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Консультация № 196154
18.08.2019, 16:57
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Какую работу A надо совершить, чтобы втащить сани с грузом (общей массой m = 30 кг) на гору высотой H = 10 м? Угол наклона горы α = 30°. Коэффициент трения между санями и горой линейно убывает вдоль пути от k1 = 0,5 у подножия до k2 = 0,1 у вершины.
Какую работу A надо совершить, чтобы втащить сани с грузом (общей массой m = 30 кг) на гору высотой H = 10 м? Угол наклона горы α = 30°. Коэффициент трения между санями и горой линейно убывает вдоль пути от k1 = 0,5 у подножия до k2 = 0,1 у вершины.
Обсуждение
19.08.2019, 11:44
общий
это ответ
Здравствуйте, dar777!
Расчётная схема находится в прикреплённом файле. В проекциях на оси координат уравнение второго закона Ньютона выглядит так [1, с. 32 -- 39]:
Тогда
Предположим, что требуется вычислить минимальную работу, то есть работу при a=0. Тогда
Выведем зависимость коэффициента трения k от координаты x, используя уравнение прямой, проходящей через две заданные точки [2, с. 58]:
Искомая работа силы F на пути l=H/sin[$945$] составляет, согласно [1, с. 61],
Литература
1. Аксенович Л. А., Ракина Н. Н., Фарино К. С. Физика в средней школе. -- Минск: Адукацыя i выхаванне, 2004. -- 720 с.
2. Письменный Д. Т. Конспект лекций по высшей математике. В 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
Расчётная схема находится в прикреплённом файле. В проекциях на оси координат уравнение второго закона Ньютона выглядит так [1, с. 32 -- 39]:
m*a=F-m*g*sin[$945$]-k*N;
0=-m*g*cos[$945$]+N.
Тогда
m*a=F-m*g*sin[$945$]-k*m*g*cos[$945$],
F=m*a+m*g*sin[$945$]+k*m*g*cos[$945$].
Предположим, что требуется вычислить минимальную работу, то есть работу при a=0. Тогда
F=m*g*sin[$945$]+k*m*g*cos[$945$].
Выведем зависимость коэффициента трения k от координаты x, используя уравнение прямой, проходящей через две заданные точки [2, с. 58]:
(x-0)/(l-0)=(k-0,5)/(0,1-0,5),
x/l=(k-0,5)/-0,4,
-0,4*x=(k-0,5)*l,
-0,4*x=k*l-0,5*l,
k=(-0,4*x+0,5*l)/l=-0,4*x/l+0,5.
Искомая работа силы F на пути l=H/sin[$945$] составляет, согласно [1, с. 61],
A=0[$8747$]lFdx=0[$8747$]l(m*g*sin[$945$]+k*m*g*cos[$945$])*dx=m*g*(sin[$945$]0[$8747$]ldx+cos[$945$]*0[$8747$]lk*dx)=
=m*g*(sin[$945$]*l+cos[$945$]*0[$8747$]l(-0,4*x/l+0,5)*dx=m*g*(sin[$945$]*H/sin[$945$]-0,4*cos[$945$]/l*l2/2+l*cos[$945$]/2)=
=m*g*(H-0,2*H/tg[$945$]+0,5*H/tg[$945$])=m*g*(H+0,3*H/tg[$945$])=m*g*H*(1+0,3/tg[$945$])=
=30*9,81*10*(1+0,3/tg30[$186$])[$8776$]4,47*103 (Дж).
Литература
1. Аксенович Л. А., Ракина Н. Н., Фарино К. С. Физика в средней школе. -- Минск: Адукацыя i выхаванне, 2004. -- 720 с.
2. Письменный Д. Т. Конспект лекций по высшей математике. В 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
Прикрепленные файлы:
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Facta loquuntur.
19.08.2019, 15:05
общий
Добрый день) Решите пожалуйста задачки по магнетизму и по механике ещё несколько хотя бы)
Об авторе:
Лучшая увеличительная линза - ноги.
Лучшая увеличительная линза - ноги.
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