Question

ПОМОГИТЕ Найти радиус шкива, если постоянная сила в 2 кН приложенная к его ободу раскручивает систему из состояния покоя до 20 об/с за с. Момент инерции системы 0,5 кг*м²

Answer 1

Дано
F=2кН=2000 Н
ω0 = 0 рад/с
f=20 об/с
t = 1 c
J =0,5 кг*м²
найти
R - ?
решение
ω=2пf
ε = (ω-ω0) /t = ω/t=2пf/t
угловое ускорение ε = M/J = F*R/J ;
радиус  R =εJ/F=2пf/t *J/F=2*3.14*20/1 *0.5/2000 = 0.0314 м =3.14 см
ОТВЕТ  3.14 см

Answer 2

Finding the Radius of the Pulley

To find the radius of the pulley, we can use the formula for torque:

Torque (τ) = Force (F) * Radius (r)

Given that the constant force applied to the rim of the pulley is 2 kN (kilonewtons) and the system goes from rest to a speed of 20 revolutions per second in 1 second, we can calculate the torque.

First, let's convert the force from kilonewtons to newtons:

Force (F) = 2 kN = 2000 N

Next, let's calculate the torque:

Torque (τ) = Force (F) * Radius (r)

We know the moment of inertia of the system is 0.5 kg*m².

Using the equation for rotational motion:

Torque (τ) = Moment of Inertia (I) * Angular Acceleration (α)

We can rearrange the equation to solve for the angular acceleration:

Angular Acceleration (α) = Torque (τ) / Moment of Inertia (I)

The angular acceleration can also be calculated using the formula:

Angular Acceleration (α) = Change in Angular Velocity (Δω) / Time (t)

Given that the system goes from rest to 20 revolutions per second in 1 second, we can calculate the angular acceleration:

Angular Acceleration (α) = (20 rev/s - 0 rev/s) / 1 s = 20 rev/s²

Now, we can equate the two expressions for angular acceleration:

Torque (τ) / Moment of Inertia (I) = Angular Acceleration (α)

Substituting the values we have:

2000 N * r / 0.5 kg*m² = 20 rev/s²

Simplifying the equation:

r = (20 rev/s² * 0.5 kg*m²) / 2000 N

Calculating the radius:

r = 0.01 m = 10 mm

Therefore, the radius of the pulley is 10 mm.