁰󰁥󰁣󰁩󰁡󰁬 󰁤󰁥 󰁬󰁡 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤. A 󰁦󰁩󰁮󰁡󰁬󰁥󰁳 󰁤󰁥󰁬 󰁳󰁩󰁧󰁬󰁯 󰁘I󰁘 󰁬󰁡 󰁴󰁥󰁯󰁲󰃭󰁡 󰁥󰁬󰁥󰁣󰁴󰁲󰁯󰁭󰁡󰁧󰁮󰃩󰁴󰁩󰁣󰁡 󰁨󰁡󰁢󰃭󰁡 󰁤󰁥󰁭󰁯󰁳󰁴󰁲󰁡󰁤󰁯 󰁳󰁵 󰁶󰁥󰁲󰁡󰁣󰁩󰁤󰁡󰁤. P󰁯󰁲 󰁯󰁴󰁲󰁯 󰁬󰁡󰁤󰁯 󰁬󰁡 󰁭󰁥󰁣󰃡󰁮󰁩󰁣󰁡 󰁤󰁥 N󰁥󰁷󰁴󰁯󰁮 󰁨󰁡󰁢󰃭󰁡 󰁨󰁥󰁣󰁨󰁯 󰁰󰁲󰁥󰁤󰁩󰁣󰁣󰁩󰁯󰁮󰁥󰁳 󰁶󰃡󰁬󰁩󰁤󰁡󰁳 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁱󰁵󰁥 󰁳󰁥 󰁰󰁵󰁳󰁯 󰁡 󰁰󰁲󰁵󰁥󰁢󰁡. S󰁩󰁮 󰁥󰁭󰁢󰁡󰁲󰁧󰁯, 󰁡󰁭󰁢󰁡󰁳 󰁴󰁥󰁯󰁲󰃭󰁡󰁳 󰁥󰁲󰁡󰁮 󰁩󰁮󰁣󰁯󰁭󰁰󰁡󰁴󰁩󰁢󰁬󰁥󰁳 󰁥󰁮󰁴󰁲󰁥 󰁳󰃭: 󰁭󰁩󰁥󰁮󰁴󰁲󰁡󰁳 󰁬󰁡󰁳 󰁥󰁣󰁵󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁤󰁥 N󰁥󰁷󰁴󰁯󰁮 󰁥󰁲󰁡󰁮 󰁩󰁮󰁶󰁡󰁲󰁩󰁡󰁮󰁴󰁥󰁳 󰁤󰁥 G󰁡󰁬󰁩󰁬󰁥󰁯, 󰁬󰁡󰁳 󰁥󰁣󰁵󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁤󰁥 M󰁡󰁸󰁷󰁥󰁬󰁬 󰁲󰁥󰁳󰁵󰁬󰁴󰁡󰁲󰁯󰁮 󰁮󰁯 󰁳󰁥󰁲󰁬󰁯. A󰁤󰁥󰁭󰃡󰁳 󰁥󰁮 󰁥󰁬󰁬󰁡󰁳 󰁡󰁰󰁡󰁲󰁥󰁣󰃭󰁡 󰁵󰁮󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥 (󰁣) 󰁱󰁵󰁥 󰁥󰁲󰁡 󰁩󰁮󰁤󰁥󰁰󰁥󰁮󰁤󰁩󰁥󰁮󰁴󰁥 󰁤󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁯 󰁤󰁥 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁦󰁵󰁥󰁮󰁴󰁥. S󰁥 󰁤󰁥󰁮󰁯󰁭󰁩󰁮󰁡 󰁩󰁮󰁶󰁡󰁲󰁩󰁡󰁮󰁣󰁩󰁡 󰁧󰁡󰁬󰁩󰁬󰁥󰁡󰁮󰁡 󰁡󰁬 󰁨󰁥󰁣󰁨󰁯 󰁤󰁥󰁲󰁩󰁶󰁡󰁤󰁯 󰁤󰁥󰁬 󰁰󰁲󰁩󰁮󰁣󰁩󰁰󰁩󰁯 󰁤󰁥 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤 󰁳󰁥󰁧󰃺󰁮 󰁥󰁬 󰁣󰁵󰁡󰁬 󰁬󰁡󰁳 󰁬󰁥󰁹󰁥󰁳 󰁦󰁵󰁮󰁤󰁡󰁭󰁥󰁮󰁴󰁡󰁬󰁥󰁳 󰁤󰁥 󰁬󰁡 󰁦󰃭󰁳󰁩󰁣󰁡 󰁳󰁯󰁮 󰁬󰁡󰁳 󰁭󰁩󰁳󰁭󰁡󰁳 󰁭󰁩 󰁳󰁭󰁡󰁳 󰁥󰁮 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁳󰁩󰁳󰁴󰁥󰁭󰁡󰁳 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬󰁥󰁳. U󰁮 󰁳󰁩󰁳󰁴󰁥󰁭󰁡 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 󰁥󰁳 󰁡󰁱󰁵󰁥󰁬 󰁥󰁮 󰁥󰁬 󰁱󰁵󰁥 󰁵󰁮 󰁯󰁢󰁪󰁥󰁴󰁯 󰁳󰁯󰁢󰁲󰁥 󰁥󰁬 󰁱󰁵󰁥 󰁮󰁯 󰁡󰁣󰁴󰃺󰁥󰁮 󰁦󰁵󰁥󰁲󰁺󰁡󰁳 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥 󰁥󰁮 󰁬󰃭󰁮󰁥󰁡 󰁲󰁥󰁣󰁴󰁡 󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥. P󰁯󰁲 󰁥󰁪󰁥󰁭󰁰󰁬󰁯 󰁳󰁩 󰁵󰁮 󰁳󰁩󰁳󰁴󰁥󰁭󰁡 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁱󰁵󰁥 󰁡󰁣󰁥󰁬󰁥󰁲󰁡 󰁥󰁮 󰁬󰃭󰁮󰁥󰁡 󰁲󰁥󰁣󰁴󰁡 󰁯 󰁧󰁩󰁲󰁡 󰁣󰁯󰁮 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 󰁵󰁮 󰁳󰁩󰁳󰁴󰁥󰁭󰁡 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬, 󰁥󰁳󰁴󰁥 󰁳󰁥󰁲󰃡 󰁮󰁯 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬.  T󰁥󰁯󰁲󰃭󰁡 󰁥󰁳󰁰󰁥󰁣󰁩󰁡󰁬 󰁤󰁥 󰁬󰁡 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤. C󰁯󰁮 󰁥󰁳󰁴󰁡 󰁴󰁥󰁯󰁲󰃭󰁡 󰁴 󰁥󰁯󰁲󰃭󰁡 󰁥󰁳 󰁰󰁯󰁳󰁩󰁢󰁬󰁥 󰁰󰁲󰁥󰁤󰁥󰁣󰁩󰁲 󰁣󰁯󰁲󰁲󰁥󰁣󰁴󰁡󰁭󰁥󰁮󰁴󰁥 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁥󰁸󰁰󰁥󰁲󰁩󰁭󰁥󰁮󰁴󰁡󰁬󰁥󰁳 󰁥󰁮 󰁥󰁬 󰁩󰁮󰁴󰁥󰁲󰁶󰁡󰁬󰁯 󰁤󰁥 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁱󰁵󰁥 󰁶󰁡󰁮 󰁤󰁥󰁳󰁤󰁥 󰁥󰁬 󰁲󰁥󰁰󰁯󰁳󰁯 󰁲 󰁥󰁰󰁯󰁳󰁯 󰁨󰁡󰁳󰁴󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁱󰁵󰁥 󰁳󰁥 󰁡󰁰󰁲󰁯󰁸󰁩󰁭󰁡󰁮 󰁡 󰁬󰁬󰁡󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺. 󰁐󰁯󰁳󰁴󰁵󰁬󰁡󰁤󰁯󰁳 󰁤󰁥 󰁬󰁡 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤 󰁥󰁳󰁰󰁥󰁣󰁩󰁡󰁬  1.  P󰁲󰁩󰁭󰁥󰁲 󰁰󰁯󰁳󰁴󰁵󰁬󰁡󰁤󰁯 (󰁰󰁲󰁩󰁮󰁣󰁩󰁰󰁩󰁯 󰁤󰁥 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤) L󰁡󰁳 󰁬󰁥󰁹󰁥󰁳 󰁤󰁥 󰁬󰁡 󰁦󰃭󰁳󰁩󰁣󰁡 󰁳󰁯󰁮 󰁬󰁡󰁳 󰁭󰁩󰁳󰁭󰁡󰁳 󰁥󰁮 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁬 󰁯󰁳 󰁳󰁩󰁳󰁴󰁥󰁭󰁡󰁳 󰁤󰁥 dp F  󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥󰁮 󰁵󰁮󰁩󰁦󰁯󰁲󰁭󰁥󰁭󰁥󰁮󰁴󰁥 󰁥󰁮󰁴󰁲󰁥 󰁳󰃭. E󰁳 󰁤󰁥󰁣󰁩󰁲, 󰁬󰁥󰁹󰁥󰁳 󰁦󰁵󰁮󰁤󰁡󰁭󰁥󰁮󰁴󰁡󰁬󰁥󰁳 󰁣󰁯󰁭󰁯   =   󰁴󰁩󰁥󰁮󰁥󰁮 󰁬󰁡 dt  󰁭󰁩󰁳󰁭󰁡 󰁦󰁯󰁲󰁭󰁡 󰁭󰁡󰁴󰁥󰁭󰃡󰁴󰁩󰁣󰁡 󰁰󰁡󰁲󰁡 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳 󰁱󰁵󰁥 󰁳󰁥 󰁤󰁥󰁳󰁰󰁬󰁡󰁺󰁡󰁮 󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥 󰁥󰁮󰁴󰁲󰁥 󰁳󰃭. 2.  S󰁥󰁧󰁵󰁮󰁤󰁯 󰁰󰁯󰁳󰁴󰁵󰁬󰁡󰁤󰁯 (󰁩󰁮󰁶󰁡󰁲󰁩󰁡󰁢󰁩󰁬󰁩󰁤󰁡󰁤 󰁤󰁥 󰁣) L󰁡 L󰁵󰁺 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁳󰁥 󰁰󰁲󰁯󰁰󰁡󰁧󰁡 󰁥󰁮 󰁥󰁬 󰁶󰁡󰁣󰃭󰁯 󰁣󰁯󰁮 󰁵󰁮󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥 󰁣 󰁱󰁵󰁥 󰁥󰁳 󰁩󰁮󰁤󰁥󰁰󰁥󰁮󰁤󰁩󰁥󰁮󰁴󰁥 󰁤󰁥󰁬 󰁥󰁳󰁴󰁡󰁤󰁯 󰁤󰁥 󰁭󰁯󰁶󰁩󰁭󰁩󰁥󰁮󰁴󰁯 󰁤󰁥󰁬 󰁣󰁵󰁥󰁲󰁰󰁯 󰁥󰁭󰁩󰁳󰁯󰁲 󰁹 󰁤󰁥󰁬 󰁥󰁳󰁴󰁡󰁤󰁯 󰁤󰁥 󰁭󰁯󰁶󰁩󰁭󰁩󰁥󰁮󰁴󰁯 󰁤󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲.

