Question

Металлический шарик массой 100 г висит на нити длиной 1 м.Шарик рас скручивают на нити в вертикальной плоскости. С какой постоянной угловой скоростью могут вращать нить , если максимальный вес, который она удерживает T=11 Н ?

Answer 1

Согласно 2-му закону Ньютона
ma=mg+ T    а- центростремительное ускорение
m*омега^2*R=mg+T откуда
омега= корень квадратный из([g/R]+(T/mg))=корень квадратный ([9.8/1]+[11/1*0.1])=
=10.9 [рад/с]

Answer 2

Calculation of the Constant Angular Velocity

To determine the constant angular velocity at which the string can rotate, we can use the principle of equilibrium. The maximum weight that the string can support is given as T = 11 N.

The weight of the metal ball can be calculated using the formula:

Weight = mass x acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s^2. Given that the mass of the ball is 100 g (or 0.1 kg), we can calculate the weight:

Weight = 0.1 kg x 9.8 m/s^2 = 0.98 N

Since the maximum weight the string can support is T = 11 N, the weight of the ball is well within the limit.

To find the constant angular velocity at which the string can rotate, we can use the formula:

Tension = mass x length x angular velocity^2

where: - Tension is the tension in the string, - mass is the mass of the ball, - length is the length of the string, and - angular velocity is the constant angular velocity at which the string can rotate.

Rearranging the formula, we can solve for the angular velocity:

angular velocity = sqrt(Tension / (mass x length))

Substituting the given values, we have:

angular velocity = sqrt(11 N / (0.1 kg x 1 m))

Calculating this, we find:

angular velocity ≈ 10.49 rad/s

Therefore, the string can rotate with a constant angular velocity of approximately 10.49 rad/s while supporting a maximum weight of 11 N.

Please note that the above calculation assumes ideal conditions and neglects factors such as air resistance and the mass of the string itself.