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Консультация № 130901
06.04.2008, 23:06
0.00 руб.
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1
1
Здравствуйте, уважаемые эксперты, помогите пожалуйста с задачей
1,59
диск вращается с угловым ускорением -2 рад/с^2. сколько оборотов сделает диск при изменении частоты вращения от 240 до 90 минут в минус первой степени? Найти время дельта t, в течение которого это произойдет.
1,59
диск вращается с угловым ускорением -2 рад/с^2. сколько оборотов сделает диск при изменении частоты вращения от 240 до 90 минут в минус первой степени? Найти время дельта t, в течение которого это произойдет.
Обсуждение
07.04.2008, 04:28
общий
это ответ
Здравствуйте, Николай Фаворисович Басманов!
Прежде всего переводим частОты вращения начальную n<sub>1</sub> = 240 об/мин и конечную n<sub>2</sub> = 90 об/мин из "оборотов в минуту" в "обороты в секунду", для чего делим их на 60: n<sub>1(об/с)</sub> = 240/60 = 4 об/с; n<sub>2(об/с)</sub> = 90/60 = 1.5 об/с. При угловом ускорении ε = -2 рад/с<sup>2</sup> время Δt, в течение которого произойдет снижение частоты вращения от n<sub>1(об/с)</sub> до n<sub>2(об/с)</sub> равно: Δt = 2*π*(n<sub>2(об/с)</sub> - n<sub>1(об/с)</sub>)/ε = 2*π*(1.5 - 4)/(-2) = 7.854 с. Средняя частота вращения n<sub>ср(об/с)</sub> за это время равна: n<sub>ср(об/с)</sub> = (n<sub>1(об/с)</sub> + n<sub>2(об/с)</sub>)/2 = (4 + 1.5)/2 = 2.75 об/с. При частоте вращения n<sub>ср(об/с)</sub> за время Δt диск сделает n<sub>ср(об/с)</sub>*Δt = 2.75*7.854 = 21.6 оборотов.
Прежде всего переводим частОты вращения начальную n<sub>1</sub> = 240 об/мин и конечную n<sub>2</sub> = 90 об/мин из "оборотов в минуту" в "обороты в секунду", для чего делим их на 60: n<sub>1(об/с)</sub> = 240/60 = 4 об/с; n<sub>2(об/с)</sub> = 90/60 = 1.5 об/с. При угловом ускорении ε = -2 рад/с<sup>2</sup> время Δt, в течение которого произойдет снижение частоты вращения от n<sub>1(об/с)</sub> до n<sub>2(об/с)</sub> равно: Δt = 2*π*(n<sub>2(об/с)</sub> - n<sub>1(об/с)</sub>)/ε = 2*π*(1.5 - 4)/(-2) = 7.854 с. Средняя частота вращения n<sub>ср(об/с)</sub> за это время равна: n<sub>ср(об/с)</sub> = (n<sub>1(об/с)</sub> + n<sub>2(об/с)</sub>)/2 = (4 + 1.5)/2 = 2.75 об/с. При частоте вращения n<sub>ср(об/с)</sub> за время Δt диск сделает n<sub>ср(об/с)</sub>*Δt = 2.75*7.854 = 21.6 оборотов.
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