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анонимm = 200 г = 0,2 кг.
g = 9,8 м/с2.
l = 1 м.
k = 124 Н/м.
х - ?
На шарик при прохождении положения равновесия действует 2 силы: сила тяжести Fт, направленная вертикально вниз, сила N натяжения нити, направленная вертикально вверх.
m * a = F + N - 2 закон Ньютона в векторной форме.
Для проекций на вертикальную ось 2 закон Ньютона примет вид: m * a = - Fт + N.
N = m * a + Fт.
Сила тяжести Fт определяется формулой: Fт = m * g.
N = m * a + m * g = m * (a + g).
Центростремительное ускорение а выразим формулой: a = V2 / l.
Скорость шарика найдём по закону сохранения энергии: m * g * l = m * V2/ 2.
V2 = 2 * g * l.
N = m * (V2 / l + g) = m * (2 * g * l / l + g) = m * 3 * g.
Силу натяжения нити выразим N законом Гука: N = k * х.
k * х = 3 * m * g.
х = 3 * m * g / k.
х = 3 * 0,2 кг * 9,8 м/с2 / 124 Н/м = 0,047 м.
Ответ: при прохождении положения равновесия растяжении нити составляет х = 0,047 м.
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