Лабораторная работа №2 / LAB2.DOC

Л а б о р а т о р н а я р а б о т а № 2.[Author ID1: at Wed Mar 14 09:54:00 2001 ]

[Author ID0: at ]

[Author ID2: at Wed Oct 18 11:16:00 2000 ]

ИЗУЧЕНИЕ ЗАКОНОВ ПРЯМОЛИНЕЙНОГО ДВИЖЕНИЯ

НА МАШИНЕ АТВУДА.[Author ID1: at Wed Mar 14 09:55:00 2001 ]

[Author ID2: at Wed Oct 18 11:17:00 2000 ]

Цель работы [Author ID1: at Wed Mar 14 09:55:00 2001 ]: [Author ID1: at Wed Mar 14 09:56:00 2001 ] изучение законов равноускоренного движения.

Оборудование: стойка с вращающимся блоком и подвижными грузами [Author ID1: at Mon Feb 19 15:19:00 2001 ], фотодатчики, электронный секундомер, шайбы-перегрузки, миллиметровая линейка.[Author ID1: at Mon Feb 19 15:18:00 2001 ]

[Author ID1: at Wed Mar 14 09:56:00 2001 ]

Продолжительность работы: 4 ч.

[Author ID2: at Wed Oct 18 11:17:00 2000 ]

Описание установки. Теоретическая часть.

Основу машины Атвуда составляет укрепленный на стойке блок с двумя грузами равной массы, подвешенными на концах перекинутой через него нити [Author ID2: at Thu Sep 28 15:21:00 2000 ] [Author ID2: at Thu Sep 28 15:22:00 2000 ] (см. рис.[Author ID2: at Wed Oct 18 14:48:00 2000 ]1[Author ID2: at Thu Nov 9 13:13:00 2000 ]). [Author ID2: at Thu Sep 28 15:22:00 2000 ] Система находится в равновесии. Чтобы вызвать[Author ID1: at Tue Nov 28 07:54:00 2000 ]привести[Author ID1: at Tue Nov 28 07:54:00 2000 ] ее в [Author ID1: at Tue Nov 28 07:54:00 2000 ]движение, на грузы помещают ″перегрузки″-[Author ID1: at Wed Mar 14 09:56:00 2001 ]-[Author ID1: at Wed Mar 14 09:56:00 2001 ] шайбы массы[Author ID1: at Wed Mar 14 09:56:00 2001 ]ой[Author ID1: at Wed Mar 14 09:56:00 2001 ] Δm[Author ID2: at Thu Sep 28 15:21:00 2000 ]m[Author ID2: at Thu Sep 28 15:21:00 2000 ].

[Author ID0: at ]

[Author ID2: at Tue Oct 24 11:37:00 2000 ]

[Author ID2: at Wed Oct 18 19:17:00 2000 ] [Author ID2: at Wed Oct 18 19:18:00 2000 ]-->[Author ID2: at Wed Oct 18 19:21:00 2000 ]

[Author ID2: at Thu Oct 19 10:58:00 2000 ]Т[Author ID2: at Tue Oct 24 11:38:00 2000 ]₁[Author ID2: at Tue Oct 24 11:38:00 2000 ] [Author ID2: at Thu Oct 19 10:58:00 2000 ][Author ID0: at ]

[Author ID0: at ]

[Author ID2: at Thu Oct 19 10:58:00 2000 ] [Author ID2: at Wed Oct 18 19:13:00 2000 ] [Author ID2: at Wed Oct 18 19:13:00 2000 ] [Author ID2: at Sat Sep 30 12:31:00 2000 ] T[Author ID2: at Wed Oct 18 19:13:00 2000 ]1[Author ID2: at Sat Sep 30 12:04:00 2000 ] [Author ID0: at ]

[Author ID2: at Wed Oct 18 19:13:00 2000 ] [Author ID2: at Sat Sep 30 12:29:00 2000 ]-->_M1[Author ID2: at Fri Sep 29 17:13:00 2000 ][Author ID2: at Fri Sep 29 17:14:00 2000 ] [Author ID2: at Sat Sep 30 12:29:00 2000 ] [Author ID2: at Fri Sep 29 17:11:00 2000 ]= [Author ID2: at Sat Sep 30 12:29:00 2000 ] [Author ID2: at Fri Sep 29 17:11:00 2000 ]M + ( [Author ID2: at Sat Sep 30 12:29:00 2000 ]N[Author ID2: at Fri Sep 29 19:07:00 2000 ]-[Author ID2: at Thu Sep 28 15:10:00 2000 ]n[Author ID2: at Fri Sep 29 19:06:00 2000 ]1[Author ID2: at Fri Sep 29 17:15:00 2000 ] [Author ID2: at Fri Sep 29 19:06:00 2000 ]) [Author ID2: at Sat Sep 30 12:29:00 2000 ]Δ[Author ID2: at Sat Sep 30 12:29:00 2000 ]m[Author ID2: at Fri Sep 29 19:07:00 2000 ] [Author ID2: at Sat Sep 30 12:29:00 2000 ]-->[Author ID2: at Sat Sep 30 12:29:00 2000 ][Author ID2: at Fri Sep 29 17:12:00 2000 ]

[Author ID2: at Sat Sep 30 12:14:00 2000 ][Author ID2: at Sat Sep 30 12:12:00 2000 ]

