Rotational motion, using torque to find power

[ba726]

Homework Statement

An electric motor can accelerate a Ferris wheel of moment of inertia 19200kgm2 from rest to 9.11 rev/min in 10.7s. When the motor is turned off, friction causes the wheel to slow down from 9.11 rev/min to 7.36 rev/min in 9.55s. Determine the torque generated by the motor to bring the wheel to 9.11 rev/min. Answer in units of Nm. Also, determine the power needed to maintain the rotational speed at 9.11 rev/min. Answer in units of W.

Homework Equations

torquenet= Inertia x angular acceleration
angular velocity (final)= angular velocity (initial) + ang accel x time
Power=torque x ang velocity

The Attempt at a Solution

I already found part 1, the torque generated by the motor (2080.257403 Nm) and I'm completely stuck on part 2. I don't know if I'm doing it wrong or what. I originally used the torque from the motor times the ang velocity converted to radians/s from rev/min. I've used net torque times the same ang velocity. I forgot to convert the 9.11 ang velocity so I've used both torques with ang velocity in rev/min. What am I doing wrong?!?

 

[Andrew Mason]

Homework Statement

An electric motor can accelerate a Ferris wheel of moment of inertia 19200kgm2 from rest to 9.11 rev/min in 10.7s. When the motor is turned off, friction causes the wheel to slow down from 9.11 rev/min to 7.36 rev/min in 9.55s. Determine the torque generated by the motor to bring the wheel to 9.11 rev/min. Answer in units of Nm. Also, determine the power needed to maintain the rotational speed at 9.11 rev/min. Answer in units of W.

Homework Equations

torquenet= Inertia x angular acceleration
angular velocity (final)= angular velocity (initial) + ang accel x time
Power=torque x ang velocity

The Attempt at a Solution

I already found part 1, the torque generated by the motor (2080.257403 Nm) and I'm completely stuck on part 2. I don't know if I'm doing it wrong or what. I originally used the torque from the motor times the ang velocity converted to radians/s from rev/min. I've used net torque times the same ang velocity. I forgot to convert the 9.11 ang velocity so I've used both torques with ang velocity in rev/min. What am I doing wrong?!?

You do not use the torque generated by the motor in accelerating the wheel to solve the second part. You have to determine how much power is needed to keep the wheel going. That is a function of the rate of energy loss due to friction on the wheel.

Use:

$$\Delta L = I\Delta \omega$$

$$\tau = \frac{\Delta L}{\Delta t}$$

$$\Delta E = \tau \theta$$

AM

 

[kerimek]

I would approach this problem by first understanding the concept of power in rotational motion. Power is the rate at which work is done or energy is transferred, and in rotational motion, it is given by the product of torque and angular velocity. Therefore, to determine the power needed to maintain the rotational speed at 9.11 rev/min, we need to calculate the torque and angular velocity at this speed.

To calculate the torque at 9.11 rev/min, we can use the equation torquenet= Inertia x angular acceleration. We already know the moment of inertia (19200 kgm2) and the angular acceleration (9.11 rev/min in 10.7s), so we can solve for the torque:

torque = (19200 kgm2) x (9.11 rev/min / 10.7s) = 16353.271 Nm

To find the angular velocity at 9.11 rev/min, we can use the equation angular velocity (final)= angular velocity (initial) + ang accel x time. We know the initial angular velocity is 0 (since the wheel starts from rest) and the final angular velocity is 9.11 rev/min, so we can solve for the angular acceleration:

angular acceleration = (9.11 rev/min - 0) / 10.7s = 0.851402 radians/s2

Now, we can calculate the angular velocity at 9.11 rev/min:

angular velocity = 0 + (0.851402 radians/s2) x (10.7s) = 9.105 rev/min

Finally, we can calculate the power needed to maintain the rotational speed at 9.11 rev/min using the equation Power= torque x ang velocity:

Power = (16353.271 Nm) x (9.105 rev/min) = 148741.429 W

Therefore, the power needed to maintain the rotational speed at 9.11 rev/min is 148741.429 W or 148.741 kW.