∑

E󰁬 󰁳󰁩󰁧󰁬󰁯 󰁘VII 󰁥󰁳󰁴󰃡 󰁣󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁡󰁤󰁯 󰁣󰁯󰁭󰁯 󰁥󰁬 󰁣󰁯󰁭󰁩󰁥󰁮󰁺󰁯 󰁤󰁥 󰁬󰁡 󰁥󰁲󰁡 󰁣󰁩󰁥󰁮󰁴󰃭󰁦󰁩󰁣󰁡; 󰁥󰁮 󰃩󰁬 󰁳󰁥 󰁯󰁰󰁥󰁲󰃳 󰁵󰁮 󰁣󰁡󰁭󰁢󰁩󰁯 󰁥󰁮 󰁬󰁡 󰁣󰁯󰁮󰁣󰁥󰁰󰁣󰁩󰃳󰁮 󰁤󰁥󰁬 󰁵󰁮󰁩󰁶󰁥󰁲󰁳󰁯 󰁮󰁡󰁴󰁵󰁲󰁡󰁬 󰁹 󰁬󰁡 󰁩󰁮󰁶󰁥󰁳󰁴󰁩󰁧󰁡󰁣󰁩󰃳󰁮 󰁩 󰁮󰁶󰁥󰁳󰁴󰁩󰁧󰁡󰁣󰁩󰃳󰁮 󰁣󰁩󰁥󰁮󰁴󰃭󰁦󰁩󰁣󰁡 󰁥󰁭󰁰󰁲󰁥󰁮󰁤󰁩󰃳 󰁵󰁮󰁡 󰁳󰁥󰁲󰁩󰁥 󰁤󰁥 󰁡󰁣󰁴󰁩󰁴󰁵󰁤󰁥󰁳 󰁱󰁵󰁥 󰁬󰁬󰁥󰁶󰃳 󰁡 󰁬󰁡 󰁮󰁥󰁣󰁥󰁳󰁩󰁤󰁡󰁤 󰁰󰁲󰃡󰁣󰁴󰁩󰁣󰁡 󰁤󰁥 󰁮󰁵󰁥󰁶󰁯󰁳 󰁩󰁮󰁶󰁥󰁮󰁴󰁯󰁳 󰁹 󰁮󰁵󰁥󰁶󰁡󰁳 󰁥󰁸󰁰󰁬󰁩󰁣󰁡󰁣󰁩󰁯󰁮󰁥󰁳. H󰁡󰁣󰁩󰁡 󰁬󰁯󰁳 󰁡󰃱󰁯󰁳 1970󰀭79, 󰁬󰁡 󰁥󰁬󰁥󰁣󰁴󰁲󰁩󰁣󰁩󰁤󰁡󰁤 󰁹 󰁥󰁬 󰁭󰁡󰁧󰁮󰁥󰁴󰁩󰁳󰁭󰁯 󰁳󰁥 󰁥󰁳󰁴󰁵󰁤󰁩󰁡󰁢󰁡󰁮 󰁣󰁯󰁭󰁯 󰁣󰁯󰁮󰁴󰁲󰁡󰁣󰁣󰁩󰁯󰁮󰁥󰁳 󰁹 󰁤󰁥󰁳󰁰󰁬󰁡󰁺󰁡󰁭󰁩󰁥󰁮󰁴󰁯󰁳 󰁤󰁥 󰃩󰁴󰁥󰁲, 󰁹 󰁬󰁡󰁳 󰁥󰁣󰁵󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁤󰁥 J󰁡󰁭󰁥󰁳 C󰁬󰁥󰁲󰁫 M󰁡󰁸󰁷󰁥󰁬󰁬 󰁥󰁸󰁰󰁲󰁥󰁳󰁡󰁢󰁡󰁮 󰁥󰁮 󰁴󰃩󰁲󰁭󰁩󰁮󰁯󰁳 󰁭󰁡󰁴󰁥󰁭󰃡󰁴󰁩󰁣󰁯󰁳 󰁬󰁡󰁳 󰁤󰁩󰁦󰁥󰁲󰁥󰁮󰁴󰁥󰁳 󰁲󰁥󰁬󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁥󰁸󰁩󰁳󰁴󰁥󰁮󰁴󰁥󰁳 󰁥󰁮󰁴󰁲󰁥 󰁬󰁡󰁳 󰁦󰁵󰁥󰁲󰁺󰁡󰁳 󰁥󰁬󰁥󰁣󰁴󰁲󰁯󰁭󰁡󰁧󰁮󰃩󰁴󰁩󰁣󰁡󰁳, 󰁶󰁩󰁳󰁵󰁡󰁬󰁩󰁺󰁡󰁤󰁡󰁳 󰁥󰁮 󰁥󰁬 󰁭󰁡󰁲󰁣󰁯 󰁤󰁥󰁬 󰃩󰁴󰁥󰁲. M󰁩󰁥󰁮󰁴󰁲󰁡󰁳 󰁱󰁵󰁥 󰁬󰁡 󰁡󰁢󰁥󰁲󰁲󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺 (S󰁥 󰁤󰁥󰁮󰁯󰁭󰁩󰁮󰁡 󰁡󰁢󰁥󰁲󰁲󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺 󰁯 󰁡󰁢󰁥󰁲󰁲󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁂󰁲󰁡󰁤󰁬󰁥󰁹 󰁡 󰁬󰁡 󰁤󰁩󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁥󰁮󰁴󰁲󰁥 󰁬󰁡 󰁰󰁯󰁳󰁩󰁣󰁩󰃳󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁡 󰁤󰁥 󰁵󰁮󰁡 󰁥󰁳󰁴󰁲󰁥󰁬󰁬󰁡 󰁹 󰁳󰁵 󰁰󰁯󰁳󰁩󰁣󰁩󰃳󰁮 󰁲󰁥󰁡󰁬, 󰁤󰁥󰁢󰁩󰁤󰁯 󰁡 󰁬󰁡 󰁣󰁯󰁭󰁢󰁩󰁮󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁹 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺) 󲀜󰁤󰁥󰁭󰁯󰁳󰁴󰁲󰁡󰁢󰁡󲀝 󰁱󰁵󰁥 󰁥󰁬 󰃩󰁴󰁥󰁲 󰁳󰁥 󰁥󰁮󰁣󰁯󰁮󰁴󰁲󰁡󰁢󰁡 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯, 󰁹 󰁢󰁡󰁪󰁯 󰁥󰁳󰁴󰁡󰁳 󰁣󰁯󰁮󰁤󰁩󰁣󰁩󰁯󰁮󰁥󰁳, 󰁳󰁥󰁧󰃺󰁮 󰁥󰁬 󰁡󰁳󰁴󰁲󰃳󰁮󰁯󰁭󰁯 󰁩󰁮󰁧󰁬󰃩󰁳 J󰁡󰁭󰁥󰁳 B󰁲󰁡󰁤󰁬󰁥󰁹, B 󰁲󰁡󰁤󰁬󰁥󰁹, 󰁬󰁡 󰁴󰁩󰁥󰁲󰁲󰁡 󰁡󰁬 󰁤󰁥󰁳󰁣󰁲󰁩󰁢󰁩󰁲 󰁳󰁵 󰁲󰁥󰁶󰁯󰁬󰁵󰁣󰁩󰃳󰁮 󰁡󰁮󰁵󰁡󰁬 󰁡󰁬󰁲󰁥󰁤󰁥󰁤󰁯󰁲 󰁤󰁥󰁬 󰁳󰁯󰁬 (󰁭󰁯󰁶󰁩󰁭󰁩󰁥󰁮󰁴󰁯 󰁤󰁥 󰁴󰁲󰁡󰁳󰁬󰁡󰁣󰁩󰃳󰁮), 󰁴󰁥󰁮󰃭󰁡 󰁱󰁵󰁥 󰁭󰁯󰁶󰁥󰁲󰁳󰁥 󰁡 󰁴󰁲󰁡󰁶󰃩󰁳 󰁤󰁥󰁬 󰃩󰁴󰁥󰁲 󰁹 󰁣󰁲󰁥󰁡󰁲 󰁡󰁬󰁧󰁯 󰁡󰁳󰃭 󰁣󰁯󰁭󰁯 󲀜󰁶󰁩󰁥󰁮󰁴󰁯 󰁤󰁥󰁬 󰃩󰁴󰁥󰁲󲀝; 󰁡󰁬󰁧󰁯 󰁰󰁡󰁲󰁥󰁣󰁩󰁤󰁯 󰁡 󰁬󰁯 󰁱󰁵󰁥 󰁯󰁣󰁵󰁲󰁲󰁥 󰁣󰁵󰁡󰁮󰁤󰁯 󰁥󰁮 󰁵󰁮 󰁤󰃭󰁡 󰁳󰁩󰁮 󰁣󰁯󰁲󰁲󰁩󰁥󰁮󰁴󰁥󰁳 󰁤󰁥 󰁶󰁩󰁥󰁮󰁴󰁯 󰁥󰁮 󰁬󰁡 󰁡󰁴󰁭󰃳󰁳󰁦󰁥󰁲󰁡 󰁴󰁥 󰁳󰁵󰁢󰁥󰁳 󰁡 󰁵󰁮 󰁡󰁵󰁴󰁯󰁭󰃳󰁶󰁩󰁬 󰁱󰁵󰁥 󰁡󰁬 󰁤󰁥󰁳󰁰󰁬󰁡󰁺󰁡󰁲󰁳󰁥 󰁯󰁲󰁩󰁧󰁩󰁮󰁡 󰁵󰁮 󰁶󰁩󰁥󰁮󰁴󰁯 󰁰󰁡󰁲󰁡 󰁬󰁯󰁳 󰁯󰁣󰁵󰁰󰁡󰁮󰁴󰁥󰁳 󰁤󰁥󰁬 󰁶󰁥󰁨󰃭󰁣󰁵󰁬󰁯. P󰁯󰁲 󰁯󰁴󰁲󰁯 󰁬󰁡󰁤󰁯, 󰁬󰁯󰁳 󰁥󰁸 󰁥󰁸󰁰󰁥󰁲󰁩󰁭󰁥󰁮󰁴󰁯󰁳 󰁰󰁥󰁲󰁩󰁭󰁥󰁮󰁴󰁯󰁳 󰁤󰁥 M󰁩󰁣󰁨󰁥󰁬󰁳󰁯󰁮󰀭M󰁯󰁲󰁬󰁥󰁹 󰁭󰁯󰁳󰁴󰁲󰁡󰁢󰁡󰁮 󰁱󰁵󰁥 󰁡󰁬 󰁮󰁯 󰁳󰁥󰁲 󰁤󰁥󰁴󰁥󰁣󰁴󰁡󰁤󰁯, 󰃩󰁳󰁴󰁥 󰁤󰁥󰁢󰃭󰁡 󰁭󰁯󰁶󰁥󰁲󰁳󰁥 󰁪󰁵󰁮󰁴󰁯 󰁣󰁯󰁮 󰁬󰁡 󰁴󰁩󰁥󰁲󰁲󰁡.

