How Does a Flywheel Power a Car?

[Drey0287]

Help and Fast please!

A car is designed to get its energy from a rotating flywheel whth a radius of 2 m and a mass of 500 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5000 rev/min. (a) Find the kinetic energy stored in the flywheel. (b) If the flywheel is to supply energy to the car as would a 10 hp motor, find the length of time the car could run before the flywheel would have to be brought back up to speed. 1 hp = 746 Watts

Can somebody walk my through this process...i already know I have to convert 5000 rev/min to radians/sec but i don't even know how to do that! please i really need this!

 

[futb0l]

5000/60 = 83.3 revolutions per second
83.3 * 2pi = 523 rad/sec

Remember that 1 revolution is equivalent to 2pi radians.

The kinetic energy stored in the flywheel would be...

<br /> KE = \frac{1}{2}I\omega^2<br />

I is equivalent to the moment of inertia and in this case, if i am not mistaken should be...

<br /> KE = \frac{1}{2}m\omega^2r^2<br />

Remember that...

<br /> Power = \frac{dW}{dt}<br />

so you should now be able to figure out b.

 

[wais]

Hi there! I can definitely help you with this problem. Let's break it down step by step.

(a) First, we need to find the angular velocity of the flywheel. We know that 5000 rev/min means that the flywheel is rotating 5000 times in one minute. To convert this to radians per second, we need to multiply by 2π. This is because one revolution (or one full rotation) is equal to 2π radians. So, the angular velocity (ω) of the flywheel is:

ω = (5000 rev/min) * (2π radians/rev) * (1 min/60 sec) = 523.6 radians/sec

Next, we can use the formula for kinetic energy (KE) to find the energy stored in the flywheel:

KE = 1/2 * I * ω^2

Where I is the moment of inertia, which is equal to 1/2 * m * r^2 (for a solid cylinder). So, we can plug in the values we know:

KE = 1/2 * (1/2 * 500 kg * (2 m)^2) * (523.6 radians/sec)^2 = 81,976,000 Joules

So, the kinetic energy stored in the flywheel is 81,976,000 Joules.

(b) To find the length of time the car can run before the flywheel needs to be brought back up to speed, we can use the formula for power (P):

P = ΔE/Δt

Where ΔE is the change in energy and Δt is the change in time. In this case, we know that the power of the flywheel is 10 hp, which is equal to 10 * 746 = 7,460 Watts. So, we can plug in the values we know:

7,460 Watts = (81,976,000 Joules - 0 Joules)/Δt

Solving for Δt, we get:

Δt = 11,000 seconds

Therefore, the car can run for 11,000 seconds (or approximately 3 hours) before the flywheel needs to be brought back up to speed.

I hope this helps! Let me know if you have any other questions or if you need further clarification. Good luck!