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Уважаемые эксперты помогите решить задачу. Не могу понять как использовать силу трения между нитью и блоком (бруском):
На вершине наклонной плоскости, составляющей угол α=40 с горизонтом, жестко закреплен цилиндрический блок. Тело m2 лежит на плоскости, тело m1 висит вниз. Невесомая и нерастяжимая нить, перекинутая через блок, связывает тела массами m1=2 кг и m2=1 кг. Коэффициент трения между нитью и блоком равен μ=0,1, а между телом m2 и плоскостью k=0,15. Силы натяжения нити по обе стороны блока T1 и T2, соответственно. Найти неизвестные величины: силы натяжения нитей Т1 и Т2 и ускорение, с которым движутся грузы.
Обсуждение
Неизвестный
25.10.2010, 10:17
общий
Подскажите, пожалуйста. Можно ли связать какой-нибудь формулой различие между силами натяжения нитей и коэффициентом трения между нитью и бруском. Я нигде не могу найти такой зависимости.
http://www.abitura.com/open_lessons/dynamics/ - тут не плохо расписано как решаются подобные задачи, нужно все аккуратно разрисовать, и записать законы для каждого бруска получится система уравнений решая которую находятся величины.
Об авторе:
to live is to die
Неизвестный
25.10.2010, 14:44
общий
Я понимаю как рассмотреть силы трения между телами, движущимися по поверхности, но я не понимаю как применить силу трения между нитью и блоком. Ведь получается, что именно из-за трения между нитью и блоком силы натяжения нитей Т1 и Т2 различны. У блока нет ни массы, ни радиуса и вообще он не вращается. Нить не имеет массы и нерастяжима, а силы натяжения нитей различны...
Для определения силы трения требуется найти силу взаимодействия нити и блока Силы натяжения нити: T1=m1(g-a) T2=m2(g*sin[$945$]+k*g*cos[$945$]+a) Если рассматривать воздействие на блок, эти силы берём по направлениям соответствующих участков нити к грузам и складываем векторно. Умножим полученный результат на [$956$] и получаем силу трения, равную T1-T2
DmitriyZub: T1 = T2*[size=3]e[/size][$956$]*[$946$], где [$946$] = 90[$186$] + [$945$] (но перевести в радианы!) - "угол охвата", т.е. радиальный угол, охватывающий ту часть окружности "блока", в которой нить его касается. (Это "формула Эйлера").
Roman Chaplinsky / Химик CH: Проще и точнее воспользоваться "формулой Эйлера": T1 = T2*[size=3]e[/size][$956$]*[$946$], где [$946$] = 90[$186$] + [$945$] (но перевести в радианы!) - "угол охвата", т.е. радиальный угол, охватывающий ту часть окружности "блока", в которой нить его касается. (Формула широко используется в технике для расчёта ремённых передач, приводов ленточных транспортёров и т.п.)
Полагаю, что ход решения может быть таким, как показано ниже.
Надеюсь, что не ошибся.
С уважением.
Об авторе:
Facta loquuntur.
Неизвестный
27.10.2010, 16:15
общий
Большое спасибо. Вчера сдал контрольную, надеюсь, что преподавателю понравится решение. Воспользовался формулой Эйлера. Формулу видел раньше, но не мог понять как расчитать угол β, надеюсь, что ваша подсказка верна.
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