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Консультация № 138669
30.05.2008, 13:16
0.00 руб.
0
1
1
125. К пружинным весам подвешен блок. Через блок перекинули шнур, к концам которого привязали грузы массой 1,5 кг и 3 кг. Каково будет показание весов во время движения грузов? Массой блока и шнура пренебречь.
Обсуждение
01.06.2008, 11:26
общий
это ответ
Здравствуйте, Павел Сергеевич!
Обозначим массы гирь: m<sub>1</sub> = 1.5 кг; m<sub>2</sub> = 3 кг. В одну сторону на шнур действует вес G<sub>1</sub> = m<sub>1</sub>*g (1), где g - ускорение свободного падения; в обратную сторону на шнур действует вес G<sub>2</sub> = m<sub>2</sub>*g (2). Равнодействующая сила F = G<sub>2</sub> - G<sub>1</sub> = g*(m<sub>2</sub> - m<sub>1</sub>) сообщает суммарной массе m<sub>с</sub> = m<sub>1</sub> + m<sub>2</sub> ускорение, равное a; на основании 2-го закона Ньютона: a = F/m<sub>с</sub> = g*(m<sub>2</sub> - m<sub>1</sub>)/(m<sub>1</sub> + m<sub>2</sub>) (3). При этом меньший груз m<sub>1</sub> движется с ускорением, равным a, вверх, силой T<sub>1</sub> натяжения соответствующей ветви шнура, т.е. эта сила преодолевает и вес G<sub>1</sub> = m<sub>1</sub>*g, и силу инерции F<sub>и1</sub> = m<sub>1</sub>*a: T<sub>1</sub> = m<sub>1</sub>*(g + a) (4). Груз m<sub>2</sub> движется с ускорением, равным a, вниз; сила инерции F<sub>и2</sub> = m<sub>2</sub>*a действует против силы тяжести G<sub>2</sub> = m<sub>2</sub>*g, поэтому натяжение соответствующей ветви шнура T<sub>2</sub> = m<sub>2</sub>*(g - a) (5). Из (4) и (5) после подстановки (3) получается: T<sub>1</sub> = T<sub>2</sub> = 2*g*m<sub>1</sub>*m<sub>2</sub>/(m<sub>1</sub> + m<sub>2</sub>) (6). На блок и пружинные весы действует сумма T<sub>1</sub> + T<sub>2</sub> = 4*g*m<sub>1</sub>*m<sub>2</sub>/(m<sub>1</sub> + m<sub>2</sub>) (6). Поскольку весы градуируются в килограммах веса, их показание G<sub>с</sub> будет равно: G<sub>с</sub> = 4*G<sub>1</sub>*G<sub>2</sub>/(G<sub>1</sub> + G<sub>2</sub>) = 4*1.5*3/(1.5 + 3) = 4 кГс.
Обозначим массы гирь: m<sub>1</sub> = 1.5 кг; m<sub>2</sub> = 3 кг. В одну сторону на шнур действует вес G<sub>1</sub> = m<sub>1</sub>*g (1), где g - ускорение свободного падения; в обратную сторону на шнур действует вес G<sub>2</sub> = m<sub>2</sub>*g (2). Равнодействующая сила F = G<sub>2</sub> - G<sub>1</sub> = g*(m<sub>2</sub> - m<sub>1</sub>) сообщает суммарной массе m<sub>с</sub> = m<sub>1</sub> + m<sub>2</sub> ускорение, равное a; на основании 2-го закона Ньютона: a = F/m<sub>с</sub> = g*(m<sub>2</sub> - m<sub>1</sub>)/(m<sub>1</sub> + m<sub>2</sub>) (3). При этом меньший груз m<sub>1</sub> движется с ускорением, равным a, вверх, силой T<sub>1</sub> натяжения соответствующей ветви шнура, т.е. эта сила преодолевает и вес G<sub>1</sub> = m<sub>1</sub>*g, и силу инерции F<sub>и1</sub> = m<sub>1</sub>*a: T<sub>1</sub> = m<sub>1</sub>*(g + a) (4). Груз m<sub>2</sub> движется с ускорением, равным a, вниз; сила инерции F<sub>и2</sub> = m<sub>2</sub>*a действует против силы тяжести G<sub>2</sub> = m<sub>2</sub>*g, поэтому натяжение соответствующей ветви шнура T<sub>2</sub> = m<sub>2</sub>*(g - a) (5). Из (4) и (5) после подстановки (3) получается: T<sub>1</sub> = T<sub>2</sub> = 2*g*m<sub>1</sub>*m<sub>2</sub>/(m<sub>1</sub> + m<sub>2</sub>) (6). На блок и пружинные весы действует сумма T<sub>1</sub> + T<sub>2</sub> = 4*g*m<sub>1</sub>*m<sub>2</sub>/(m<sub>1</sub> + m<sub>2</sub>) (6). Поскольку весы градуируются в килограммах веса, их показание G<sub>с</sub> будет равно: G<sub>с</sub> = 4*G<sub>1</sub>*G<sub>2</sub>/(G<sub>1</sub> + G<sub>2</sub>) = 4*1.5*3/(1.5 + 3) = 4 кГс.
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