[Author ID2: at Sat Sep 30 12:12:00 2000 ] [Author ID2: at Thu Oct 19 11:01:00 2000 ]0[Author ID2: at Tue Oct 24 11:39:00 2000 ] [Author ID2: at Sat Sep 30 12:12:00 2000 ] [Author ID2: at Thu Sep 28 15:09:00 2000 ] [Author ID2: at Thu Sep 28 15:10:00 2000 ] [Author ID2: at Sat Sep 30 12:30:00 2000 ][Author ID2: at Sat Sep 30 12:44:00 2000 ][Author ID2: at Sat Sep 30 12:44:00 2000 ][Author ID2: at Sat Sep 30 12:44:00 2000 ]

[Author ID2: at Thu Oct 19 10:59:00 2000 ] [Author ID2: at Sat Sep 30 12:33:00 2000 ] T[Author ID2: at Sat Sep 30 12:50:00 2000 ]2[Author ID2: at Sat Sep 30 12:05:00 2000 ] [Author ID2: at Sat Sep 30 12:50:00 2000 ] [Author ID2: at Sat Sep 30 12:30:00 2000 ]T[Author ID2: at Thu Oct 19 11:01:00 2000 ]₂[Author ID2: at Thu Oct 19 11:01:00 2000 ][Author ID2: at Wed Oct 18 11:18:00 2000 ]

-->[Author ID2: at Thu Oct 19 11:02:00 2000 ][Author ID2: at Thu Oct 19 11:02:00 2000 ]

[Author ID2: at Sat Sep 30 12:45:00 2000 ] [Author ID2: at Thu Oct 19 11:02:00 2000 ] [Author ID2: at Thu Oct 19 11:03:00 2000 ] [Author ID2: at Thu Oct 19 11:02:00 2000 ] M[Author ID2: at Tue Oct 24 11:39:00 2000 ]₁[Author ID2: at Tue Oct 24 11:39:00 2000 ]g [Author ID2: at Tue Oct 24 11:39:00 2000 ] M[Author ID2: at Sat Sep 30 12:45:00 2000 ]2[Author ID2: at Fri Sep 29 17:21:00 2000 ] = M + n1 [Author ID2: at Sat Sep 30 12:45:00 2000 ]Δ[Author ID2: at Sat Sep 30 12:45:00 2000 ]m[Author ID2: at Sat Sep 30 12:45:00 2000 ] [Author ID2: at Thu Nov 9 13:16:00 2000 ] [Author ID2: at Fri Sep 29 17:19:00 2000 ]

[Author ID2: at Sat Sep 30 12:36:00 2000 ]M[Author ID2: at Sat Sep 30 12:35:00 2000 ]1[Author ID2: at Sat Sep 30 12:04:00 2000 ] g[Author ID2: at Sat Sep 30 12:35:00 2000 ]

[Author ID2: at Fri Sep 29 17:20:00 2000 ]

S[Author ID2: at Tue Oct 24 11:39:00 2000 ] S [Author ID2: at Sat Sep 30 12:52:00 2000 ] [Author ID2: at Wed Oct 18 19:14:00 2000 ] [Author ID2: at Sat Sep 30 12:53:00 2000 ] M[Author ID2: at Wed Oct 18 19:14:00 2000 ]2[Author ID2: at Sat Sep 30 12:05:00 2000 ] g[Author ID2: at Wed Oct 18 19:14:00 2000 ] M[Author ID2: at Tue Oct 24 11:39:00 2000 ]₂[Author ID2: at Tue Oct 24 11:40:00 2000 ]g[Author ID2: at Tue Oct 24 11:40:00 2000 ]-->[Author ID2: at Tue Oct 24 11:40:00 2000 ]

[Author ID2: at Sat Sep 30 12:52:00 2000 ] [Author ID2: at Thu Oct 19 11:04:00 2000 ]-->[Author ID2: at Thu Oct 19 11:05:00 2000 ]

X[Author ID2: at Tue Oct 24 11:39:00 2000 ] [Author ID2: at Thu Oct 19 11:05:00 2000 ]

X[Author ID2: at Wed Oct 18 19:14:00 2000 ]

[Author ID2: at Thu Oct 19 11:05:00 2000 ]

[Author ID1: at Tue Nov 28 07:56:00 2000 ] Рис. 1[Author ID1: at Tue Nov 28 07:56:00 2000 ].[Author ID1: at Wed Mar 14 10:00:00 2001 ] Схема установки.[Author ID1: at Tue Nov 28 07:56:00 2000 ] [Author ID1: at Tue Nov 28 07:56:00 2000 ] [Author ID1: at Tue Nov 28 07:55:00 2000 ] Рис. 1 Схема установки[Author ID2: at Thu Oct 19 11:06:00 2000 ][Author ID1: at Tue Nov 28 07:56:00 2000 ] [Author ID2: at Thu Oct 19 11:06:00 2000 ] Рис. 1 Схема установки[Author ID2: at Thu Oct 19 11:06:00 2000 ].[Author ID1: at Tue Nov 28 07:56:00 2000 ]

[Author ID2: at Wed Oct 18 11:23:00 2000 ]

[Author ID2: at Thu Oct 19 10:58:00 2000 ]

[Author ID2: at Thu Oct 19 11:07:00 2000 ]

