Question

Помогите пожалуйста! Маховик массой 1 т свя­зан со шкивом. К шкиву, радиус которого 0,15 м, приложе­на постоянная сила 500 н по ка­сательной. Определите, через сколь­ко времени после начала враще­ния маховик достигнет скорости 6,28 сек^-1. Маховик представляет собой диск радиусом 1 м.

Answer 1

Должно

быть  через 42 секунды.

Answer 2

Problem Analysis

We are given a scenario where a flywheel with a mass of 1 ton is connected to a pulley. A constant force of 500 N is applied tangentially to the pulley, which has a radius of 0.15 m. We need to determine the time it takes for the flywheel to reach a speed of 6.28 rad/s.

Solution

To solve this problem, we can use the principles of rotational motion and torque. The torque applied to an object is equal to the product of the force applied tangentially and the radius at which the force is applied. The torque can be calculated using the formula:

Torque = Force × Radius

In this case, the torque applied to the flywheel is equal to the torque applied to the pulley. The torque can also be expressed as the product of the moment of inertia and the angular acceleration:

Torque = Moment of Inertia × Angular Acceleration

The moment of inertia of a disk can be calculated using the formula:

Moment of Inertia = (1/2) × Mass × Radius^2

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

Angular Acceleration = Torque / Moment of Inertia

The angular acceleration is related to the angular velocity and time by the equation:

Angular Velocity = Initial Angular Velocity + (Angular Acceleration × Time)

We can rearrange this equation to solve for time:

Time = (Angular Velocity - Initial Angular Velocity) / Angular Acceleration

In this case, the initial angular velocity is 0 rad/s, and the target angular velocity is 6.28 rad/s.

Now, let's calculate the values and solve the problem step by step.

Calculation

Given: - Mass of the flywheel = 1 ton = 1000 kg - Radius of the pulley = 0.15 m - Force applied tangentially = 500 N - Target angular velocity = 6.28 rad/s

1. Calculate the moment of inertia of the flywheel: - Moment of Inertia = (1/2) × Mass × Radius^2 - Moment of Inertia = (1/2) × 1000 kg × (1 m)^2 - Moment of Inertia = 500 kg·m^2

2. Calculate the torque applied to the flywheel: - Torque = Force × Radius - Torque = 500 N × 0.15 m - Torque = 75 N·m

3. Calculate the angular acceleration: - Angular Acceleration = Torque / Moment of Inertia - Angular Acceleration = 75 N·m / 500 kg·m^2 - Angular Acceleration = 0.15 rad/s^2

4. Calculate the time taken to reach the target angular velocity: - Time = (Angular Velocity - Initial Angular Velocity) / Angular Acceleration - Time = (6.28 rad/s - 0 rad/s) / 0.15 rad/s^2 - Time = 41.87 s

Answer

After starting the rotation, the flywheel will reach a speed of 6.28 rad/s after approximately 41.87 seconds.

Please note that the calculations provided are based on the given information and assumptions.