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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите решить задачи 1.11.3. Материальная точка массой 9 кг движется по горизонтальной прямой под действием силы F1=45 Н и тормозящей движение силы F2= 15t (F - Н, t - с). Найти закон движения точки, если она начинает двигаться из начала координат без начальной скорости. Определить, через какой промежуток времени точка остановится, и какой путь она пройдёт до остановки. 1.11.4. Материальная точка массой 1,2 кг движется вниз по гладкой поверхности, наклонённой к горизонту под углом 30. На точку действует постоянная сила F= 20 Н в направлении движения и сила сопротивления среды R=4V ( R- Н, V- м/с). Найти закон движения точки, если её начальная скорость равнялась нулю. Определить, через какой промежуток времени её скорость станет вдвое меньше максимальной. 1.11.5. Материальная точка массой 7 кг движется под действием двух сил F1= 21 sin2t i и F2= 14i - 7 y(с точкой) j (F- Н, t- с, y с точкой - м/с) в горизонтальной плоскости. Найти уравнения движения точки, если она начинает движение из начала координат с начальной скоростью 2 м/с, параллельной оси Oy. 1.11.6. Вес парашютиста вместе с парашютом равен 900 Н. Площадь проекции раскрытого парашюта на плоскость, перпендикулярную направлению движения, S = 64 м^2. Определить максимальную скорость опускания парашютиста, если сила сопротивления воздуха R= 0,5cpSV^2(R - Н, V- м/с, постоянная c=4, плотность воздуха p= 1,25 кг/м^3).
Материальная точка массой 9 кг движется по горизонтальной прямой под действием силы F1=45 Н и тормозящей движение силы F2= 15t (F - Н, t - с). Найти закон движения точки, если она начинает двигаться из начала координат без начальной скорости. Определить, через какой промежуток времени точка остановится, и какой путь она пройдёт до остановки.
Дано: материальная точка движется по прямой линии; кг -- масса материальной точки; Н, Н -- проекции сил, действующих на материальную точку, на направление её движения; -- начальная скорость материальной точки.
Определить: -- промежуток времени, через который материальная точка остановится; -- путь, пройденный материальной точкой до остановки.
Решение
Материальная точка движется под действием геометрической суммы сил и Её ускорение, в соответствии со вторым законом Ньютона, составляет или, в проекциях на направление движения (которое примем совпадающим с положительным направлением оси абсцисс), м/с2. Из формулы, выражающей связь между скоростью и ускорением материальной точки, получим
что при даёт
и
с -- промежуток времени, через который материальная точка остановится.
Путь, пройденный материальной точкой до остановки, учитывая, что она движется в одном и том же направлении, составляет
(м).
Ответ: с; м.
Литература Яворский Б. М., Детлаф А. А., Лебедев А. К. Справочник по физике для инженеров и студентов вузов. -- М.: ООО "Издательство Оникс", 2007. -- 1056 с.
Об авторе:
Facta loquuntur.
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apostelnyy 
кг -- масса материальной точки; 
Н, 
Н -- проекции сил, действующих на материальную точку, на направление её движения; 
-- начальная скорость материальной точки.
-- промежуток времени, через который материальная точка остановится; 
-- путь, пройденный материальной точкой до остановки.
сил 
и 
Её ускорение, в соответствии со вторым законом Ньютона, составляет 
или, в проекциях на направление движения (которое примем совпадающим с положительным направлением оси абсцисс), 
м/с2. Из формулы, выражающей связь между скоростью и ускорением материальной точки, получим
даёт
с -- промежуток времени, через который материальная точка остановится.
(м).
м.