Во время движения левый груз пересекает лучи света фотодатчиков ,[Author ID2: at Thu Nov 9 13:32:00 2000 ].[Author ID2: at Thu Nov 9 13:32:00 2000 ] П[Author ID2: at Thu Nov 9 13:33:00 2000 ]ри пересечении луча верхнего фотодатчика[Author ID2: at Thu Nov 9 13:32:00 2000 ] миллисекундомер включается, а при пересечении луча нижнего[Author ID2: at Thu Nov 9 13:33:00 2000 ] фотодатчика[Author ID1: at Wed Mar 14 10:02:00 2001 ] выключается.[Author ID2: at Thu Nov 9 13:33:00 2000 ] [Author ID2: at Thu Nov 9 13:34:00 2000 ]в результате чего происходит включение и выключение электронного миллисекундомера. Т[Author ID2: at Thu Nov 9 13:34:00 2000 ]Т[Author ID2: at Thu Nov 9 13:34:00 2000 ]ем самым осуществляется измерение времени [Author ID2: at Thu Nov 9 13:35:00 2000 ]t[Author ID2: at Thu Nov 9 13:35:00 2000 ] прохождения грузом пути [Author ID2: at Thu Nov 9 13:35:00 2000 ]S[Author ID2: at Thu Nov 9 13:36:00 2000 ] между фотодатчиками. Для подготовки миллисекундомера к работе [Author ID1: at Wed Mar 14 10:03:00 2001 ]П[Author ID1: at Wed Mar 14 10:03:00 2001 ]п[Author ID1: at Wed Mar 14 10:03:00 2001 ]еред каждым измерением для подготовки миллисекундомера к работе [Author ID1: at Wed Mar 14 10:02:00 2001 ]следует нажать кнопку ”Сброс”.

Вычислим [Author ID2: at Thu Nov 9 13:37:00 2000 ]Найдем величину [Author ID2: at Thu Nov 9 13:37:00 2000 ]ускорения,[Author ID1: at Wed Mar 14 10:03:00 2001 ] с которыми[Author ID1: at Wed Mar 14 15:52:00 2001 ] двигают[Author ID2: at Thu Nov 9 13:37:00 2000 ]жу[Author ID1: at Wed Mar 14 15:54:00 2001 ]жу[Author ID2: at Thu Nov 9 13:37:00 2000 ][Author ID1: at Wed Mar 14 15:54:00 2001 ]т[Author ID2: at Thu Nov 9 13:37:00 2000 ]ся грузы. [Author ID2: at Thu Nov 9 13:45:00 2000 ]Будем считать[Author ID2: at Thu Nov 9 13:44:00 2000 ],[Author ID1: at Wed Mar 14 10:03:00 2001 ] что нить нерастяжима[Author ID2: at Thu Nov 9 13:44:00 2000 ],[Author ID1: at Wed Mar 14 10:03:00 2001 ] и ее масса много мен[Author ID2: at Thu Nov 9 13:44:00 2000 ]ь[Author ID2: at Thu Nov 9 13:45:00 2000 ]ше[Author ID2: at Thu Nov 9 13:44:00 2000 ] массы грузов[Author ID2: at Thu Nov 9 13:45:00 2000 ]. Кроме того[Author ID2: at Thu Nov 9 14:01:00 2000 ],[Author ID1: at Wed Mar 14 10:03:00 2001 ] [Author ID2: at Thu Nov 9 14:04:00 2000 ]будем считать, что между блоком и нитью нет проскальзывания.[Author ID2: at Thu Nov 9 14:02:00 2000 ] [Author ID2: at Thu Nov 9 14:01:00 2000 ] [Author ID2: at Thu Nov 9 14:02:00 2000 ]Пусть масса каждого [Author ID2: at Thu Sep 28 15:24:00 2000 ]груза [Author ID2: at Thu Sep 28 15:24:00 2000 ]M[Author ID2: at Thu Sep 28 15:25:00 2000 ] [Author ID2: at Thu Sep 28 15:24:00 2000 ],[Author ID2: at Sat Sep 30 12:54:00 2000 ]-->груз[Author ID2: at Thu Sep 28 15:24:00 2000 ][Author ID2: at Thu Sep 28 15:24:00 2000 ] [Author ID2: at Thu Sep 28 15:23:00 2000 ]-->а[Author ID2: at Thu Sep 28 15:23:00 2000 ][Author ID2: at Thu Sep 28 15:23:00 2000 ] [Author ID2: at Thu Sep 28 15:23:00 2000 ]М[Author ID2: at Thu Sep 28 15:22:00 2000 ],[Author ID2: at Thu Sep 28 15:23:00 2000 ] общее число перегрузков N[Author ID2: at Thu Sep 28 15:25:00 2000 ]N[Author ID2: at Thu Sep 28 15:26:00 2000 ],[Author ID1: at Wed Mar 14 10:04:00 2001 ],[Author ID2: at Thu Nov 9 13:47:00 2000 ] разность их количеств на левом и правом грузах [Author ID2: at Thu Nov 9 13:47:00 2000 ]n[Author ID2: at Thu Sep 28 15:25:00 2000 ] и пусть[Author ID2: at Thu Nov 9 13:48:00 2000 ] на правом грузе находи[Author ID1: at Wed Mar 14 10:04:00 2001 ]я[Author ID1: at Wed Mar 14 10:04:00 2001 ]ть[Author ID1: at Wed Mar 14 15:53:00 2001 ]ся -->n[Author ID2: at Thu Sep 28 15:26:00 2000 ][Author ID2: at Thu Sep 28 15:26:00 2000 ]n[Author ID2: at Thu Sep 28 15:26:00 2000 ]-->1[Author ID2: at Sat Sep 30 12:53:00 2000 ][Author ID2: at Thu Sep 28 15:26:00 2000 ]₀[Author ID2: at Thu Nov 9 13:49:00 2000 ] перегрузков. Запишем для грузов с перегрузками второй закон Ньютона:

