A rotating flywheel can be used as a method to store energy. If it has 2.0 × 106 J of kinetic energy when rotating at 350 rad/s, and if a frictional torque of 4.0 Nm acts on the system, in what interval of time would the flywheel come to rest?Select one:a.2 860 minb.32.7 minc.47.6 mind.190 min

To solve this problem, we need to use the concept of work and energy. The work done by the frictional torque will be equal to the kinetic energy of the flywheel.

Work done is given by the formula: Work = Torque * Angular Displacement

Since the work done by the friction is equal to the kinetic energy of the flywheel, we can set them equal to each other:

Torque * Angular Displacement = Kinetic Energy

We know the torque (4.0 Nm) and the kinetic energy (2.0 × 10^6 J), so we can solve for the angular displacement:

Angular Displacement = Kinetic Energy / Torque Angular Displacement = 2.0 × 10^6 J / 4.0 Nm = 5.0 × 10^5 rad

The angular velocity of the flywheel decreases linearly from its initial value to zero, because the torque (and therefore the angular deceleration) is constant. So the average angular velocity during this process is half the initial angular velocity:

Average Angular Velocity = Initial Angular Velocity / 2 Average Angular Velocity = 350 rad/s / 2 = 175 rad/s

The time it takes for the flywheel to come to rest can be found by dividing the total angular displacement by the average angular velocity:

Time = Angular Displacement / Average Angular Velocity Time = 5.0 × 10^5 rad / 175 rad/s = 2,857.14 s

Converting seconds to minutes (since the options are given in minutes), we get:

Time = 2,857.14 s / 60 = 47.6 min

So, the correct answer is c. 47.6 min.

To solve this problem, we need to use the formula for work done, which is equal to the change in kinetic energy. The work done by the frictional force to bring the flywheel to rest is equal to the initial kinetic energy of the flywheel.

Work done = Torque * Angular displacement

But we also know that Angular displacement = Angular speed * time

So, Work done = Torque * Angular speed * time

We can rearrange this to find time:

Time = Work done / (Torque * Angular speed)

Given: Work done = 2.0 × 10^6 J (which is the initial kinetic energy) Torque = 4.0 Nm Angular speed = 350 rad/s

Substitute these values into the equation:

Time = 2.0 × 10^6 J / (4.0 Nm * 350 rad/s) = 1428.57 seconds

To convert this to minutes, divide by 60:

Time = 1428.57 seconds / 60 = 23.81 minutes

So, the flywheel would come to rest in approximately 23.81 minutes. However, this option is not available in the choices given. There might be a mistake in the problem or the given choices.