Question

Шарик массой 100 г подвешен на длиной нити. Шарик отклоняют от положения равновесия на угол 60 градусов, сдерживая нить слегка натянутой, и отпускают. Определите силу натяжения нити в момент, когда шарик проходит положение равновесия.

Answer 1

Модуль натяжения нити равен сумме из двух сил:
весу шарика P=mg
и центростермительной силе, связанной с движением шарика Fc=mv²/R
Скорость движения рассчитаем из равенства потенциальной энергии  mgh
и кинетической энергии mv²/2.
Учитывая, что
h=R-R·cos(60)=R/2
получим
mgR/2=mv²/2
или
v²/R=g
сложив P+Fc=mg+mg=2mg
получим значение силы
F =2mg=2·0.1·10=2Н
Ответ: сила натяжения нити равна 2 Ньютона.

Answer 2

Calculation of Tension Force in the String

To determine the tension force in the string when the ball passes through the equilibrium position, we can consider the forces acting on the ball at that moment.

When the ball is at the equilibrium position, the net force acting on it is zero. This means that the gravitational force pulling the ball downward is balanced by the tension force in the string pulling the ball upward.

Let's denote the tension force in the string as T.

At the equilibrium position, the gravitational force acting on the ball can be calculated using the formula:

F_gravity = m * g

Where: - m is the mass of the ball (given as 100 g, which is equal to 0.1 kg) - g is the acceleration due to gravity (approximately 9.8 m/s^2)

Substituting the given values, we have:

F_gravity = 0.1 kg * 9.8 m/s^2

Now, since the tension force in the string is equal in magnitude but opposite in direction to the gravitational force, we can write:

T = F_gravity

Therefore, the tension force in the string when the ball passes through the equilibrium position is equal to the gravitational force acting on the ball.

Let's calculate the tension force:

T = 0.1 kg * 9.8 m/s^2

Using the given values, we find:

T ≈ 0.98 N

Therefore, the tension force in the string at the moment the ball passes through the equilibrium position is approximately 0.98 N.