[Author ID2: at Wed Oct 18 13:15:00 2000 ]

[Author ID2: at Sat Sep 30 13:06:00 2000 ] [Author ID2: at Sat Sep 30 13:06:00 2000 ] [Author ID2: at Sat Sep 30 13:07:00 2000 ] [Author ID2: at Sat Sep 30 13:07:00 2000 ][Author ID2: at Sat Sep 30 13:05:00 2000 ][Author ID2: at Sat Sep 30 13:05:00 2000 ][Author ID2: at Sat Sep 30 13:05:00 2000 ][Author ID2: at Sat Sep 30 12:57:00 2000 ][Author ID2: at Sat Sep 30 12:57:00 2000 ][Author ID2: at Sat Sep 30 12:57:00 2000 ] [Author ID2: at Wed Oct 18 13:16:00 2000 ]( М + ( [Author ID2: at Sat Sep 30 12:56:00 2000 ]N-[Author ID2: at Sat Sep 30 12:56:00 2000 ]n1[Author ID2: at Wed Sep 27 19:40:00 2000 ]) [Author ID2: at Sat Sep 30 12:56:00 2000 ]Δ[Author ID2: at Sat Sep 30 12:56:00 2000 ]m) g -T1 = ( M + ( N-n1) [Author ID2: at Sat Sep 30 12:56:00 2000 ]Δ[Author ID2: at Sat Sep 30 12:56:00 2000 ]m) a, [Author ID2: at Sat Sep 30 12:56:00 2000 ] [Author ID2: at Sat Sep 30 12:56:00 2000 ] [Author ID2: at Wed Oct 18 13:16:00 2000 ] [Author ID2: at Wed Oct 18 14:49:00 2000 ] [Author ID2: at Wed Oct 18 14:50:00 2000 ] [Author ID2: at Wed Oct 18 13:16:00 2000 ](1)

[Author ID2: at Thu Nov 9 13:56:00 2000 ] [Author ID2: at Thu Nov 9 13:56:00 2000 ][Author ID2: at Sat Sep 30 13:01:00 2000 ][Author ID2: at Sat Sep 30 13:01:00 2000 ][Author ID2: at Sat Sep 30 13:01:00 2000 ]( M +n1 [Author ID2: at Sat Sep 30 12:56:00 2000 ]Δ[Author ID2: at Sat Sep 30 12:56:00 2000 ]m)[Author ID2: at Sat Sep 30 12:56:00 2000 ] [Author ID2: at Sat Sep 30 12:56:00 2000 ]g - T2 = -( M[Author ID2: at Sat Sep 30 12:56:00 2000 ] + n1 [Author ID2: at Sat Sep 30 12:56:00 2000 ]Δ[Author ID2: at Sat Sep 30 12:56:00 2000 ]m ) a[Author ID2: at Sat Sep 30 12:56:00 2000 ]. [Author ID2: at Sat Sep 30 13:08:00 2000 ] [Author ID2: at Thu Nov 9 13:56:00 2000 ] [Author ID2: at Sat Sep 30 13:08:00 2000 ] [Author ID2: at Wed Oct 18 14:50:00 2000 ] [Author ID2: at Sat Sep 30 13:04:00 2000 ](2)[Author ID2: at Thu Nov 9 13:56:00 2000 ]

Из условия нерастяжимости нити следует, что [Author ID2: at Thu Nov 9 13:58:00 2000 ][Author ID2: at Thu Nov 9 13:58:00 2000 ][Author ID2: at Thu Nov 9 13:58:00 2000 ][Author ID2: at Thu Nov 9 13:58:00 2000 ]. В дальнейшем величину ускорения будем обозначать буквой [Author ID2: at Thu Nov 9 13:59:00 2000 ]a[Author ID2: at Thu Nov 9 14:00:00 2000 ], т.е. [Author ID1: at Tue Nov 28 08:00:00 2000 ][Author ID1: at Tue Nov 28 08:01:00 2000 ][Author ID1: at Tue Nov 28 08:01:00 2000 ][Author ID1: at Tue Nov 28 08:01:00 2000 ].[Author ID1: at Tue Nov 28 08:03:00 2000 ].[Author ID2: at Thu Nov 9 14:00:00 2000 ][Author ID1: at Tue Nov 28 08:00:00 2000 ]-->[Author ID2: at Thu Nov 9 14:00:00 2000 ]

[Author ID1: at Tue Nov 28 08:05:00 2000 ][Author ID2: at Wed Oct 18 13:15:00 2000 ]

[Author ID1: at Tue Nov 28 08:04:00 2000 ]Неодинаковость сил натяжения слева и справа обусловлена отличием от нуля массы блока и [Author ID1: at Mon Feb 19 12:26:00 2001 ]наличием трения между нитью и блоком.[Author ID0: at ]