 

E󰁮 󰃩󰁳󰁴󰁡 󰁵󰁮󰁩󰁤󰁡󰁤 󰁡󰁰󰁲󰁥󰁮󰁤󰁥󰁲󰁥󰁭󰁯󰁳 󰁥󰁮 󰁱󰁵󰃩 󰁳󰁥 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁮 󰁬󰁡󰁳 C󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 G󰁡󰁬󰁩󰁬󰁥󰁯, 󰁣󰁵󰁡󰁮󰁤󰁯 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥󰁬 󰁣󰁵󰁥󰁲󰁰󰁯 󰁱󰁵󰁥 󰁮󰁯󰁳 󰁩󰁮󰁴󰁥󰁲󰁥󰁳󰁡 󰁡󰁮󰁡󰁬󰁩󰁺󰁡󰁲 󰁳󰁥 󰁤󰁥󰁳󰁰󰁬󰁡󰁺󰁡 󰁣󰁯󰁮 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁶 󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁭󰁵󰁹 󰁣󰁥󰁲󰁣󰁡󰁮󰁡󰁳 󰁡 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁬󰁵󰁺. 󰁵󰁺. T󰁡󰁭󰁢󰁩󰃩󰁮 󰁶󰁡󰁳 󰁡 󰁤󰁡󰁲󰁴󰁥 󰁣󰁵󰁥󰁮󰁴󰁡 󰁰󰁯󰁲 󰁱󰁵󰃩 󰁮󰁯 󰁥󰁳 󰁰󰁯󰁳󰁩󰁢󰁬󰁥 󰁱󰁵󰁥 󰁵󰁮 󰁣󰁵󰁥󰁲󰁰󰁯 󰁳󰁥 󰁤󰁥󰁳󰁰󰁬󰁡󰁣󰁥 󰁣󰁯󰁮 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺. A󰁰󰁲󰁥󰁮󰁤󰁥󰁲󰃡󰁳 󰁱󰁵󰁥, 󰁤󰁥 󰁡󰁣󰁵󰁥󰁲󰁤󰁯 󰁣󰁯󰁮 󰁬󰁡 󰁴󰁥󰁯󰁲󰃭󰁡 󰁥󰁳󰁰󰁥󰁣󰁩󰁡󰁬 󰁤󰁥 󰁬󰁡 R󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤 󰁹 󰁤󰁥󰁰󰁥󰁮󰁤󰁩󰁥󰁮󰁤󰁯 󰁤󰁥 󰁳󰁩 󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁳󰁴󰃡 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯 󰁯 󰁳󰁥 󰁤󰁥󰁳󰁰󰁬󰁡󰁺󰁡 󰁣󰁯󰁮 󰁥󰁬 󰁣󰁵󰁥󰁲󰁰󰁯 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥, 󰁬󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤, 󰁥󰁬 󰁴󰁩󰁥󰁭󰁰󰁯, 󰁬󰁡 󰁤󰁩󰁳󰁴󰁡󰁮󰁣󰁩󰁡 󰁹 󰁬󰁡 󰁭󰁡󰁳󰁡 󰁹󰁡 󰁮󰁯 󰁳󰁯󰁮 󰁬󰁡󰁳 󰁭󰁩󰁳󰁭󰁡󰁳 󰁱󰁵󰁥 󰁥󰁮 󰁬󰁡 M󰁥󰁣󰃡󰁮󰁩󰁣󰁡 C󰁬󰃡󰁳󰁩󰁣󰁡, 󰁹 󰁱󰁵󰁥 󰁬󰁯 󰁡󰁮󰁴󰁥󰁲󰁩󰁯󰁲 󰁴󰁡󰁭󰁢󰁩󰃩󰁮 󰁳󰁵󰁣󰁥󰁤󰁥 󰁰󰁡󰁲󰁡 󰁬󰁡 󰁥󰁮󰁥󰁲󰁧󰃭󰁡.

󰁔󰁒󰁁󰁎󰁓󰁆󰁏󰁒󰁍󰁁󰁃󰁉󰁏󰁎󰁅󰁓 󰁄󰁅 󰁇󰁁󰁌󰁉󰁌󰁅󰁏

E󰁮 󰁬󰁯󰁳 󰁣󰁵󰁲󰁳󰁯󰁳 󰁡󰁮󰁴󰁥󰁲󰁩󰁯󰁲󰁥󰁳 󰁤󰁥 F󰃭󰁳󰁩󰁣󰁡, 󰁮󰁯󰁳 󰁨󰁥󰁭󰁯󰁳 󰁤󰁡󰁤󰁯 󰁣󰁵󰁥󰁮󰁴󰁡 󰁱󰁵󰁥 󰁬󰁡 M󰁥󰁣󰃡󰁮󰁩󰁣󰁡 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁤󰁥󰁳󰁣󰁲󰁩󰁢󰁥 󰁬󰁡 󰁭󰁡󰁮󰁥󰁲󰁡 󰁥󰁮 󰁱󰁵󰁥 󰁬󰁯󰁳 󰁣󰁵󰁥󰁲󰁰󰁯󰁳 󰁣󰁡󰁭󰁢󰁩󰁡󰁮 󰁥󰁮 󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 󰁹 󰁥󰁮 󰁥󰁬 󰁴󰁩󰁥󰁭󰁰󰁯. E󰁳 󰁤󰁥󰁣󰁩󰁲, 󰁱󰁵󰁥 󰁴󰁯󰁤󰁯 󰁥󰁶󰁥󰁮󰁴󰁯 󰁤󰁥 󰁬󰁡 󰁮󰁡󰁴󰁵󰁲󰁡󰁬󰁥󰁺󰁡 󰁴󰁩󰁥󰁮󰁥 󰁬󰁵󰁧󰁡󰁲 󰁥󰁮 󰁵󰁮 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 󰁤󰁥 󰁣󰁵󰁡󰁴󰁲󰁯 󰁤󰁩󰁭󰁥󰁮󰁳󰁩󰁯󰁮󰁥󰁳, 󰁹 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁱󰁵󰁥 󰁨󰁡󰁢󰁬󰁥󰁭󰁯󰁳 󰁤󰁥 󰁬󰁡 󰁴󰁥󰁯󰁲󰃭󰁡 󰁤󰁥 󰁬󰁡 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤 󰁥󰁭󰁰󰁬󰁥󰁡󰁲󰁥󰁭󰁯󰁳 󰁬󰁡 󰁦󰁲󰁡󰁳󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁯󰀭󰁴󰁩󰁥󰁭󰁰󰁯. 󰃉󰁳󰁴󰁡 󰁦󰁵󰁥 󰁵󰁮󰁡 󰁤󰁥 󰁬󰁡󰁳 󰁦󰁲󰁡󰁳󰁥󰁳 󰁭󰃡󰁳 󰁮󰁯󰁶󰁥󰁤󰁯󰁳󰁡󰁳 󰁩󰁮󰁴󰁲󰁯󰁤󰁵󰁣󰁩󰁤󰁡󰁳 󰁰󰁯󰁲 M󰁩󰁮󰁫󰁯󰁷󰁳󰁫󰁩, 󰁱󰁵󰁥 󰁤󰁥󰁳󰁰󰁵󰃩󰁳 󰁵󰁴󰁩󰁬󰁩󰁺󰃳 A󰁬󰁢󰁥󰁲󰁴 E󰁩󰁮󰁳󰁴󰁥󰁩󰁮. P󰁥󰁲󰁯, 󰂿󰁱󰁵󰃩 󰁥󰁮󰁣󰁩󰁥󰁲󰁲󰁡 󰁬󰁡 󰁦󰁲󰁡󰁳󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁯󰀭󰁴󰁩󰁥󰁭󰁰󰁯? A󰁮󰁴󰁥󰁳 󰁤󰁥 󰁬󰁡 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤 󰁤󰁥 E󰁩󰁮󰁳󰁴󰁥󰁩󰁮, 󰁬󰁡 󰁰󰁡󰁬󰁡󰁢󰁲󰁡 󰁳󰁥 󰁵󰁳󰁡󰁢󰁡 󰁣󰁯󰁭󰁯 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 󰁹 󰁴󰁩󰁥󰁭󰁰󰁯. E󰁳󰁴󰁯 󰁥󰁳, 󰁤󰁯󰁳 󰁣󰁯󰁮󰁣󰁥󰁰󰁴󰁯󰁳 󰁩󰁮󰁤󰁥󰁰󰁥󰁮󰁤󰁩󰁥󰁮󰁴󰁥󰁳, 󰁮󰁯 󰁩󰁮󰁴󰁥󰁲󰁣󰁯󰁮󰁥󰁣󰁴󰁡󰁤󰁯󰁳. H󰁯󰁹 󰁳󰁡󰁢󰁥󰁭󰁯󰁳 󰁱󰁵󰁥 󰁥󰁳󰁴󰁯 󰁥󰁳 󰁦󰁡󰁬󰁳󰁯. C󰁵󰁡󰁮󰁤󰁯 󰁱󰁵󰁥󰁲󰁡󰁭󰁯󰁳 󰁤󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁡󰁲 󰁤󰃳󰁮󰁤󰁥 󰁹 󰁣󰁵󰃡󰁮󰁤󰁯 󰁴󰁩󰁥󰁮󰁥󰁮 󰁬󰁵󰁧󰁡󰁲 󰁣󰁩󰁥󰁲󰁴󰁯󰁳 󰁨󰁥󰁣󰁨󰁯󰁳, 󰁴󰁥󰁮󰁤󰁲󰁥󰁭󰁯󰁳 󰁱󰁵󰁥 󰁭󰁥󰁮󰁣󰁩󰁯󰁮󰁡󰁲 󰁣󰁵󰁡󰁴󰁲󰁯 󰁤󰁩󰁭󰁥󰁮󰁳󰁩󰁯󰁮󰁥󰁳 󰁱󰁵󰁥, 󰁳󰁥󰁧󰃺󰁮 󰁬󰁡 󰁩󰁤󰁥󰁡 󰁴󰁲󰁡󰁤󰁩󰁣󰁩󰁯󰁮󰁡󰁬, 󰁬󰁡󰁳 󰁴󰁲󰁥󰁳 󰁰󰁲󰁩󰁭󰁥󰁲󰁡󰁳 󰁤󰁡󰁮 󰁬󰁡 󰁰󰁯󰁳󰁩󰁣󰁩󰃳󰁮 󰁥󰁮 󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯, 󰁭󰁩󰁥󰁮󰁴󰁲󰁡󰁳 󰁱󰁵󰁥 󰁬󰁡 󰁣󰁵󰁡󰁲󰁴󰁡 󰁤󰁡 󰁬󰁡 󰁰󰁯󰁳󰁩󰁣󰁩󰃳󰁮 󰁥󰁮 󰁥󰁬 󰁴󰁩󰁥󰁭󰁰󰁯. E󰁳󰁴󰁡󰁭󰁯󰁳 󰁤󰁥 󰁡󰁣󰁵󰁥󰁲󰁤󰁯 󰁱󰁵󰁥 󰁥󰁮 󰁬󰁡󰁳 󰁬󰁡 󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁱󰁵󰁥 󰁨󰁡󰁣󰁥󰁭󰁯󰁳 󰁤󰁥 󰁬󰁡󰁳 󰁣󰁯󰁳󰁡󰁳, 󰁵󰁮󰁡 󰁤󰁥 󰁥󰁬󰁬󰁡󰁳 󰁳󰁥 󰁲󰁥󰁦󰁩󰁥󰁲󰁥 󰁡󰁬 󰁭󰁯󰁶󰁩󰁭󰁩󰁥󰁮󰁴󰁯; 󰁹 󰁱󰁵󰁥 󰁣󰁵󰁡󰁮󰁤󰁯 󰁵󰁮 󰁣󰁵󰁥󰁲󰁰󰁯 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥, 󰁥󰁳 󰁰󰁯󰁲󰁱󰁵󰁥 󰁣󰁡󰁭󰁢󰁩󰁡 󰁤󰁥 󰁰󰁯󰁳󰁩󰁣󰁩󰃳󰁮. O 󰁤󰁩󰁣󰁨󰁯 󰁤󰁥 󰁯󰁴󰁲󰁡 󰁭󰁡󰁮󰁥󰁲󰁡, 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁱󰁵󰁥 󰁱󰁵󰁥󰁲󰁥󰁭󰁯󰁳 󰁬󰁯󰁣󰁡󰁬󰁩󰁺󰁡󰁲 󰁵󰁮 󰁥󰁶󰁥󰁮󰁴󰁯, 󰁯 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁲 󰁬󰁡 󰁤󰁥󰁳󰁣󰁲󰁩󰁰󰁣󰁩󰃳󰁮 󰁤󰁥 󰁵󰁮 󰁦󰁥󰁮󰃳󰁭󰁥󰁮󰁯, 󰁬󰁯 󰁨󰁡󰁣󰁥󰁭󰁯󰁳 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 󰁵󰁮 󰁣󰁵󰁥󰁲󰁰󰁯 󰁦󰁩󰁪󰁯 󰁯 󰁳󰁩󰁳󰁴󰁥󰁭󰁡 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡. E󰁳 󰁡󰁳󰃭 󰁱󰁵󰁥 󰁥󰁬󰁥󰁧󰁩󰁭󰁯󰁳 󰁵󰁮 󰁳󰁩󰁳󰁴󰁥󰁭󰁡 󰁤󰁥 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳. E󰁳󰁴󰁥 󰁣󰁯󰁮󰁣󰁥󰁰󰁴󰁯 󰁥󰁳 󰁭󰁵󰁹 󰁩󰁭 󰁩󰁭󰁰󰁯󰁲󰁴󰁡󰁮󰁴󰁥 󰁰󰁯󰁲󰁴󰁡󰁮󰁴󰁥 󰁥 󰁩󰁮󰁶󰁯󰁬󰁵󰁣󰁲󰁡 󰁴󰁯󰁤󰁡 󰁵󰁮󰁡 󰁳󰁥󰁲󰁩󰁥 󰁤󰁥 󰁣󰁯󰁮󰁣󰁥󰁰󰁴󰁯󰁳 󰁱󰁵󰁥, 󰁬󰁬󰁥󰁶󰁡 󰁡󰁬 󰁥󰁳󰁴󰁡󰁢󰁬󰁥󰁣󰁩󰁭󰁩󰁥󰁮󰁴󰁯 󰁤󰁥 󰁳󰁩󰁳󰁴󰁥󰁭󰁡󰁳 󰁤󰁥 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 󰁰󰁡󰁲󰁡 󰁩󰁮󰁴󰁥󰁲󰁰󰁲󰁥󰁴󰁡󰁲 󰁡󰁤󰁥󰁣󰁵󰁡󰁤󰁡󰁭󰁥󰁮󰁴󰁥 󰁬󰁯󰁳 󰁣󰁯󰁮󰁣󰁥󰁰󰁴󰁯󰁳 󰁤󰁥 󰁤󰁩󰁳󰁴󰁡󰁮󰁣󰁩󰁡, 󰁴󰁲󰁡󰁹󰁥󰁣󰁴󰁯󰁲󰁩󰁡, 󰁣󰁡󰁭󰁢󰁩󰁯 󰁤󰁥 󰁰󰁯󰁳󰁩󰁣󰁩󰃳󰁮, 󰁥󰁴󰁣󰃩󰁴󰁥󰁲󰁡. • 

