Question

Диск вращается вокруг вертикальной оси с частотой 30 об/мин. На расстоянии 20 см от оси вращения на диске лежит тело. Найти коэффициент трения к между телом и диском, при котором тело не соскальзывало бы с диска.

Answer 1

На тело действует центростремительная сила F=m*w^2*R=m*4*pi^2*n^2*R
Тело не будет соскальзывать, пока Fтр>=F    Fтр=k*m*g
m*4*pi^2*n^2*R=k*m*g      k=4*pi^2*n*R/g=4*9,86*0,5*0,2/9,8=0,4

Answer 2

Finding the Coefficient of Friction Between the Body and the Disk

To find the coefficient of friction between the body and the disk, we need to consider the forces acting on the body and the conditions for it to not slip off the disk.

Given: - The disk rotates around a vertical axis with a frequency of 30 revolutions per minute (rpm). - The body is located at a distance of 20 cm from the axis of rotation.

To prevent the body from slipping off the disk, the frictional force between the body and the disk must be equal to or greater than the force that tends to make the body slip off. This force is the product of the body's mass and the acceleration due to gravity.

Let's calculate the required frictional force and then determine the coefficient of friction.

Calculating the Required Frictional Force

The required frictional force can be calculated using the formula:

Frictional force = mass of the body × acceleration due to gravity

The mass of the body is not provided in the question, so we'll assume a mass of 1 kg for simplicity.

The acceleration due to gravity is approximately 9.8 m/s^2.

Therefore, the required frictional force is:

Frictional force = 1 kg × 9.8 m/s^2 = 9.8 N

Determining the Coefficient of Friction

The frictional force between the body and the disk can be calculated using the formula:

Frictional force = coefficient of friction × normal force

The normal force is the force exerted by the disk on the body and is equal to the weight of the body. The weight of the body can be calculated using the formula:

Weight = mass of the body × acceleration due to gravity

Substituting the values, we get:

Weight = 1 kg × 9.8 m/s^2 = 9.8 N

Since the body is located at a distance of 20 cm from the axis of rotation, the normal force is equal to the centripetal force acting on the body. The centripetal force can be calculated using the formula:

Centripetal force = mass of the body × angular velocity^2 × radius

The angular velocity can be calculated by converting the frequency of rotation from revolutions per minute (rpm) to radians per second (rad/s). One revolution is equal to 2π radians.

Converting the frequency of rotation:

Angular velocity = 30 rpm × (2π rad/1 rev) × (1 min/60 s) = 1.57 rad/s

Substituting the values, we get:

Centripetal force = 1 kg × (1.57 rad/s)^2 × 0.2 m = 0.494 N

Since the normal force is equal to the centripetal force, we have:

Normal force = 0.494 N

Now, we can determine the coefficient of friction by rearranging the formula:

Coefficient of friction = Frictional force / Normal force

Substituting the values, we get:

Coefficient of friction = 9.8 N / 0.494 N ≈ 19.84

Therefore, the coefficient of friction between the body and the disk, at which the body would not slip off, is approximately 19.84.

Please note that the coefficient of friction calculated here is dimensionless and does not have any units.