[Author ID1: at Tue Nov 28 07:58:00 2000 ]З[Author ID1: at Tue Nov 28 08:13:00 2000 ]апишем[Author ID1: at Tue Nov 28 08:10:00 2000 ] для блока[Author ID1: at Tue Nov 28 08:13:00 2000 ] у[Author ID1: at Tue Nov 28 08:10:00 2000 ]равнение динамики вращательного движения[Author ID1: at Tue Nov 28 07:58:00 2000 ]:[Author ID1: at Wed Mar 14 10:04:00 2001 ] [Author ID1: at Tue Nov 28 07:58:00 2000 ][Author ID0: at ]

[Author ID1: at Tue Nov 28 08:10:00 2000 ] [Author ID1: at Tue Nov 28 08:14:00 2000 ][Author ID1: at Tue Nov 28 08:11:00 2000 ][Author ID1: at Tue Nov 28 08:11:00 2000 ][Author ID1: at Tue Nov 28 08:11:00 2000 ],[Author ID1: at Tue Nov 28 08:14:00 2000 ] [Author ID1: at Tue Nov 28 08:15:00 2000 ](3)[Author ID1: at Tue Nov 28 08:16:00 2000 ]

где [Author ID1: at Tue Nov 28 08:16:00 2000 ]J [Author ID1: at Tue Nov 28 08:17:00 2000 ]- момент инерции блока, [Author ID1: at Tue Nov 28 08:17:00 2000 ]R[Author ID1: at Tue Nov 28 08:17:00 2000 ] - его радиус, [Author ID1: at Tue Nov 28 08:18:00 2000 ]β[Author ID1: at Tue Nov 28 08:18:00 2000 ] - угловое ускорение.[Author ID1: at Tue Nov 28 08:18:00 2000 ][Author ID0: at ]

Поскольку между блоком и нитью нет проскальзывания, угловое ускорение блока [Author ID1: at Tue Nov 28 08:19:00 2000 ]β[Author ID1: at Tue Nov 28 08:20:00 2000 ] и ускорение грузов [Author ID1: at Tue Nov 28 08:20:00 2000 ]a[Author ID1: at Tue Nov 28 08:21:00 2000 ] связаны соотношением[Author ID1: at Tue Nov 28 08:21:00 2000 ]:[Author ID1: at Wed Mar 14 10:05:00 2001 ][Author ID1: at Tue Nov 28 08:21:00 2000 ]

[Author ID1: at Tue Nov 28 08:22:00 2000 ] [Author ID1: at Tue Nov 28 08:23:00 2000 ][Author ID1: at Tue Nov 28 08:22:00 2000 ][Author ID1: at Tue Nov 28 08:22:00 2000 ][Author ID1: at Tue Nov 28 08:22:00 2000 ].[Author ID1: at Tue Nov 28 08:23:00 2000 ] (4)[Author ID1: at Tue Nov 28 08:24:00 2000 ]-->[Author ID1: at Tue Nov 28 08:21:00 2000 ][Author ID1: at Tue Nov 28 08:21:00 2000 ]

Из уравнения[Author ID1: at Tue Nov 28 08:31:00 2000 ]й (3) и (4) [Author ID1: at Tue Nov 28 08:31:00 2000 ] динамики вращательного движения[Author ID1: at Tue Nov 28 08:31:00 2000 ] следует, что

[Author ID2: at Wed Oct 18 13:17:00 2000 ]

[Author ID2: at Sat Sep 30 13:11:00 2000 ]Т2 - Т1 = [Author ID2: at Sat Sep 30 13:08:00 2000 ]μ[Author ID2: at Sat Sep 30 13:08:00 2000 ] а, [Author ID2: at Sat Sep 30 13:08:00 2000 ][Author ID2: at Sat Sep 30 13:09:00 2000 ][Author ID2: at Sat Sep 30 13:09:00 2000 ][Author ID2: at Sat Sep 30 13:09:00 2000 ][Author ID2: at Sat Sep 30 13:09:00 2000 ],[Author ID1: at Wed Mar 14 10:05:00 2001 ] [Author ID2: at Sat Sep 30 13:10:00 2000 ] [Author ID2: at Thu Nov 9 14:05:00 2000 ](3[Author ID1: at Tue Nov 28 08:24:00 2000 ]5[Author ID1: at Tue Nov 28 08:24:00 2000 ])

где μ - коэффициент пропорциональности,[Author ID1: at Wed Mar 14 10:05:00 2001 ] равный [Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ].[Author ID1: at Tue Nov 28 08:36:00 2000 ], зависящий от массы и формы блока[Author ID1: at Tue Nov 28 08:35:00 2000 ], [Author ID2: at Thu Nov 9 14:11:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID2: at Thu Nov 9 14:11:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID2: at Thu Nov 9 14:11:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ][Author ID2: at Thu Nov 9 14:11:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ].[Author ID2: at Thu Nov 9 14:12:00 2000 ][Author ID1: at Tue Nov 28 08:35:00 2000 ].[Author ID2: at Thu Nov 9 14:11:00 2000 ]