S󰁩 󰁴󰁥 󰁥󰁮󰁣󰁵󰁥󰁮󰁴󰁲󰁡󰁳 󰁥󰁮 󰁵󰁮 󰁣󰁡󰁲󰁲󰁯 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥 󰁣󰁯󰁮 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁶 󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁵󰁮󰁩󰁦󰁯󰁲󰁭󰁥 󰁹 󰁤󰁥󰁳󰁤󰁥 󰁬󰁡 󰁶󰁥󰁮󰁴󰁡󰁮󰁩󰁬󰁬󰁡 󰁤󰁥󰁪󰁡󰁳 󰁣󰁡󰁥󰁲 󰁬󰁩󰁢󰁲󰁥󰁭󰁥󰁮󰁴󰁥 󰁵󰁮󰁡 󰁰󰁥󰁱󰁵󰁥󰃱󰁡 󰁰󰁩󰁥󰁤󰁲󰁡 󰁦󰁵󰁥󰁲󰁡 󰁤󰁥󰁬 󰁣󰁡󰁲󰁲󰁯 󰁳󰁩󰁮 󰁱󰁵󰁥 󰁬󰁥 󰁤󰁥󰁳 󰁡󰁬󰁧󰃺󰁮 󰁩󰁭󰁰󰁵󰁬󰁳󰁯, 󰁤󰁥󰁳󰁤󰁥 󰁥󰁬 󰁣󰁡󰁲󰁲󰁯 󰁥󰁮 󰁭󰁯󰁶󰁩󰁭󰁩󰁥󰁮󰁴󰁯 󰁶󰁥󰁲󰃡󰁳 󰁱󰁵󰁥 󰁬󰁡 󰁴󰁲󰁡󰁹󰁥󰁣󰁴󰁯󰁲󰁩󰁡 󰁤󰁥 󰁬󰁡 󰁰󰁩󰁥󰁤󰁲󰁩󰁴󰁡 󰁥󰁳 󰁵󰁮󰁡 󰁬󰃭󰁮󰁥󰁡 󰁲󰁥󰁣󰁴󰁡, 󰁰󰁥󰁲󰁯 󰁰󰁡󰁲󰁡 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁱󰁵󰁥 󰁳󰁥 󰁥󰁮󰁣󰁵󰁥󰁮󰁴󰁲󰁥 󰁥󰁮 󰁬󰁡 󰁣󰁡󰁲󰁲󰁥󰁴󰁥󰁲󰁡, 󰁯 󰁵󰁮 󰁰󰁥󰁡󰁴󰃳󰁮 󰁱󰁵󰁥 󰁳󰁥 󰁥󰁮󰁣󰁵󰁥󰁮󰁴󰁲󰁡 󰁥󰁮 󰁬󰁡 󰁡󰁣󰁥󰁲󰁡 󰁦󰁵󰁥󰁲󰁡 󰁤󰁥󰁬 󰁣󰁡󰁲󰁲󰁯, 󰁬󰁡 󰁴󰁲󰁡󰁹󰁥󰁣󰁴󰁯󰁲󰁩󰁡 󰁴󰁲 󰁡󰁹󰁥󰁣󰁴󰁯󰁲󰁩󰁡 󰁱󰁵󰁥 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁲󰃡󰁮 󰁳󰁥󰁲󰃡 󰁬󰁡 󰁤󰁥 󰁵󰁮󰁡 󰁰󰁡󰁲󰃡󰁢󰁯󰁬󰁡. 󰂿C󰁵󰃡󰁬 󰁤󰁥 󰁬󰁡󰁳 󰁤󰁯󰁳 󰁴󰁲󰁡󰁹󰁥󰁣󰁴󰁯󰁲󰁩󰁡󰁳 󰁥󰁳 󰁬󰁡 󰁶󰁥󰁲󰁤󰁡󰁤󰁥󰁲󰁡?  󰁶󰁥󰁲󰁤󰁡󰁤󰁥󰁲󰁡?  A󰁭󰁢󰁯󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳 󰁥󰁳󰁴󰃡󰁮 󰁲󰁥󰁰󰁯󰁲󰁴󰁡󰁮󰁤󰁯 󰁬󰁡 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰃳󰁮 󰁣󰁯󰁲󰁲󰁥󰁣󰁴󰁡󰁭󰁥󰁮󰁴󰁥 󰁣󰁯󰁲󰁲󰁥󰁣󰁴󰁡󰁭󰁥󰁮󰁴󰁥,, 󰂿󰁰󰁯󰁲 󰁱󰁵󰃩? 󰁱󰁵󰃩? E󰁳󰁴󰁡󰁲󰃡󰁳  E󰁳󰁴󰁡󰁲󰃡󰁳 󰁤󰁥 󰁡󰁣󰁵󰁥󰁲󰁤󰁯 󰁥󰁮 󰁱󰁵󰁥 󰁴󰁡󰁮󰁴󰁯 󰁴󰃺 󰁣󰁯󰁭󰁯 󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁤󰁥 󰁬󰁡 󰁣󰁡󰁲󰁲󰁥󰁴󰁥󰁲󰁡, 󰁴󰁩󰁥󰁮󰁥󰁮 󰁳󰁵 󰁰󰁲󰁯󰁰󰁩󰁯 󰁭󰁡󰁲󰁣󰁯 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁲 󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 󰁹, 󰁰󰁯󰁲 󰁬󰁯 󰁴󰁡󰁮󰁴󰁯, 󰁡󰁭󰁢󰁯󰁳 󰁴󰁩󰁥󰁮󰁥󰁮 󰁲󰁡󰁺󰃳󰁮 󰁰󰁯󰁲󰁱󰁵󰁥 󰁰󰁡󰁲󰁡 󰁣󰁡󰁤󰁡 󰁵󰁮󰁯 󰁥󰁳 󰁥󰁬 󲀜󰁰󰁵󰁮󰁴󰁯 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡󲀝 󰁥󰁮 󰁥󰁬 󰁱󰁵󰁥 󰁳󰁥 󰁥󰁮󰁣󰁵󰁥󰁮󰁴󰁲󰁡󰁮 󰁤󰁯󰁮󰁤󰁥 󰁳󰁥 󰁯󰁢󰁳󰁥󰁲󰁶󰁡 󰁥󰁬 󰁦󰁥󰁮󰃳󰁭󰁥󰁮󰁯.

󰁍󰁡󰁲󰁣󰁯 󰁤󰁥 󰁒󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁉󰁮󰁥󰁲󰁣󰁩󰁡󰁬

U󰁮 󰁳󰁩󰁳󰁴󰁥󰁭󰁡, 󰁯 󰁭󰁡󰁲󰁣󰁯 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 󰁥󰁳 󰁡󰁱󰁵󰃩󰁬 󰁥󰁮 󰁤󰁯󰁮󰁤󰁥 󰁳󰁯󰁮 󰁶󰃡󰁬󰁩󰁤󰁡󰁳 󰁬󰁡󰁳 󰁬󰁥󰁹󰁥󰁳 󰁤󰁥 N󰁥󰁷󰁴󰁯󰁮; 󰁥󰁳󰁴󰁯 󰁥󰁳, 󰁤󰁯󰁮󰁤󰁥 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁭󰁯󰁳 󰁱󰁵󰁥 󰁵󰁮 󰁣󰁵󰁥󰁲󰁰󰁯 󰁬󰁩󰁢󰁲󰁥 󰁤󰁥 󰁦󰁵󰁥󰁲󰁺󰁡󰁳, 󰁳󰁩 󰁥󰁳󰁴󰃡 󰁩󰁮󰁩󰁣󰁩󰁡󰁬󰁭󰁥󰁮󰁴󰁥 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯, 󰁰󰁥󰁲󰁭󰁡󰁮󰁥󰁣󰁥 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯, 󰁹 󰁳󰁩 󰁥󰁳󰁴󰃡 󰁩󰁮󰁩󰁣󰁩󰁡󰁬󰁭󰁥󰁮󰁴󰁥 󰁣󰁯󰁮 󰁵󰁮󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤, 󰁭󰁡󰁮󰁴󰁩󰁥󰁮󰁥 󰁥󰁳󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤.

