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Задать вопрос экспертам

Консультация № 193482

21.08.2018, 23:11

0.00 руб.

0 2 1

Образование

Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
9-6. Найти работу, произведённую машиной за промежуток времени 0<t<1 с, если мощность машины зависит от времени по закону N = A(t/тау)<sup>3</sup>. Если тау = 1 с, А = 1 Вт. Сделать рисунок.

Обсуждение

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18345

22.08.2018, 06:57

общий

Адресаты:

Как связаны между собой работа и мощность?

Об авторе:
Facta loquuntur.

давно

Лангваген Сергей Евгеньевич

Советник
165461
578

23.08.2018, 13:38

общий

это ответ

Здравствуйте, dar777!
Нужно вспомнить, что мощность -- это работа, произведенная в единицу времени, или P = dW/dt.
Работу можно найти интегрированием по выбранному промежутку времени.
W = [$8747$]P(t)dt.
В задаче P(t) = A*(t/tau)³, интервал времени (0, t₁).
Интегрируя, получим
W = A*t₁⁴/(4*tau³).
Подставляя численные значения A = 1 Вт, tau = 1c, t₁ = 1 c, найдем
W = 1/4 Дж.
На рисунке можно показать зависимость мощности от времени.
Совершенная работа будет площадью под кривой.

5

Спасибо огромное уважаемый эксперт!

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