Пусть разность[Author ID2: at Thu Nov 9 14:17:00 2000 ] между[Author ID1: at Wed Mar 14 10:07:00 2001 ] количеств[Author ID2: at Thu Nov 9 14:17:00 2000 ]ами[Author ID1: at Wed Mar 14 10:07:00 2001 ] перегрузков на левом и правом грузах равна [Author ID2: at Thu Nov 9 14:17:00 2000 ]п. [Author ID2: at Thu Nov 9 14:18:00 2000 ]Нетрудно показать, что величины N, n[Author ID2: at Thu Sep 28 15:26:00 2000 ]N,[Author ID2: at Thu Sep 28 15:26:00 2000 ] [Author ID1: at Wed Mar 14 10:08:00 2001 ]n[Author ID2: at Thu Sep 28 15:26:00 2000 ] [Author ID1: at Wed Mar 14 10:08:00 2001 ]и [Author ID1: at Wed Mar 14 10:08:00 2001 ] [Author ID1: at Wed Mar 14 10:08:00 2001 ]-->n[Author ID2: at Thu Sep 28 15:27:00 2000 ][Author ID2: at Thu Sep 28 15:27:00 2000 ]n[Author ID2: at Thu Sep 28 15:27:00 2000 ]-->1[Author ID2: at Sat Sep 30 13:10:00 2000 ][Author ID2: at Thu Sep 28 15:27:00 2000 ]₀[Author ID2: at Thu Nov 9 14:14:00 2000 ] связаны [Author ID2: at Thu Nov 9 14:18:00 2000 ]соотр[Author ID1: at Wed Mar 14 10:09:00 2001 ]н[Author ID1: at Wed Mar 14 10:09:00 2001 ]ошением:[Author ID1: at Wed Mar 14 15:56:00 2001 ]

[Author ID0: at ]

[Author ID2: at Wed Oct 18 13:17:00 2000 ]

N - n[Author ID2: at Sat Sep 30 13:11:00 2000 ]

[Author ID2: at Sat Sep 30 13:11:00 2000 ] n1 = [Author ID2: at Sat Sep 30 13:11:00 2000 ] [Author ID2: at Sat Sep 30 13:14:00 2000 ] [Author ID2: at Sat Sep 30 13:12:00 2000 ] [Author ID2: at Sat Sep 30 13:13:00 2000 ][Author ID2: at Sat Sep 30 13:13:00 2000 ][Author ID2: at Sat Sep 30 13:13:00 2000 ][Author ID2: at Sat Sep 30 13:13:00 2000 ] [Author ID2: at Sat Sep 30 13:14:00 2000 ] [Author ID2: at Wed Oct 18 13:18:00 2000 ] [Author ID2: at Sat Sep 30 13:14:00 2000 ] (4[Author ID1: at Tue Nov 28 08:24:00 2000 ]6[Author ID1: at Tue Nov 28 08:24:00 2000 ])[Author ID2: at Wed Oct 18 13:17:00 2000 ]

[Author ID2: at Sat Sep 30 13:11:00 2000 ] [Author ID2: at Sat Sep 30 13:11:00 2000 ] [Author ID2: at Fri Sep 29 17:42:00 2000 ] 2 [Author ID2: at Sat Sep 30 13:11:00 2000 ] .[Author ID0: at ]

[Author ID2: at Wed Sep 27 18:50:00 2000 ]

[Author ID2: at Wed Sep 27 19:33:00 2000 ]

Решая совместно уравнения (1),(2),(5) и[Author ID1: at Tue Nov 28 08:26:00 2000 ] ÷[Author ID1: at Tue Nov 28 08:26:00 2000 ] [Author ID1: at Tue Nov 28 08:26:00 2000 ](4[Author ID1: at Tue Nov 28 08:26:00 2000 ]6[Author ID1: at Tue Nov 28 08:26:00 2000 ]), получае[Author ID2: at Thu Nov 9 14:50:00 2000 ]и[Author ID2: at Thu Nov 9 14:50:00 2000 ]м:[Author ID1: at Wed Mar 14 10:12:00 2001 ] [Author ID1: at Tue Nov 28 08:26:00 2000 ],[Author ID1: at Wed Mar 14 10:10:00 2001 ] что[Author ID1: at Wed Mar 14 10:10:00 2001 ] величин[Author ID2: at Thu Nov 9 14:21:00 2000 ][Author ID1: at Wed Mar 14 10:12:00 2001 ]а[Author ID2: at Thu Nov 9 14:21:00 2000 ][Author ID1: at Wed Mar 14 10:11:00 2001 ] [Author ID2: at Thu Nov 9 14:21:00 2000 ][Author ID1: at Wed Mar 14 10:12:00 2001 ] ускорения [Author ID1: at Wed Mar 14 10:11:00 2001 ]каждого груза[Author ID2: at Thu Nov 9 14:21:00 2000 ][Author ID1: at Wed Mar 14 10:11:00 2001 ]с которыми[Author ID2: at Thu Nov 9 14:21:00 2000 ] [Author ID2: at Wed Sep 27 18:44:00 2000 ]движутся грузы[Author ID2: at Thu Nov 9 14:22:00 2000 ] равн[Author ID1: at Wed Mar 14 10:11:00 2001 ]ы[Author ID2: at Thu Nov 9 14:22:00 2000 ]а[Author ID2: at Thu Nov 9 14:22:00 2000 ][Author ID1: at Wed Mar 14 10:11:00 2001 ] [Author ID1: at Wed Mar 14 10:11:00 2001 ]:[Author ID1: at Wed Mar 14 10:12:00 2001 ] [Author ID2: at Wed Sep 27 18:27:00 2000 ][Author ID2: at Thu Sep 28 14:38:00 2000 ]