 

 

S󰁵󰁰󰁯󰁮󰁧󰁡 󰁱󰁵󰁥 󰁳󰁥 󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡 󰁡󰁬󰁧󰃺󰁮 󰁦󰁥󰁮󰃳󰁭󰁥󰁮󰁯 󰁦󰃭󰁳󰁩󰁣󰁯, 󰁱󰁵󰁥 󰁬󰁬󰁡󰁭󰁡󰁲󰁥󰁭󰁯󰁳 󰁥󰁶󰁥󰁮󰁴󰁯󰀬 󰁥󰁬 󰁣󰁵󰁡󰁬 󰁥󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯 󰁰󰁯󰁲 󰁡󰁬󰁧󰁵󰁩󰁥󰁮 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯 󰁥󰁮 󰁵󰁮 󰁭󰁡󰁲󰁣󰁯 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡. A󰁬 󰁤󰁥󰁣󰁩󰁲 󰁱󰁵󰁥 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁳󰁴󰁡 󲀜󰁥󰁮 󰁵󰁮 󰁭󰁡󰁲󰁣󰁯󲀝, 󰁳󰁩󰁧󰁮󰁩󰁦󰁩󰁣󰁡 󰁱󰁵󰁥 󰁥󰁳󰁴󰃡 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡󰁬 󰁯󰁲󰁩󰁧󰁥󰁮 󰁤󰁥 󰁥󰁳󰁥 󰁭󰁡󰁲󰁣󰁯. L󰁡 󰁵󰁢󰁩󰁣󰁡󰁣󰁩󰃳󰁮 󰁹 󰁴󰁩󰁥󰁭󰁰󰁯 󰁤󰁥󰁬 󰁥󰁶󰁥󰁮󰁴󰁯 󰁰󰁵󰁥󰁤󰁥󰁮 󰁳󰁥󰁲 󰁥󰁳󰁰󰁥󰁣󰁩󰁦󰁩󰁣󰁡󰁤󰁯󰁳 󰁰󰁯󰁲 󰁬󰁡󰁳 󰁣󰁵󰁡󰁴󰁲󰁯 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 ( 󰁸󰀬 ). L󰁯 󰁤󰁥󰁳󰁥󰁡󰁢󰁬󰁥 󰁥󰁳 󰁰󰁯󰁤󰁥󰁲 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁲 󰁬󰁡󰁳 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 󰁤󰁥 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁮 󰁵󰁮 󰁭󰁡󰁲󰁣󰁯 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 󰁡  󰁸󰀬 󰁹 , 󰁺󰀬 󰁴 ). 󰁬󰁡󰁳 󰁤󰁥 󰁯󰁴󰁲󰁯 󰁥󰁮 󰁵󰁮 󰁭󰁡󰁲󰁣󰁯 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥 󰁣󰁯󰁮 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁡 󰁵󰁮󰁩󰁦󰁯󰁲󰁭󰁥 󰁥󰁮 󰁣󰁯󰁭󰁰󰁡󰁲󰁡󰁣󰁩󰃳󰁮 󰁣󰁯󰁮 󰁥󰁬 󰁰󰁲󰁩󰁭󰁥󰁲 󰁭󰁡󰁲󰁣󰁯. 󰁭 󰁡󰁲󰁣󰁯. C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁥 󰁤󰁯󰁳 󰁭󰁡󰁲󰁣󰁯󰁳 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬󰁥󰁳 S 󰁹 S󰂴. E󰁬 󰁭󰁡󰁲󰁣󰁯 S󰂴 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥 󰁣󰁯󰁮 󰁵󰁮󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥, 󰁖, 󰁡 󰁬󰁯 󰁬󰁡󰁲󰁧󰁯 󰁤󰁥 󰁬󰁯󰁳 󰁥󰁪󰁥󰁳 󰁣󰁯󰁭󰁵󰁮󰁥󰁳 󰁸 󰁹 󰁸 󰂴 󰁤󰁯󰁮󰁤󰁥 󰁖 󰁳󰁥 󰁭󰁩󰁤󰁥 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 S. S󰁵󰁰󰁯󰁮󰁧󰁡 󰁱󰁵󰁥 󰁬󰁯󰁳 󰁯󰁲󰃭󰁧󰁥󰁮󰁥󰁳 󰁤󰁥 S 󰁹 S󰂴 󰁣󰁯󰁩󰁮󰁣󰁩󰁤󰁥󰁮 󰁥󰁮 󰁴 =0 󰁹 󰁱󰁵󰁥 󰁳󰁥 󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡 󰁵󰁮 󰁥󰁶󰁥󰁮󰁴󰁯 󰁥󰁮 󰁥󰁬 󰁰󰁵󰁮󰁴󰁯 󰁐 󰁥󰁮 󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 󰁥󰁮 󰁡󰁬󰁧󰃺󰁮 󰁩󰁮󰁳󰁴󰁡󰁮󰁴󰁥. U󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁮 S 󰁤󰁥󰁳󰁣󰁲󰁩󰁢󰁥 󰁥󰁬 󰁥󰁶󰁥󰁮󰁴󰁯 󰁣󰁯󰁮 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 󰁥󰁳󰁰󰁡󰁣󰁩󰁯󲀓󰁴󰁩󰁥󰁭󰁰󰁯 ( 󰁸󰀬  󰁸󰀬 󰁹 , 󰁺󰀬 󰁴 ), ), 󰁭󰁩󰁥󰁮󰁴󰁲󰁡󰁳 󰁱󰁵󰁥 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁮 S󰂴 󰁵󰁳󰁡 󰁬󰁡󰁳 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 󰁰󰁲󰁩󰁭󰁡󰁳 ( 󰁸󰂴󰀬 󰂴) 󰁰󰁡󰁲󰁡 󰁤󰁥󰁳󰁣󰁲󰁩󰁢󰁩󰁲 󰁥󰁬 󰁭󰁩󰁳󰁭󰁯 󰁥󰁶󰁥󰁮󰁴󰁯. C󰁯󰁭󰁯 󰁭󰁵󰁥󰁳󰁴󰁲󰁡 󰁬󰁡  󰁸󰂴󰀬 󰁹 󰂴󰂴,, 󰁺󰂴 󰀬  󰀬 󰁴 󰂴) 󰁧󰁥󰁯󰁭󰁥󰁴󰁲󰃭󰁡 󰁤󰁥 󰁬󰁡 󰁦󰁩󰁧󰁵󰁲󰁡, 󰁬󰁡󰁳 󰁣󰁯󰁲󰁲󰁥󰁳󰁰󰁯󰁮󰁤󰁥󰁮󰁣󰁩󰁡󰁳 󰁥󰁮󰁴󰁲󰁥 󰁥󰁳󰁴󰁡󰁳 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 󰁳󰁥 󰁥󰁳󰁣󰁲󰁩󰁢󰁥󰁮 󰁣󰁯󰁭󰁯: 

E󰁳󰁴󰁡󰁳 󰁳󰁯󰁮 󰁬󰁡󰁳 󰁥󰁣󰁵󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁤󰁥 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁣󰁩󰃳󰁮 󰁧󰁡󰁬󰁩󰁬󰁥󰁡󰁮󰁡 󰁤󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯󲀓󰁴󰁩󰁥󰁭󰁰󰁯. O󰁢󰁳󰁥󰁲󰁶󰁥 󰁱󰁵󰁥 󰁥󰁬 󰁴󰁩󰁥󰁭󰁰󰁯 󰁳󰁥 󰁳󰁵󰁰󰁯󰁮󰁥 󰁩󰁧󰁵󰁡󰁬 󰁥󰁮 󰁡󰁭󰁢󰁯󰁳 󰁭󰁡󰁲󰁣󰁯󰁳 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬󰁥󰁳; 󰁥󰁳 󰁤󰁥󰁣󰁩󰁲, 󰁤󰁥󰁮󰁴󰁲󰁯 󰁤󰁥 󰁬󰁡 󰁥󰁳󰁴󰁲󰁵󰁣󰁴󰁵󰁲󰁡 󰁤󰁥 󰁬󰁡 󰁭󰁥󰁣󰃡󰁮󰁩󰁣󰁡 󰁣󰁬󰃡󰁳󰁩󰁣󰁡, 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁲󰁥󰁬󰁯󰁪󰁥󰁳 󰁦󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁮 󰁡󰁬 󰁭󰁩󰁳󰁭󰁯 󰁲󰁩󰁴󰁭󰁯, 󰁣󰁵󰁡󰁬󰁱󰁵󰁩󰁥󰁲󰁡 󰁱󰁵󰁥 󰁳󰁥󰁡 󰁳󰁵 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤, 󰁤󰁥 󰁭󰁯󰁤󰁯 󰁱󰁵󰁥 󰁥󰁬 󰁴󰁩󰁥󰁭󰁰󰁯 󰁥󰁮 󰁥󰁬 󰁱󰁵󰁥 󰁳󰁥 󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡 󰁵󰁮 󰁥󰁶󰁥󰁮󰁴󰁯 󰁰󰁡󰁲󰁡 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁮 S 󰁥󰁳 󰁥󰁬 󰁭󰁩󰁳󰁭󰁯 󰁴󰁩󰁥󰁭󰁰󰁯 󰁰󰁡󰁲󰁡 󰁥󰁬 󰁭󰁩󰁳󰁭󰁯 󰁥󰁶󰁥󰁮󰁴󰁯 󰁥󰁮 S󰂴. S󰃳󰁬󰁯 󰁳󰁯󰁮 󰁳 󰁯󰁮 󰁶󰃡󰁬󰁩󰁤󰁡󰁳 󰁰󰁡󰁲󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁭󰁵󰁹 󰁰󰁥󰁱󰁵󰁥󰃱󰁡󰁳 󰁣󰁯󰁮 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺 󲀜󰁣󲀝. P󰁡󰁲󰁡 󰁥󰁬 󰁣󰁡󰁳󰁯 󰁤󰁥 󰁬󰁡󰁳 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳:

Ejercicio # 1 Verificar el principio de conservación del momento lineal, para observadores en diferentes marcos de referencia inercial.

