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Консультация № 193850
08.11.2018, 20:55
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Здравствуйте! Прошу помощи в следующем вопросе:
Во сколько раз изменилась потенциальная энергия гравитационного
взаимодействия двух одинаковых соприкасающихся однородных шаров, если
радиус одного из них: 1) уменьшили в 1,5 раза; 2) увеличили в 1,5 раза?
Во сколько раз изменилась потенциальная энергия гравитационного
взаимодействия двух одинаковых соприкасающихся однородных шаров, если
радиус одного из них: 1) уменьшили в 1,5 раза; 2) увеличили в 1,5 раза?
Обсуждение
08.11.2018, 21:08
общий
Адресаты:
У Вас есть собственные соображения по решению этой задачи?
Об авторе:
Facta loquuntur.
Facta loquuntur.
09.11.2018, 10:13
общий
это ответ
Здравствуйте, li.a!
Пусть два одинаковых соприкасающихся однородных шара имеют радиусы
Если плотность вещества шаров обозначить через 
массы -- через 
то
Будем считать, что сила гравитационного взаимодействия между сферически симметричными телами эквивалентна силе взаимодействия между точечными телами таких же масс. Тогда потенциальная энергия гравитационного взаимодействия шаров (при выборе нулевого значения на бесконечности) составляет
а) Пусть радиус одного из шаров (например, первого) уменьшили в
раза. Тогда
При этом
то есть потенциальная энергия гравитационного взаимодействия двух шаров, оставаясь отрицательной, уменьшилась по абсолютной величине в
раза.
б) Пусть радиус одного из шаров (например, первого) увеличили в раза. Тогда
При этом
то есть потенциальная энергия гравитационного взаимодействия двух шаров, оставаясь отрицательной, увеличилась по абсолютной величине в
раза.
Пусть два одинаковых соприкасающихся однородных шара имеют радиусы
Если плотность вещества шаров обозначить через массы -- через тоБудем считать, что сила гравитационного взаимодействия между сферически симметричными телами эквивалентна силе взаимодействия между точечными телами таких же масс. Тогда потенциальная энергия гравитационного взаимодействия шаров (при выборе нулевого значения на бесконечности) составляет
а) Пусть радиус одного из шаров (например, первого) уменьшили в
раза. ТогдаПри этом
то есть потенциальная энергия гравитационного взаимодействия двух шаров, оставаясь отрицательной, уменьшилась по абсолютной величине в
раза.б) Пусть радиус одного из шаров (например, первого) увеличили в
раза. ТогдаПри этом
то есть потенциальная энергия гравитационного взаимодействия двух шаров, оставаясь отрицательной, увеличилась по абсолютной величине в
раза.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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