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Консультация № 190884
17.04.2017, 00:45
0.00 руб.
17.04.2017, 23:19
1
1
1
Здравствуйте,уважаемые эксперты! У меня возникли сложности со следующим вопросом:
По результатам геофизических исследований установлено, что за последние [$964$]=40 лет продолжительность суток на Земле увеличилась на [$916$]T=0,001 c (замедление осевого вращения Земли обусловлено, в первую очередь, действием приливов). Вычислите по этим данным угловое ускорение [$949$] Земли. Считая вращение Земли равнозамедленным, определите, через сколько миллионов лет продолжительность суток на Земле увеличится на 1 минуту?
По результатам геофизических исследований установлено, что за последние [$964$]=40 лет продолжительность суток на Земле увеличилась на [$916$]T=0,001 c (замедление осевого вращения Земли обусловлено, в первую очередь, действием приливов). Вычислите по этим данным угловое ускорение [$949$] Земли. Считая вращение Земли равнозамедленным, определите, через сколько миллионов лет продолжительность суток на Земле увеличится на 1 минуту?
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Обсуждение
17.04.2017, 23:45
общий
это ответ
Здравствуйте, moonfox!
Сразу отметим, что с такими малыми относительными изменениями нужно использовать приближение [$916$](1/T)=-(1/T)[$183$][$916$]T/T=-[$916$]T/T2
Таким образом с периодом оборота T=8,616[$183$]104 с
и изменением этого периода на [$916$]T=10-3 с
за время [$964$]=1,262[$183$]109 с
угловое ускорение равно [$949$]=[$916$](2[$960$]/T)/[$964$]=-2[$960$][$916$]T/T2[$964$]=-6.705[$183$]10-22 рад/с2
по второй части вопроса всё элементарно - принимаем изменения периода за линейный процесс (поскольку отклонение от линейности исчезающе мало, что и было использовано в вышеприведённом приближении)
[$964$]2=[$964$][$916$]T2/[$916$]T=40лет[$183$]60с/0,001с=2,4[$183$]106 лет=2,4 миллиона лет
Сразу отметим, что с такими малыми относительными изменениями нужно использовать приближение [$916$](1/T)=-(1/T)[$183$][$916$]T/T=-[$916$]T/T2
Таким образом с периодом оборота T=8,616[$183$]104 с
и изменением этого периода на [$916$]T=10-3 с
за время [$964$]=1,262[$183$]109 с
угловое ускорение равно [$949$]=[$916$](2[$960$]/T)/[$964$]=-2[$960$][$916$]T/T2[$964$]=-6.705[$183$]10-22 рад/с2
по второй части вопроса всё элементарно - принимаем изменения периода за линейный процесс (поскольку отклонение от линейности исчезающе мало, что и было использовано в вышеприведённом приближении)
[$964$]2=[$964$][$916$]T2/[$916$]T=40лет[$183$]60с/0,001с=2,4[$183$]106 лет=2,4 миллиона лет
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