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Консультация № 198920
16.06.2020, 23:08
0.00 руб.
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5
1
Здравствуйте! Прошу помощи в следующем вопросе:
Астероид из-за пределов Солнечной системы приближается к Солнцу со скоростью 15 км/с. Какой будет его максимальная скорость, если минимальное расстояние будет равно расстоянию от Земли до Солнца, а скорость Земли 30 км/с?
Астероид из-за пределов Солнечной системы приближается к Солнцу со скоростью 15 км/с. Какой будет его максимальная скорость, если минимальное расстояние будет равно расстоянию от Земли до Солнца, а скорость Земли 30 км/с?
Обсуждение
17.06.2020, 01:08
общий
Владимир Николаевич обратите внимание на эту консультацию)))
Об авторе:
Лучшая увеличительная линза - ноги.
Лучшая увеличительная линза - ноги.
18.06.2020, 12:37
общий
Адресаты:
Как Вам удалось найти столь простой и удачный вариант Решения? А мне всё интегралы 3х-этажные попадались 
18.06.2020, 12:44
общий
это ответ
Здравствуйте, dar777!
В этой задаче используем законы 1)Сохранения энергии; 2) Всемирного тяготения; 3) II закон Ньютона
Дано:
v1=15 км/с
V=30 км/с
r2=r=150 млн.км
Найти: v2
Решение:
[img]
[/img]
1. З.С.Э.
EK1+EP1=EK2+EP2
здесь
EK=mv2/2 - кинетическая энергия астероида (m-масса, v-скорость астероида)
EP=-GMСm/r - потенциальная энергия астероида в гравитационном поле Солнца (G=6,67*10-11 Н*м2/кг2 - гравитационная постоянная, MС-масса Солнца,r-расстояние до Солнца).
Поскольку r1=[$8734$], EP1=0
Следовательно, сокращая m, получаем
v22=v12+2GMС/r (1)
2. II з.Н. для Земли
F=MЗ*an
Земля движется в поле тяготения Солнца с центростремительным ускорением an=V2/r
Следовательно
F=MЗ*V2/r (2)
3. Закон всемирного тяготения (для Земли и Солнца)
F=GMCMЗ/r2 (3)
4. Приравниваем правые части выражений (2) и (3), сокращаем МЗ, получаем
GMC/r=V2 (4)
5. Подставляем (4) в (1) и находим v2
v2=[$8730$](v12+2V2)
После подстановки и вычислений получаем
v2=45 км/с
В этой задаче используем законы 1)Сохранения энергии; 2) Всемирного тяготения; 3) II закон Ньютона
Дано:
v1=15 км/с
V=30 км/с
r2=r=150 млн.км
Найти: v2
Решение:
[img]
1. З.С.Э.
EK1+EP1=EK2+EP2
здесь
EK=mv2/2 - кинетическая энергия астероида (m-масса, v-скорость астероида)
EP=-GMСm/r - потенциальная энергия астероида в гравитационном поле Солнца (G=6,67*10-11 Н*м2/кг2 - гравитационная постоянная, MС-масса Солнца,r-расстояние до Солнца).
Поскольку r1=[$8734$], EP1=0
Следовательно, сокращая m, получаем
v22=v12+2GMС/r (1)
2. II з.Н. для Земли
F=MЗ*an
Земля движется в поле тяготения Солнца с центростремительным ускорением an=V2/r
Следовательно
F=MЗ*V2/r (2)
3. Закон всемирного тяготения (для Земли и Солнца)
F=GMCMЗ/r2 (3)
4. Приравниваем правые части выражений (2) и (3), сокращаем МЗ, получаем
GMC/r=V2 (4)
5. Подставляем (4) в (1) и находим v2
v2=[$8730$](v12+2V2)
После подстановки и вычислений получаем
v2=45 км/с
5
Это самое лучшее решение!
Об авторе:
С уважением
shvetski
С уважением
shvetski
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