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Консультация № 191375
23.09.2017, 14:31
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Здравствуйте! У меня возникли сложности с таким вопросом:
Соломинка массы М и длины L лежит на гладкой горизонтальной поверхности. На концах соломинки сидят два жука одинаковой массы m. Одновременно жуки поползли навстречу друг другу со скоростями V1 и V2 (V1>V2) относительно соломинки. С какой скоростью v движется при этом соломинка? найдите перемещение Sx соломинки, к тому моменту времени, когда жуки встретятся.
Здравствуйте! У меня возникли сложности с таким вопросом:
Соломинка массы М и длины L лежит на гладкой горизонтальной поверхности. На концах соломинки сидят два жука одинаковой массы m. Одновременно жуки поползли навстречу друг другу со скоростями V1 и V2 (V1>V2) относительно соломинки. С какой скоростью v движется при этом соломинка? найдите перемещение Sx соломинки, к тому моменту времени, когда жуки встретятся.
Обсуждение
02.10.2017, 14:43
общий
это ответ
Здравствуйте, gethan!
Выделим систему тел, состоящую из соломинки и двух жуков. Внешние силы в плоскости в плоскости движения этой системы можно считать отсутствующими. Тогда по закону сохранения импульса
где v[sub]СЗ[/sub], v[sub]1З[/sub], v[sub]2З[/sub] - скорости соломинки, первого жука, второго жука относительно Земли. Поскольку
постольку в проекциях на ось, положительное направление которой совпадает с направлением движения первого жука относительно Земли, получим
Двигаясь относительно соломинки, жуки встретятся через время
При этом соломинка переместится на рсстояние
Выделим систему тел, состоящую из соломинки и двух жуков. Внешние силы в плоскости в плоскости движения этой системы можно считать отсутствующими. Тогда по закону сохранения импульса
Mv[sub]СЗ[/sub]+mv[sub]1З[/sub]+mv[sub]2З[/sub]=0,
где v[sub]СЗ[/sub], v[sub]1З[/sub], v[sub]2З[/sub] - скорости соломинки, первого жука, второго жука относительно Земли. Поскольку
v[sub]1З[/sub]=v[sub]1[/sub]+v[sub]СЗ[/sub], v[sub]2З[/sub]=v[sub]2[/sub]+v[sub]СЗ[/sub],
постольку в проекциях на ось, положительное направление которой совпадает с направлением движения первого жука относительно Земли, получим
-MvСЗ+m(v1-vСЗ)+m(-v2-vСЗ)=0,
-(M+2m)vСЗ+m(v1-v2)=0,
vСЗ=m(v1-v2)/(M+2m).
Двигаясь относительно соломинки, жуки встретятся через время
t=L/(v1+v2).
При этом соломинка переместится на рсстояние
s=vСЗt=mL(v1-v2)/((M+2m)(v1+v2)).
Об авторе:
Facta loquuntur.
Facta loquuntur.
14.11.2017, 16:00
общий
Адресаты:
Я уже забыл про эту задачу, и восстанавливать ход решения нет желания. Если Вы увидели ошибку в моём решении, то учтите её в своём. 
Об авторе:
Facta loquuntur.
Facta loquuntur.
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