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1) С помощью тонкой линзы на экране получено изображение предмета, расположенного перпендикулярно главной оптической оси линзы. Расстояние между предметом и экраном в 9 раз больше расстояния от предмета до ближайшего к нему фокуса линзы. С каким увеличением изображается предмет?
2) Брусок массой m колеблется с амплитудой А0 вдоль прямой на гладкой горизонтальной поверхности стола под действием упругой пружины. В момент, когда смещение бруска от положения равновесия было А0/3, на него упал и прилип кусок пластилина массой m/3, двигавшийся перед ударом вертикально. Время соударения значительно меньше периода колебаний и при соударении брусок не отрывается от стола. а) Как и во сколько раз изменился период колебаний? б) Найдите амплитуду колебаний бруска после прилипания пластилина.
Здравствуйте, Болдырев Тимофей. 1)Дано: d+f=9*(d-F) Найти: Г Решение:
Из условия d+f=9*(d-F)=9d-9F [$8658$] f= 8d - 9F (1)
Из формулы линзы 1/F = 1/d + 1/(8d-9F)
1/F = 9(d-F)/(8d2-9Fd) 8d2-18Fd+9F2=0 Пусть F=1 8d2-18d+9=0 Решаем квадратное уравнение относительно d Дискриминант D=36 d1=0.75 тогда с учетом уравнения (1) f1=-3 - мнимое изображение (не удовлетворяет условию задачи, поскольку мнимое изображение не может быть получено на экране) d2= 1.5 тогда с учетом (1) f2 = 3 Увеличение линзы Г=H/h=f/d = 3/1,5 = 2
Рискну предложить свое решение второй задачи Вашего вопроса. Оно не совсем удовлетворяет меня и имеет, скорее, черновой характер, но, надеюсь, поможет Вам найти путь к более изящному решению, не требующему такого обилия выкладок. Надеюсь, что на вопрос (а) был дан правильный ответ, по крайней мере...
Полагаю, что задача носит олимпиадный характер. Стало быть, Вы готовитесь к поступлению в учебное заведение, требующее повышенной подготовки по физике и математике. В таком случае Вам не следует обращаться к экспертам Портала с прямой просьбой решить задачу. Нужно попытаться решить ее самостоятельно, а затем, в случае необходимости, просить о помощи. Иначе Вы не сможете нормально учиться дальше...
С уважением.
5
Спасибо за помощь в решении данной задачи.<br>Действительно, это задача из ФЗФТШ при МФТИ, в котором я учусь (заочная школа при институте).<br>С физикой у меня не очень, поэтому и прошу у вас помощи в решении данных задач.<br>А вот с математикой проблем нет, так что поступать буду на математический факультет.<br>Ещё раз спасибо за решение и совет.
Об авторе:
Facta loquuntur.
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