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Консультация № 196239
28.08.2019, 10:00
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
На гладкой горизонтальной поверхности лежит соломинка массой M и длиной L. На одном конце соломинки находятся два жука. Масса каждого жука равна m/ Найдите скорость соломинки после того , как оба жука, двигаясь по соломинке , спрыгнут с неё с относительной скоростью u:
а) одновременно,
б) поочередно (при этом второй жук начинает движение после того, как спрыгнет первый).
В каком случае скорость соломинки будет больше?
На гладкой горизонтальной поверхности лежит соломинка массой M и длиной L. На одном конце соломинки находятся два жука. Масса каждого жука равна m/ Найдите скорость соломинки после того , как оба жука, двигаясь по соломинке , спрыгнут с неё с относительной скоростью u:
а) одновременно,
б) поочередно (при этом второй жук начинает движение после того, как спрыгнет первый).
В каком случае скорость соломинки будет больше?
Обсуждение
01.09.2019, 13:30
общий
это ответ
Здравствуйте, irinasoboleva76!
Из закона сохранения импульса легко вывести, что если 2 объекта массами m и M разделяются с относительной скоростью u, то изменение скоростей их в инерциальной системе отсчёта обратно пропорционально массам, поэтому скорость объекта массой M изменится на v=um/(m+M)
a)
оба жука (общей массой 2m) спрыгивают одновременно и скорость соломинки изменяется на
vA=2um/(2m+M)
б) после того, как первый жук спрыгнул, скорость соломинки со вторым жуком
v1=um/(2m+M)
далее, с неё спрыгивант второй жук и скорость соломинки увеличивается ещё на
v2=um/(m+M)
итого, скорость соломинки во втором случае
vB=v1+v2=um(1/(2m+M)+1/(m+M))
поскольку 1/(m+M)>1/(2m+M), делаем вывод, что vB>vA
Из закона сохранения импульса легко вывести, что если 2 объекта массами m и M разделяются с относительной скоростью u, то изменение скоростей их в инерциальной системе отсчёта обратно пропорционально массам, поэтому скорость объекта массой M изменится на v=um/(m+M)
a)
оба жука (общей массой 2m) спрыгивают одновременно и скорость соломинки изменяется на
vA=2um/(2m+M)
б) после того, как первый жук спрыгнул, скорость соломинки со вторым жуком
v1=um/(2m+M)
далее, с неё спрыгивант второй жук и скорость соломинки увеличивается ещё на
v2=um/(m+M)
итого, скорость соломинки во втором случае
vB=v1+v2=um(1/(2m+M)+1/(m+M))
поскольку 1/(m+M)>1/(2m+M), делаем вывод, что vB>vA
5
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