E󰁳󰁴󰁡󰁭󰁯󰁳 󰁩󰁮󰁴󰁥󰁲󰁥󰁳󰁡󰁤󰁯󰁳 󰁥󰁮 󰁶󰁥󰁲󰁩󰁦󰁩󰁣󰁡󰁲 󰁥󰁬 󰁨󰁥󰁣󰁨󰁯 󰁤󰁥 󰁱󰁵󰁥 󰁳󰁩 󰁬󰁡󰁳 󰁬󰁥󰁹󰁥󰁳 󰁤󰁥 󰁬󰁡 M󰁥󰁣󰃡󰁮󰁩󰁣󰁡 󰁳󰁯󰁮 󰁶󰃡󰁬󰁩󰁤󰁡󰁳 󰁰󰁡󰁲󰁡 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬, 󰁴󰁡󰁭󰁢󰁩󰃩󰁮 󰁬󰁯 󰁳󰁯󰁮 󰁰󰁡󰁲󰁡 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁤󰁥󰁭󰃡󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬󰁥󰁳. E󰁮 󰁲󰁥󰁡󰁬󰁩󰁤󰁡󰁤 󰁥󰁳 󰁮󰁥󰁣󰁥󰁳󰁡󰁲󰁩󰁯 󰁣󰁯󰁮󰁦󰁩󰁲󰁭󰁡󰁲󰁬󰁯 󰃺󰁮󰁩󰁣󰁡󰁭󰁥󰁮󰁴󰁥 󰁰󰁡󰁲󰁡 󰁥󰁬 󰁰󰁲󰁩󰁮󰁣󰁩󰁰󰁩󰁯 󰁤󰁥 󰁣󰁯󰁮󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰃳󰁮 󰁤󰁥󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯 󰁬󰁩󰁮󰁥󰁡󰁬 󰁹 󰁰󰁡󰁲󰁡 󰁬󰁡 󰁤󰁥󰁦󰁩󰁮󰁩󰁣󰁩󰃳󰁮 󰁤󰁥 󰁦󰁵󰁥󰁲󰁺󰁡, 󰁹󰁡 󰁱󰁵󰁥 󰁬󰁡󰁳 󰁤󰁥󰁭󰃡󰁳 󰁬󰁥󰁹󰁥󰁳 󰁤󰁥 󰁬󰁡 M󰁥󰁣󰃡󰁮󰁩󰁣󰁡 󰁳󰁥 󰁤󰁥󰁲󰁩󰁶󰁡󰁮 󰁤󰁥 󰁥󰁳󰁡󰁳 󰁤󰁯󰁳. D󰁥󰁳󰁡󰁲󰁲󰁯󰁬󰁬󰁯: C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁥󰁭󰁯󰁳 󰁤󰁯󰁳 󰁰󰁡󰁲󰁴󰃭󰁣󰁵󰁬󰁡󰁳 󰁤󰁥 󰁭󰁡󰁳󰁡󰁳 󰁭 1 󰁹 󰁭2 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥󰁮 󰁡 󰁬󰁯 󰁬󰁡󰁲󰁧󰁯 󰁤󰁥󰁬 󰁥󰁪󰁥 󲀜O󰁘󲀝 󰁤󰁥 󰁵󰁮 󰁳󰁩󰁳󰁴󰁥󰁭󰁡 󰁤󰁥 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳, 󰁹 󰁳󰁥󰁡󰁮 󰁶1 󰁹 󰁶2 󰁳󰁵󰁳 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁭󰁥󰁤󰁩󰁤󰁡󰁳 󰁰󰁯󰁲 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 O, 󰁣󰁯󰁭󰁯 󰁳󰁥 󰁭󰁵󰁥󰁳󰁴󰁲󰁡 󰁥󰁮 󰁬󰁡 󰁦󰁩󰁧󰁵󰁲󰁡. E󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯 󰁬󰁩󰁮󰁥󰁡󰁬 󰁳󰁥 󰁤󰁥󰁦󰁩󰁮󰁥 󰁣󰁯󰁭󰁯 󰁥󰁬 󰁰󰁲󰁯󰁤󰁵󰁣󰁴󰁯 󰁤󰁥 󰁬󰁡 󰁭󰁡󰁳󰁡 󰁰󰁯󰁲 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 (󰁰=󰁭󰁶). S󰃭 󰁬󰁡󰁳 󰁦󰁵󰁥󰁲󰁺󰁡󰁳 󰁥󰁸󰁴󰁥󰁲󰁮󰁡󰁳 󰁱󰁵󰁥 󰁡󰁣󰁴󰃺󰁡󰁮 󰁳󰁯󰁢󰁲󰁥 󰁬󰁡󰁳 󰁰󰁡󰁲󰁴󰃭󰁣󰁵󰁬󰁡󰁳 󰁳󰁥 󰁡󰁮󰁵󰁬󰁡󰁮, 󰁬󰁡 󰁬󰁥󰁹 󰁤󰁥 󰁬󰁡 󰁣󰁯󰁮󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰃳󰁮 󰁤󰁥󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯 󰁲󰁥󰁱󰁵󰁩󰁥󰁲󰁥 󰁱󰁵󰁥:  p1 +  p 2 = m1  v1  + m2 v2 = cte P󰁡󰁲󰁡 󰁯󰁴󰁲󰁯 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬 O󰂴 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥 󰁲󰁥󰁬󰁡󰁴󰁩󰁶󰁡󰁭󰁥󰁮󰁴󰁥 󰁡 O 󰁡 󰁬󰁯 󰁬󰁡󰁲󰁧󰁯 󰁤󰁥 󰁤󰁥󰁬󰁬 󰁥󰁪󰁥 󲀜O󰁘󲀝 󰁣󰁯󰁭󰃺󰁮 󰁣󰁯󰁮 󰁵󰁮󰁡 󰁶󰁥 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥 V, 󰁶󰁥󰁲 󰁦󰁩󰁧󰁵󰁲󰁡, 󰁬󰁡󰁳 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁤󰁥 󰁭1 󰁹 󰁭2 󰁳󰁯󰁮: v´1 = v1 − V   ⇒  v1 = v´1 +V  v´2 = v2 − V    ⇒  v 2 = v´2 +V  V󰁯󰁬󰁶󰁩󰁥󰁮󰁤󰁯 󰁡 󰁣󰁡󰁬󰁣󰁵󰁬󰁡󰁲 󰁥󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯:  p1 +  p 2 = m1v1 + m2 v 2 = m1 (v´1 +V )  +   ⇒ m1v´1 + m2 v´2 = kte   m2 (v´2 +V ) = cte

 

P󰁯󰁲 󰁣󰁯󰁮󰁳󰁩󰁧󰁵󰁩󰁥󰁮󰁴󰁥 󰁡󰁭󰁢󰁯󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳 󰁣󰁯󰁮󰁳󰁴󰁡󰁴󰁡󰁮 󰁬󰁡 󰁣󰁯󰁮󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰃳󰁮 󰁣 󰁯󰁮󰁳󰁥󰁲󰁶󰁡󰁣󰁩󰃳󰁮 󰁤󰁥󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯 󰁬󰁩󰁮󰁥󰁡󰁬. Ejercicio # 2 Verificar la validez de la segunda ley de newton newton, newton, para observadores en diferentes marcos de referencia inercial.

V󰁥󰁡󰁭󰁯󰁳 󰁡󰁨󰁯󰁲󰁡 󰁬󰁡 󰁦󰁵󰁥󰁲󰁺󰁡 󰁭󰁥󰁤󰁩󰁤󰁡 󰁰󰁯󰁲 󰁬󰁯󰁳 󰁤󰁯󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳. T󰁥󰁮󰁥󰁭󰁯󰁳 󰁱󰁵󰁥: v´= v − V   ⇒     v = v´+V  A󰁨󰁯󰁲󰁡 󰁢󰁩󰁥󰁮, 󰁬󰁡 󰁡󰁣󰁥󰁬󰁥󰁲󰁡󰁣󰁩󰃳󰁮 󰁥󰁮 P 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 O 󰁹 󰁬󰁡 󰁡󰁣󰁥󰁬󰁥󰁲󰁡󰁣󰁩󰃳󰁮 󰁥󰁮 P 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 O󰂴   dv´ dv 󰁳󰁥 󰁤󰁥󰁦󰁩󰁮󰁥󰁮 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁩󰁶󰁡󰁭󰁥󰁮󰁴󰁥 󰁣󰁯󰁭󰁯: a  =   󰁹 a´=   dt  dt  dv d (v´+V ) dv´ dV  dv´ a= E󰁮󰁴󰁯󰁮󰁣󰁥󰁳 = =     + = = a´ dt  dt  dt  dt  dt  D󰁥 󰁡󰁣󰁵󰁥󰁲󰁤󰁯 󰁡 󰁬󰁡 󰁥󰁸󰁰󰁲󰁥󰁳󰁩󰃳󰁮 󰁡󰁮󰁴󰁥󰁲󰁩󰁯󰁲, 󲀜O󲀝 󰁹 󲀜O󰂴󲀝 󰁭󰁩󰁤󰁥󰁮 󰁬󰁡 󰁭󰁩󰁳󰁭󰁡 󰁡󰁣󰁥󰁬󰁥󰁲󰁡󰁣󰁩󰃳󰁮 󰁰󰁯󰁲 󰁥󰁮󰁤󰁥 󰁭󰁩󰁤󰁥󰁮 󰁬󰁡 󰁭󰁩󰁭󰁡 󰁦󰁵󰁥󰁲󰁺󰁡 󰁳󰁯󰁢󰁲󰁥 󰁬󰁡 󰁰󰁡󰁲󰁴󰃭󰁣󰁵󰁬󰁡. L󰁡 󰁦󰁵󰁥󰁲󰁺󰁡 󰁡󰁬 󰁩󰁧󰁵󰁡󰁬 󰁱󰁵󰁥 󰁬󰁡 󰁡󰁣󰁥󰁬󰁥󰁲󰁡󰁣󰁩󰃳󰁮 󰁴󰁩󰁥󰁮󰁥 󰁥󰁬 󰁭󰁩󰁳󰁭󰁯 󰁶󰁡󰁬󰁯󰁲 󰁥󰁮 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁳󰁩󰁳󰁴󰁥󰁭󰁡󰁳 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬󰁥󰁳, 󰁬󰁡󰁳 󰁭󰁡󰁧󰁮󰁩󰁴󰁵󰁤󰁥󰁳 󰁱󰁵󰁥 󰁣󰁵󰁭󰁰󰁬󰁥󰁮 󰁥󰁳󰁴󰁡 󰁰󰁲󰁯󰁰󰁩󰁥󰁤󰁡󰁤 󰁲󰁥󰁣󰁩󰁢󰁥󰁮 󰁥󰁬 󰁮󰁯󰁭󰁢󰁲󰁥 󰁤󰁥 󰁩󰁮󰁶󰁡󰁲󰁩󰁡󰁮󰁴󰁥󰁳 󰁤󰁥 G󰁡󰁬󰁩󰁬󰁥󰁯. E󰁬 󰁨󰁥󰁣󰁨󰁯 󰁤󰁥 󰁱󰁵󰁥 󰁴󰁯󰁤󰁡󰁳 󰁴 󰁯󰁤󰁡󰁳 󰁬󰁡󰁳 󰁬󰁥󰁹󰁥󰁳 󰁤󰁥 󰁬󰁡 M󰁥󰁣󰃡󰁮󰁩󰁣󰁡 󰁤󰁥󰁢󰁥󰁮 󰁳󰁥󰁲 󰁬󰁡󰁳 󰁭󰁩󰁳󰁭󰁡󰁳 󰁰󰁡󰁲󰁡 󰁴󰁯󰁤󰁯󰁳 󰁬󰁯󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳 󰁩󰁮󰁥󰁲󰁣󰁩󰁡󰁬󰁥󰁳 󰁣󰁯󰁮󰁳󰁴󰁩󰁴󰁵󰁹󰁥 󰁥󰁬 󰁰󰁲󰁩󰁮󰁣󰁩󰁰 󰁰󰁲󰁩󰁮󰁣󰁩󰁰󰁩󰁯 󰁩󰁯 󰁣󰁬󰃡󰁳󰁩󰁣󰁯 󰁤󰁥 󰁬󰁡 R󰁥󰁬󰁡󰁴󰁩󰁶󰁩󰁤󰁡󰁤. 󰁔󰁡󰁲󰁥󰁡1󰀭󰁐󰁲󰁯󰁢󰁬󰁥󰁭󰁡1. L󰁡 󰁥󰁣󰁵󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁯󰁮󰁤󰁡 󰁤󰁥 󰁵󰁮󰁡 󰁯󰁮󰁤󰁡 󰁤󰁥 󰁰󰁲󰁯󰁰󰁡󰁧󰁡󰁣󰁩󰃳󰁮 󰁥󰁬󰃩󰁣󰁴󰁲󰁩󰁣󰁡 󰁰󰁬󰁡󰁮󰁡 󰁥󰁮 󰁬󰁡 󰁤󰁩󰁲󰁥󰁣󰁣󰁩󰃳󰁮 󰁸 󰁥󰁮 󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 2

󰁥󰁳:

∂  E  2

∂ x

2

=

1 ∂  E  2

c

2

. D󰁥󰁭󰁵󰁥󰁳󰁴󰁲󰁥 󰁱󰁵󰁥 󰁬󰁡 󰁥󰁣󰁵󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁯󰁮󰁤󰁡 󰁮󰁯 󰁥󰁳 󰁩󰁮󰁶󰁡󰁲󰁩󰁡󰁮󰁴󰁥 󰁦󰁲󰁥󰁮󰁴󰁥 󰁡 󰁵󰁮󰁡 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 G󰁡󰁬󰁩󰁬󰁥󰁯.

