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Консультация № 200677

19.04.2021, 13:06

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Образование

Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:

Угловая скорость колеса 1 меняется по закону ω1 = 2t.
Определить ускорение груза 3 в момент времени t = 2 с, если радиусы R1 = 1м,
R2 = 0,8 и r2 = 0,4 м

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cfaea3af5684f1a5e7ab1adf7e9930a6516623ec.png

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Обсуждение

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Посетитель
226425
1567

19.04.2021, 21:06

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это ответ

Здравствуйте, iranisimova36@gmail.com!
Дано:
[$969$]₁=2t (c^-1) (*)
t=2c
R1=1м
R2=0,8м
r2=0,4м
Найти: a
Решение:
Дополним ваш рисунок...

Итак,имеем
1. Линейная скорость обода колеса 1
V₁=[$969$]₁*R₁ (1)
2. Линейная скорость обода колеса 2
V₂=[$969$]₂*R₂ (2)
3. V₂=V₁=V (3)
4. Решаем систему уравнений (1), (2), (3), получаем угловую скорость колеса 2:
[$969$]₂=(R₁/R₂)*[$969$]₁ (4)
5. Линейная скорость малого радиуса колеса 2
v[sub]2[/sub]=[$969$]₂*r₂=(R₁*r₂/R₂)*[$969$]₁
или, с учетом условия (*)
v[sub]2[/sub]=(R₁*r₂/R₂)*2t (5)
6. Искомое ускорение найдем как производную скорости v₂
a=dv₂/dt = 2*(R₁*r₂/R₂) (6)
Как видим из выражения (6), ускорение груза не зависит от времени - груз в любой момент времени будет двигаться с постоянным ускорением
a=2*(1*0,4/0,8) = 1 м/с²
***
Удачи

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С уважением
shvetski

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iranisimova36@gmail.com

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19.04.2021, 21:21

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Спасибо, очень помогли

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