[Author ID2: at Wed Oct 18 13:18:00 2000 ] [Author ID2: at Thu Sep 28 14:38:00 2000 ] [Author ID2: at Thu Sep 28 14:39:00 2000 ][Author ID2: at Sat Sep 30 13:17:00 2000 ][Author ID2: at Sat Sep 30 13:17:00 2000 ][Author ID2: at Sat Sep 30 13:17:00 2000 ].[Author ID2: at Thu Nov 9 14:23:00 2000 ] [Author ID2: at Thu Sep 28 14:39:00 2000 ] [Author ID2: at Thu Sep 28 14:40:00 2000 ] [Author ID2: at Thu Sep 28 14:39:00 2000 ] [Author ID2: at Sat Sep 30 13:19:00 2000 ] [Author ID2: at Wed Oct 18 13:19:00 2000 ] ([Author ID2: at Sat Sep 30 13:19:00 2000 ]5[Author ID2: at Sat Sep 30 13:19:00 2000 ][Author ID1: at Tue Nov 28 08:27:00 2000 ]7[Author ID1: at Tue Nov 28 08:27:00 2000 ])[Author ID2: at Sat Sep 30 13:19:00 2000 ][Author ID0: at ]

Анализируя это выражение, можно сделать следущие [Author ID2: at Thu Nov 9 18:19:00 2000 ]выводы.[Author ID2: at Thu Nov 9 18:20:00 2000 ][Author ID0: at ]

Во-первых,[Author ID1: at Wed Mar 14 10:12:00 2001 ] [Author ID2: at Thu Nov 9 18:20:00 2000 ]Во-первых, у[Author ID2: at Thu Nov 9 18:20:00 2000 ][Author ID1: at Tue Nov 28 08:37:00 2000 ]у[Author ID1: at Tue Nov 28 08:37:00 2000 ]скорени[Author ID2: at Thu Nov 9 18:20:00 2000 ]е[Author ID2: at Thu Nov 9 18:20:00 2000 ][Author ID1: at Tue Nov 28 08:39:00 2000 ]е[Author ID1: at Tue Nov 28 08:39:00 2000 ] грузов не [Author ID2: at Thu Nov 9 18:20:00 2000 ]меняется с течением [Author ID2: at Thu Nov 9 18:20:00 2000 ][Author ID1: at Tue Nov 28 08:37:00 2000 ]зависит от [Author ID1: at Tue Nov 28 08:37:00 2000 ]времени,[Author ID2: at Thu Nov 9 18:20:00 2000 ] [Author ID1: at Wed Mar 14 10:13:00 2001 ]т.е. [Author ID1: at Tue Nov 28 08:38:00 2000 ]а[Author ID1: at Tue Nov 28 08:38:00 2000 ] = [Author ID1: at Tue Nov 28 08:38:00 2000 ]-->const[Author ID1: at Tue Nov 28 08:38:00 2000 ][Author ID1: at Tue Nov 28 08:38:00 2000 ],[Author ID1: at Tue Nov 28 08:39:00 2000 ] поэтому[Author ID2: at Thu Nov 9 18:20:00 2000 ] [Author ID2: at Thu Nov 9 18:21:00 2000 ]п[Author ID2: at Thu Nov 9 15:23:00 2000 ]уть[Author ID2: at Thu Nov 9 15:23:00 2000 ],[Author ID1: at Mon Feb 19 12:16:00 2001 ] [Author ID2: at Thu Nov 9 18:22:00 2000 ]пройденный грузами за время [Author ID2: at Thu Nov 9 15:23:00 2000 ] [Author ID2: at Thu Nov 9 15:23:00 2000 ]t[Author ID2: at Thu Nov 9 15:23:00 2000 ] , при условии, что их начальная скорость равна нулю, определяется выражением[Author ID2: at Thu Nov 9 15:23:00 2000 ]:[Author ID1: at Wed Mar 14 10:13:00 2001 ][Author ID0: at ]

[Author ID2: at Thu Nov 9 15:23:00 2000 ] [Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID2: at Thu Nov 9 15:23:00 2000 ].[Author ID2: at Thu Nov 9 15:24:00 2000 ] [Author ID2: at Thu Nov 9 15:23:00 2000 ] [Author ID2: at Thu Nov 9 15:25:00 2000 ] [Author ID2: at Thu Nov 9 15:26:00 2000 ] ([Author ID2: at Thu Nov 9 15:23:00 2000 ]6[Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID1: at Tue Nov 28 08:27:00 2000 ]8[Author ID1: at Tue Nov 28 08:27:00 2000 ])[Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID2: at Thu Nov 9 18:22:00 2000 ]