∂t 

󰁔󰁡󰁲󰁥󰁡1󰀭󰁐󰁲󰁯󰁢󰁬󰁥󰁭󰁡2. C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁥 󰁤󰁯󰁳 󰁰󰁥󰁲󰁳󰁯󰁮󰁡󰁳 󰁱󰁵󰁥 󰁳󰁥 󰁥󰁮󰁣󰁵󰁥󰁮󰁴󰁲󰁡󰁮 󰁡 󰁬󰁡 󰁯󰁲󰁩󰁬󰁬󰁡 󰁤󰁥 󰁵󰁮 󰁲󰃭󰁯 󰁣󰁵󰁹󰁯 󰁡󰁮󰁣󰁨󰁯 󰁥󰁳 D, 󰁥󰁬 󰁡󰁧󰁵󰁡 󰁤󰁥 󰁲󰁩󰁯 󰁲 󰁩󰁯

󰁴󰁩󰁥󰁮󰁥 󰁵󰁮󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁣󰁯󰁮󰁳󰁴󰁡󰁮󰁴󰁥 V󰁯, 󰁣󰁡󰁤󰁡 󰁵󰁮󰁡 󰁤󰁥 󰁬󰁡󰁳 󰁰󰁥󰁲󰁳󰁯󰁮󰁡󰁳 󰁤󰁩󰁳󰁰󰁯󰁮󰁥 󰁤󰁥 󰁵󰁮󰁡 󰁬󰁡󰁮󰁣󰁨󰁡; 󰁡󰁤󰁥󰁭󰃡󰁳 󰁡󰁭󰁢󰁡󰁳 󰁬󰁡󰁮󰁣󰁨󰁡󰁳 󰁣󰁵󰁥󰁮󰁴󰁡󰁮 󰁣󰁯󰁮 󰁵󰁮 󰁭󰁯󰁴󰁯󰁲 󰁱󰁵󰁥 󰁬󰁡󰁳 󰁤󰁥󰁳󰁰󰁬󰁡󰁺󰁡 󰁣󰁯󰁮 󰁬󰁡 󰁭󰁩󰁳󰁭󰁡 󰁲󰁡󰁰󰁩󰁤󰁥󰁺 V. D󰁥󰁳󰁩󰁧󰁮󰁥 󰁡 󰁣󰁡󰁤󰁡 󰁵󰁮󰁡 󰁤󰁥 󰁬󰁡󰁳 󰁬󰁡󰁮󰁣󰁨󰁡󰁳 󰁰󰁯󰁲 A 󰁹 󰁰󰁯󰁲 B. L󰁡󰁳 󰁤󰁯󰁳 󰁰󰁥󰁲󰁳󰁯󰁮󰁡󰁳 󰁲󰁥󰁡󰁬󰁩󰁺󰁡󰁮 󰁵󰁮󰁡 󰁣󰁯󰁭󰁰󰁥󰁴󰁥󰁮󰁣󰁩󰁡 󰁰󰁡󰁲󰁡 󰁶󰁥󰁲 󰁱󰁵󰁩󰁥󰁮 󰁴󰁡󰁲󰁤󰁡 󰁭󰁥󰁮󰁯󰁳 󰁴󰁩󰁥󰁭󰁰󰁯 󰁥󰁮 󰁲󰁥󰁣󰁯󰁲󰁲󰁥󰁲 󰁤󰁥 󰁩󰁤󰁡 󰁹 󰁶󰁵󰁥󰁬󰁴󰁡 󰁬󰁡 󰁤󰁩󰁳󰁴󰁡󰁮󰁣󰁩󰁡 D. L󰁯󰁳 󰁲󰁥󰁣󰁯󰁲󰁲󰁩󰁤󰁯󰁳 󰁰󰁲󰁯󰁰󰁵󰁥󰁳󰁴󰁯󰁳 󰁳󰁯󰁮 󰁬󰁯󰁳 󰁳󰁩󰁧󰁵󰁩󰁥󰁮󰁴󰁥󰁳: 1.  C󰁲󰁵󰁺󰁡󰁲 󰁥󰁬 󰁲󰃭󰁯 󰁨󰁡󰁳󰁴󰁡 󰁵󰁮 󰁰󰁵󰁮󰁴󰁯 󰁯󰁰󰁵󰁥󰁳󰁴󰁯 󰁡󰁬 󰁰󰁵󰁮󰁴󰁯 󰁤󰁥 󰁰󰁡󰁲󰁴󰁩󰁤󰁡, 󰁤󰁥 󰁭󰁡󰁮󰁥󰁲󰁡 󰁱󰁵󰁥 󰁥󰁬 󰁶󰁥󰁣󰁴󰁯󰁲 󰁲󰁥󰁳󰁵󰁬󰁴󰁡󰁮󰁴󰁥 󰁤󰁥 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁡󰁮󰁣󰁨󰁡 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁳󰁥󰁡 󰁰󰁥󰁲󰁰󰁥󰁮󰁤󰁩󰁣󰁵󰁬󰁡󰁲 󰁡󰁬 󰁶󰁥󰁣󰁴󰁯󰁲 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 V󰁯, 󰁱󰁵󰁥 󰁲󰁥󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡󰁳 󰁡󰁧󰁵󰁡󰁳 󰁤󰁥󰁬 󰁲󰃭󰁯. L󰁯 󰁱󰁵󰁥 󰁥󰁱󰁵󰁩󰁶󰁡󰁬󰁥 󰁡 󰁣󰁲󰁵󰁺󰁡󰁲 󰁥󰁬 󰁲󰃭󰁯 󰁤󰁥 󰁩󰁤󰁡 󰁹 󰁶󰁵󰁥󰁬󰁴󰁡 󰁶 󰁵󰁥󰁬󰁴󰁡 󰁹 󰁱󰁵󰁥 󰁥󰁬 󰁶󰁥󰁣󰁴󰁯󰁲 󰁲󰁥󰁳󰁵󰁬󰁴󰁡󰁮󰁴󰁥 󰁤󰁥 󰁬󰁡 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁬󰁡󰁮󰁣󰁨󰁡 󰁳󰁩󰁥󰁭󰁰󰁲󰁥 󰁳󰁩󰁧󰁡 󰁵󰁮󰁡 󰁤󰁩󰁲󰁥󰁣󰁣󰁩󰃳󰁮 󰁰󰁥󰁲󰁰󰁥󰁮󰁤󰁩󰁣󰁵󰁬󰁡󰁲 󰁡󰁬 󰁶󰁥󰁣󰁴󰁯󰁲 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤 󰁤󰁥 󰁬󰁡 󰁣󰁯󰁲󰁲󰁩󰁥󰁮󰁴󰁥 󰁤󰁥󰁬 󰁲󰃭󰁯. (󰁬󰁡󰁮󰁣󰁨󰁡 A) 2.  R󰁥󰁣󰁯󰁲󰁲󰁥󰁲 󰁬󰁡 󰁤󰁩󰁳󰁴󰁡󰁮󰁣󰁩󰁡 D 󰁤󰁥 󰁩󰁤󰁡 󰁹 󰁶󰁵󰁥󰁬󰁴󰁡, 󰁰󰁥󰁲󰁯 󰁳󰁩󰁧󰁵󰁩󰁥󰁮󰁤󰁯 󰁬󰁡 󰁤󰁩󰁲󰁥󰁣󰁣󰁩󰃳󰁮 󰁤󰁥 󰁬󰁡 󰁣󰁯󰁲󰁲󰁩󰁥󰁮󰁴󰁥 󰁤󰁥󰁬 󰁲󰃭󰁯 󰁹 󰁬󰁵󰁥󰁧󰁯 󰁲󰁥󰁧󰁲󰁥󰁳󰁡󰁲 󰁥󰁮 󰁬󰁡 󰁭󰁩󰁳󰁭󰁡 󰁤󰁩󰁲󰁥󰁣󰁣󰁩󰃳󰁮. (󰁬󰁡󰁮󰁣󰁨󰁡 B) C󰁯󰁭󰁯 󰁶󰁥󰁳 󰁥󰁮 󰁡󰁭󰁢󰁯󰁳 󰁣󰁡󰁳󰁯󰁳 󰁤󰁥󰁢󰁥 󰁲󰁥󰁣󰁯󰁲󰁲󰁥󰁲󰁳󰁥 2D. 󰂿C󰁵󰃡󰁬 󰁤󰁥 󰁬󰁡󰁳 󰁤󰁯󰁳 󰁬󰁡󰁮󰁣󰁨󰁡󰁳 󰁴󰁡󰁲󰁤󰁡 󰁭󰁥󰁮󰁯󰁳 󰁴󰁩󰁥󰁭󰁰󰁯 󰁥󰁮 󰁥󰁳󰁴󰁡󰁲 󰁤󰁥 󰁲󰁥󰁧󰁲󰁥󰁳󰁯? E󰁮󰁣󰁵󰁥󰁮󰁴󰁲󰁥 󰁬󰁡 󰁲󰁥󰁬󰁡󰁣󰁩󰃳󰁮 󰁤󰁥 󰁬󰁯󰁳 󰁴󰁩󰁥󰁭󰁰󰁯󰁳 󰁤󰁥󰁬 󰁲󰁥󰁣󰁯󰁲󰁲󰁩󰁤󰁯, 󰁥󰁳 󰁤󰁥󰁣󰁩󰁲 󰁴A / 󰁴B.

 

SIMULTANEIDAD Y RELATIVIDAD DE TIEMPO

Ya que ɣ siempre es mayor que 1, este resultado dice que el intervalo ∆t medido por un observador que se mueve respecto a un reloj es más largo que el intervalo ∆t p medido por un observador en reposo respecto res pecto al mismo reloj. Este efecto se conoce como dilatación del tiempo.

Ejercicio # 3 Suponga que una nave va a viajar a una estrella situada a 10 años luz de la Tierra. La velocidad de la nave es de de 0.8c , muy próxima a la v velocidad elocidad de la luz. llame “O” al sistema de referencia de la Tierra y astronautas. ronautas. y “0´” “0´” al de los ast ronautas. ¿Cuánto tiempo dura el viaje visto desde la tierra? ¿Cuánto tiempo dura el viaje, según los astronautas?

 

∆T O =

∆T P =

 Dis tan cia Velocidad 

∆T O γ  

=

10año * luz   = 12.5años (Tiempo según observador en la tierra) 0.8año * luz / año

2

2

 

= ∆T O 1 − v  / c   = 12.5años 1 − 0.8

2

= 7.5años (Tiempo según astronautas) astronautas)

http://www.ugr.es/~jillana/SR/sr4.pdf Lectura Recomendada, Paradoja de Gemelos http://www.ugr.es/~jillana/SR/sr4.pdf

CONTRACCIÓN DE LONGITUD L󰁡 󰁤󰁩󰁳󰁴󰁡󰁮󰁣󰁩󰁡 󰁭󰁥󰁤󰁩󰁤󰁡 󰁥󰁮󰁴󰁲󰁥 󰁤󰁯󰁳 󰁰󰁵󰁮󰁴󰁯󰁳 󰁥󰁮 󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 󰁴󰁡󰁭󰁢󰁩󰃩󰁮 󰁤󰁥󰁰󰁥󰁮󰁤󰁥 󰁤󰁥󰁬 󰁭󰁡󰁲󰁣󰁯 󰁤󰁥 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡 󰁤󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲. L󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 󰁣󰁡󰁲󰁡󰁣󰁴󰁥󰁲󰃭󰁳󰁴󰁩󰁣󰁡 L󰁰 󰁤󰁥 󰁵󰁮 󰁯󰁢󰁪󰁥󰁴󰁯 󰁥󰁳 󰁬󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 󰁭󰁥󰁤󰁩󰁤󰁡 󰁰󰁯󰁲 󰁡󰁬󰁧󰁵󰁩󰁥󰁮 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡󰁬 󰁯󰁢󰁪󰁥󰁴󰁯.

Ejercicio Ejercicio # 4 Una nave espacial pasa volando cerca de la Tierra con una rapidez de 0.990c. Un miembro de la tripulación a bordo de la nave mide la longitud de ésta, y obtiene un valor de 400 m. ¿Qué longitud miden los observadores que se hallan en la Tierra?

L󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 󰁤󰁥 400 󰁭 󰁤󰁥 󰁬󰁡 󰁮󰁡󰁶󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁡󰁬 󰁥󰁳 󰁬󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 󰁰󰁲󰁯󰁰󰁩󰁡 L0 󰁰󰁯󰁲󰁱󰁵󰁥 󰁨󰁡 󰁳󰁩󰁤󰁯 󰁭󰁥󰁤󰁩󰁤󰁡 󰁥󰁮 󰁥󰁬 󰁭󰁡󰁲󰁣󰁯 󰁤󰁯󰁮󰁤󰁥 󰁬󰁡 󰁮󰁡󰁶󰁥 󰁥󰁳󰁴󰃡 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯. S󰁥 󰁢󰁵󰁳󰁣󰁡 󰁬󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 L 󰁭󰁥󰁤󰁩󰁤󰁡 󰁰󰁯󰁲 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳 󰁳󰁩󰁴󰁵󰁡󰁤󰁯󰁳 󰁥󰁮 󰁬󰁡 T󰁩󰁥󰁲󰁲󰁡.

 

 L =

 L0 γ  

2

=  Lo 1 − v  / c

2

 

= 400 m   1 − 0.990

2

= 56.43m  

󰁔󰁡󰁲󰁥󰁡1󰀭󰁐󰁲󰁯󰁢󰁬󰁥󰁭󰁡3 M󰁥󰁤󰁩󰁤󰁡 󰁰󰁯󰁲 󰁵󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁱󰁵󰁥 󰁥󰁳󰁴󰃡 󰁥󰁮 󰁬󰁡 T󰁩󰁥󰁲󰁲󰁡, 󰁵󰁮󰁡 󰁰󰁩󰁳󰁴󰁡 󰁴󰁥󰁲󰁲󰁥󰁳󰁴󰁲󰁥 󰁰󰁡󰁲󰁡 󰁮󰁡󰁶󰁥󰁳 󰁥󰁳󰁰󰁡󰁣󰁩󰁡󰁬󰁥󰁳 󰁴󰁩󰁥󰁮󰁥

󰁵󰁮󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 󰁤󰁥 3600 󰁭. 󰁡) 󰂿C󰁵󰃡󰁬 󰁥󰁳 󰁬󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤 󰁤󰁥 󰁬󰁡 󰁰󰁩󰁳󰁴󰁡 󰁭󰁥󰁤󰁩󰁤󰁡 󰁰󰁯󰁲 󰁥󰁬 󰁰󰁩󰁬󰁯󰁴󰁯 󰁤󰁥 󰁵󰁮󰁡 󰁮󰁡󰁶󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁡󰁬 󰁱󰁵󰁥 󰁰󰁡󰁳󰁡 󰁶󰁯󰁬󰁡󰁮󰁤󰁯 󰁣󰁥󰁲󰁣󰁡 󰁤󰁥 󰁥󰁬󰁬󰁡 󰁣󰁯󰁮 󰁵󰁮󰁡 󰁲󰁡󰁰󰁩󰁤󰁥󰁺 󰁤󰁥 4.00󰁸107 󰁭/󰁳 󰁣󰁯󰁮 󰁲󰁥󰁳󰁰󰁥󰁣󰁴󰁯 󰁡 󰁬󰁡 T󰁩󰁥󰁲󰁲󰁡? 󰁢) U󰁮 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁱󰁵󰁥 󰁳󰁥 󰁨󰁡󰁬󰁬󰁡 󰁥󰁮 󰁬󰁡 T󰁩󰁥󰁲󰁲󰁡 󰁭󰁩󰁤󰁥 󰁥󰁬 󰁩󰁮󰁴󰁥󰁲󰁶󰁡󰁬󰁯 󰁤󰁥 󰁴󰁩󰁥󰁭󰁰󰁯 󰁥󰁮󰁴󰁲󰁥 󰁥󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯 󰁥󰁮 󰁱󰁵󰁥 󰁬󰁡 󰁮󰁡󰁶󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁡󰁬 󰁥󰁳󰁴󰃡 󰁤󰁩󰁲󰁥󰁣󰁴󰁡 󰁭󰁥󰁮󰁴󰁥 󰁡󰁲󰁲󰁩󰁢󰁡 󰁤󰁥 󰁵󰁮 󰁥󰁸󰁴󰁲󰁥󰁭󰁯 󰁤󰁥 󰁬󰁡 󰁰󰁩󰁳󰁴󰁡 󰁹 󰁥󰁬 󰁭󰁯󰁭󰁥󰁮󰁴󰁯 󰁥󰁮 󰁱󰁵󰁥 󰁥󰁳󰁴󰃡 󰁤󰁩󰁲󰁥󰁣󰁴󰁡󰁭󰁥󰁮󰁴󰁥 󰁡󰁲󰁲󰁩󰁢󰁡 󰁤󰁥󰁬 󰁯󰁴󰁲󰁯 󰁥󰁸󰁴󰁲󰁥󰁭󰁯. 󰂿Q󰁵󰃩 󰁲󰁥󰁳󰁵󰁬󰁴󰁡󰁤󰁯 󰁯󰁢󰁴󰁩󰁥󰁮󰁥? 󰁣) E󰁬 󰁰󰁩󰁬󰁯󰁴󰁯 󰁤󰁥 󰁬󰁡 󰁮󰁡󰁶󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁡󰁬 󰁭󰁩󰁤󰁥 󰁥󰁬 󰁴󰁩󰁥󰁭󰁰󰁯 󰁱󰁵󰁥 󰁬󰁥 󰁴󰁯󰁭󰁡 󰁶󰁩󰁡󰁪󰁡󰁲 󰁤󰁥 󰁵󰁮 󰁥󰁸󰁴󰁲󰁥󰁭󰁯 󰁤󰁥 󰁬󰁡 󰁰󰁩󰁳󰁴󰁡 󰁡󰁬 󰁯󰁴󰁲󰁯. 󰁯󰁴󰁲 󰁯. 󰂿Q󰁵󰃩 󰁶󰁡󰁬󰁯󰁲 󰁯󰁢󰁴󰁩󰁥󰁮󰁥? EXPOSICION 1: TRANSFORMACIÓNES DE LORENTZ

S󰁵󰁰󰁯󰁮󰁧󰁡 󰁱󰁵󰁥 󰁤󰁯󰁳 󰁥󰁶󰁥󰁮󰁴󰁯󰁳 󰁳󰁥 󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡󰁮 󰁥󰁮 󰁬󰁯󰁳 󰁰󰁵󰁮󰁴󰁯󰁳 P 󰁹 Q 󰁹 󰁳󰁯󰁮 󰁲󰁥󰁰󰁯󰁲󰁴󰁡󰁤󰁯󰁳 󰁰󰁯󰁲 󰁤󰁯󰁳 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲󰁥󰁳, 󰁵󰁮󰁯 󰁥󰁮 󰁲󰁥󰁰󰁯󰁳󰁯 󰁥󰁮 󰁵󰁮 󰁭󰁡󰁲󰁣󰁯 S 󰁹 󰁯󰁴󰁲󰁯 󰁥󰁮 󰁵󰁮 󰁭󰁡󰁲󰁣󰁯 S󰂴 󰁱󰁵󰁥 󰁳󰁥 󰁭󰁵󰁥󰁶󰁥 󰁡 󰁬󰁡 󰁤󰁥󰁲󰁥󰁣󰁨󰁡 󰁣󰁯󰁮 󰁵󰁮󰁡 󰁲󰁡󰁰󰁩󰁤󰁥󰁺 󰁶, 󰁣󰁯󰁭󰁯 󰁳󰁥 󰁶󰁥 󰁥󰁮 󰁬󰁡 󰁦󰁩󰁧󰁵󰁲󰁡. E󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁮 S 󰁲󰁥󰁰󰁯󰁲󰁴󰁡 󰁥󰁬 󰁥󰁶󰁥󰁮󰁴󰁯 󰁣󰁯󰁮 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 󰁤󰁥 󰁥󰁳󰁰󰁡󰁣󰁩󰁯– 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 –󰁴󰁩󰁥󰁭󰁰󰁯 (󰁸, 󰁹, 󰁺, 󰁴), 󰁭󰁩󰁥󰁮󰁴󰁲󰁡󰁳 󰁱󰁵󰁥 󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲 󰁥󰁮 S󰂴 󰁲󰁥󰁰󰁯󰁲󰁴󰁡 󰁥󰁬 󰁭󰁩󰁳󰁭󰁯 󰁥󰁶󰁥󰁮󰁴󰁯 󰁣󰁯󰁮 󰁬󰁡󰁳 󰁣󰁯󰁯󰁲󰁤󰁥󰁮󰁡󰁤󰁡󰁳 (󰁸󰂴, 󰁹󰂴, 󰁺󰂴, 󰁴󰂴). L󰁡󰁳 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁣󰁩󰁯󰁮󰁥󰁳 G󰁡󰁬󰁩󰁬󰁥󰁡󰁮󰁡󰁳 󰁰󰁲󰁥󰁤󰁩󰁣󰁥󰁮 󰁱󰁵󰁥, 󰁬󰁡 󰁤󰁩󰁳󰁴󰁡󰁮󰁣󰁩󰁡 󰁥󰁮󰁴󰁲󰁥 󰁬󰁯󰁳 󰁤󰁯󰁳 󰁰󰁵󰁮󰁴󰁯󰁳 󰁥󰁮 󰁥󰁬 󰁥󰁳󰁰󰁡󰁣󰁩󰁯 󰁥󰁮 󰁥󰁬 󰁱󰁵󰁥 󰁳󰁥 󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡󰁮 󰁬󰁯󰁳 󰁥󰁶󰁥󰁮󰁴󰁯󰁳 󰁮󰁯 󰁤󰁥󰁰󰁥󰁮󰁤󰁥 󰁤󰁥󰁬 󰁭󰁯󰁶󰁩󰁭󰁩󰁥󰁮󰁴󰁯 󰁤󰁥󰁬 󰁯󰁢󰁳󰁥󰁲󰁶󰁡󰁤󰁯󰁲: ∆󰁸 = ∆󰁸󰂴. C󰁯󰁭󰁯 󰁬󰁡 󰁰󰁲󰁥󰁤󰁩󰁣󰁣󰁩󰃳󰁮 󰁥󰁳 󰁣󰁯󰁮󰁴󰁲󰁡󰁤󰁩󰁣󰁴󰁯󰁲󰁩󰁡 󰁣󰁯󰁮 󰁬󰁡 󰁮󰁯󰁣󰁩󰃳󰁮 󰁤󰁥 󰁣󰁯󰁮󰁴󰁲󰁡󰁣󰁣󰁩󰃳󰁮 󰁤󰁥 󰁬󰁡 󰁬󰁯󰁮󰁧󰁩󰁴󰁵󰁤, 󰁬󰁡 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁣󰁩󰃳󰁮 󰁧󰁡󰁬󰁩󰁬󰁥󰁡󰁮󰁡 󰁮󰁯 󰁥󰁳 󰁶󰃡󰁬󰁩󰁤󰁡 󰁣󰁵󰁡󰁮󰁤󰁯 󰁶 󰁳󰁥 󰁡󰁰󰁲󰁯󰁸󰁩󰁭󰁡 󰁡 󰁬󰁡 󰁲󰁡󰁰󰁩󰁤󰁥󰁺 󰁤󰁥 󰁬󰁡 󰁬󰁵󰁺. L󰁡󰁳 󰁥󰁣󰁵󰁡󰁣󰁩󰁯󰁮󰁥󰁳 󰁤󰁥 󰁴󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰁣󰁩󰃳󰁮 󰁣󰁯󰁲󰁲󰁥󰁣󰁴󰁡󰁳 󰁱󰁵󰁥 󰁡󰁰󰁬󰁩󰁣󰁡󰁮 󰁰󰁡󰁲󰁡 󰁴󰁯󰁤󰁡󰁳 󰁬󰁡󰁳 󰁶󰁥󰁬󰁯󰁣󰁩󰁤󰁡󰁤󰁥󰁳 󰁥󰁮 󰁥󰁮 󰁥󰁬 󰁩󰁮󰁴󰁥󰁲󰁶󰁡󰁬󰁯 0