Во-вт[Author ID1: at Wed Mar 14 10:13:00 2001 ]о[Author ID1: at Wed Mar 14 10:14:00 2001 ]р[Author ID1: at Wed Mar 14 10:13:00 2001 ]ых, [Author ID1: at Wed Mar 14 10:14:00 2001 ]Во-вторых, при фиксированных значениях масс грузов [Author ID2: at Thu Nov 9 18:22:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]М[Author ID2: at Thu Nov 9 18:23:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ], масс перегрузков [Author ID2: at Thu Nov 9 18:23:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]Δ[Author ID2: at Thu Nov 9 18:24:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]-->m[Author ID2: at Thu Nov 9 18:24:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ][Author ID2: at Thu Nov 9 18:24:00 2000 ] [Author ID2: at Thu Nov 9 18:24:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]и общем числе перегрузков [Author ID2: at Thu Nov 9 18:25:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]N[Author ID2: at Thu Nov 9 18:25:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ], [Author ID2: at Thu Nov 9 18:25:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]величина [Author ID2: at Thu Nov 9 18:26:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]ускорени[Author ID2: at Thu Nov 9 18:25:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]я[Author ID2: at Thu Nov 9 18:26:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ] [Author ID2: at Thu Nov 9 18:25:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]а[Author ID2: at Thu Nov 9 18:26:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ] зависит[Author ID2: at Thu Nov 9 18:26:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ] [Author ID2: at Thu Nov 9 18:23:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]только от разности числа перегрузков [Author ID2: at Thu Nov 9 18:26:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]п[Author ID2: at Thu Nov 9 18:27:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ] на левом и правом грузах[Author ID2: at Thu Nov 9 18:27:00 2000 ][Author ID1: at Tue Nov 28 08:43:00 2000 ]. Это означает, что в[Author ID2: at Thu Nov 9 18:27:00 2000 ][Author ID1: at Tue Nov 28 08:44:00 2000 ]в[Author ID1: at Tue Nov 28 08:44:00 2000 ]еличина [Author ID2: at Thu Nov 9 18:27:00 2000 ][Author ID2: at Thu Nov 9 18:28:00 2000 ][Author ID2: at Thu Nov 9 18:28:00 2000 ][Author ID2: at Thu Nov 9 18:28:00 2000 ] [Author ID2: at Thu Nov 9 18:29:00 2000 ]постоянная и [Author ID2: at Thu Nov 9 18:29:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ]зависит только от параметров установки[Author ID2: at Thu Nov 9 18:29:00 2000 ] (массы груз[Author ID1: at Tue Nov 28 08:44:00 2000 ]ов[Author ID1: at Tue Nov 28 08:46:00 2000 ] [Author ID1: at Tue Nov 28 08:44:00 2000 ]М[Author ID1: at Tue Nov 28 08:45:00 2000 ], массы перегрузков [Author ID1: at Tue Nov 28 08:45:00 2000 ]Δ[Author ID1: at Tue Nov 28 08:45:00 2000 ]т[Author ID1: at Tue Nov 28 08:45:00 2000 ] и их числа [Author ID1: at Tue Nov 28 08:47:00 2000 ]N[Author ID1: at Tue Nov 28 08:47:00 2000 ])[Author ID1: at Tue Nov 28 08:47:00 2000 ], т.е.[Author ID1: at Tue Nov 28 08:47:00 2000 ]

[Author ID1: at Tue Nov 28 08:48:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ]. (9)[Author ID1: at Tue Nov 28 08:50:00 2000 ]

.[Author ID2: at Thu Nov 9 18:29:00 2000 ][Author ID1: at Tue Nov 28 08:47:00 2000 ] [Author ID2: at Thu Nov 9 18:29:00 2000 ]Действительно, из выражения ([Author ID2: at Thu Nov 9 18:29:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ]5[Author ID2: at Thu Nov 9 18:29:00 2000 ][Author ID1: at Tue Nov 28 08:27:00 2000 ]) следует, что[Author ID2: at Thu Nov 9 18:29:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ] правая часть выражения[Author ID2: at Thu Nov 9 18:33:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID2: at Thu Nov 9 18:29:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ]

[Author ID2: at Thu Nov 9 18:36:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ] [Author ID2: at Thu Nov 9 18:32:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID2: at Thu Nov 9 18:31:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID2: at Thu Nov 9 18:31:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID2: at Thu Nov 9 18:31:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ] [Author ID2: at Thu Nov 9 18:32:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ]([Author ID2: at Thu Nov 9 18:33:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ]7[Author ID2: at Thu Nov 9 18:32:00 2000 ][Author ID1: at Tue Nov 28 08:27:00 2000 ])[Author ID2: at Thu Nov 9 18:32:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID0: at ][Author ID0: at ]

определяется только параметрами установки. Это означает. что[Author ID2: at Thu Nov 9 18:33:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ]

[Author ID2: at Thu Nov 9 18:34:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ] [Author ID2: at Thu Nov 9 18:35:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ] [Author ID2: at Thu Nov 9 18:36:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID2: at Thu Nov 9 18:35:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID2: at Thu Nov 9 18:35:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ][Author ID2: at Thu Nov 9 18:35:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ]. ([Author ID2: at Thu Nov 9 18:36:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ]8[Author ID2: at Thu Nov 9 18:36:00 2000 ][Author ID1: at Tue Nov 28 08:28:00 2000 ])[Author ID2: at Thu Nov 9 18:36:00 2000 ][Author ID1: at Tue Nov 28 08:50:00 2000 ]-->[Author ID2: at Thu Nov 9 15:23:00 2000 ][Author ID1: at Tue Nov 28 08:51:00 2000 ][Author ID2: at Thu Nov 9 18:27:00 2000 ]