How Does a Glass Fibre Flywheel Store Kinetic Energy in Buses?

[Katy96]

Homework Statement

A flywheel made of glass fibre has been developed by BP to store the kinetic energy of buses when they come to a bus stop. The maximum energy stored in the flywheel is equivalent to the energy lost by a 16,000 kg bus braking from 48 km when it comes to rest. The bulk of the flywheel’s mass is in its rim which moves at 1300 km when the flywheel rotates at the maximum angular velocity of 16,000 rev . After a typical stop of two minutes during which time the flywheel slows down, four fifths of its energy is still available to accelerate the vehicle.

From this data show that the flywheel has the following properties:

1. Maximum kinetic energy = 1.42 MJ (2 marks)
2. Moment of Inertia = 1.01 kg (3 marks)
3. Radius = 0.215 m (2 marks)
4. Minimum mass = 21.9 kg (3 marks)(Each section must be answered in the order given. You may not assume data from the following sections).e) Determine also the
5. Determine also the mean frictional torque causing the slowing down in the two minute stop. (6 marks)

Homework Equations

not really sure!

The Attempt at a Solution

I can't figure out how to do this as I don't know how to do it In this order?

 

[PeroK]

Why don't you start with question 1? It's asking about the total KE of the flywheel. Where does this KE come from?

 

[Katy96]

I tried using

and then I didn't know which other equation I could use but I don't know the radius or anything

 

[PeroK]

I tried using View attachment 86949and then I didn't know which other equation I could use but I don't know the radius or anything

Where does the KE come from?

 

[Katy96]

The kinetic energy of an object is the energy it possesses because of its motion?

 

[PeroK]

The kinetic energy of an object is the energy it possesses because of its motion?

Okay, I'll get you started. The energy comes from the bus. It tells you that in the question.

 

[Katy96]

Okay, I'll get you started. The energy comes from the bus. It tells you that in the question.

well yes I understand that part, I just don't understand how I use what I've been given to work it out as I am used to using

 

[PeroK]

well yes I understand that part, I just don't understand how I use what I've been given to work it out as I am used to using View attachment 86951

How else could you work out the energy of the flywheel? Hint: think about the energy of the bus.

 

[Katy96]

E = ½mv2?

 

[PeroK]

E = ½mv2?

If you mean the energy of the flywheel is equal to the energy of the bus, and you're given the mass and velocity of the bus, then yes!

 

[Katy96]

If you mean the energy of the flywheel is equal to the energy of the bus, and you're given the mass and velocity of the bus, then yes!

yeah that's what I meant, so I use the mass of the bus and the speed from which it is braking from?

 

[PeroK]

yeah that's what I meant, so I use the mass of the bus and the speed from which it is braking from?

Yes, that's what the question implies.

 

[Katy96]

but if I do that I get that E=18432000?

 

[PeroK]

but if I do that I get that E=18432000?

What units are you using? I assume the speed is 48 km/h? What if the speed of the bus was given in mph (miles per hour)? Or cm/s?

 

[Katy96]

What units are you using? I assume the speed is 48 km/h? What if the speed of the bus was given in mph (miles per hour)? Or cm/s?

yes its 48km/h so what I did was (0.5)(16000)(48)^2

 

[PeroK]

yes its 48km/h so what I did was (0.5)(16000)(48)^2

So, why is that wrong? Note that 48 km/h is about 30 mph. So, why not (0.5)(16000)(30)^2?

 

[Katy96]

the answer, Maximum kinetic energy = 1.42 MJ, is given in the question, when 30mph is used you get 7200000 which is also the wrong answer

 

[PeroK]

the answer, Maximum kinetic energy = 1.42 MJ, is given in the question, when 30mph is used you get 7200000 which is also the wrong answer

So, if you take the speed in different units, you get different numerical answers. There is only one set of units in the SI:

Kilograms, Metres, Seconds and Joules

You must use mass in kilograms and speed in metres per second to get KE in Joules.

 

[Katy96]

so how do I change 48km/h into m/s? never mind I got it now!

 

[PeroK]

so how do I change 48km/h into m/s?

Are you really saying that if a bus is going at 48 km/h, you don't know how far it travels each second?

 

[Katy96]

Are you really saying that if a bus is going at 48 km/h, you don't know how far it travels each second?

ive done it, and done part a, I am just getting confused on which equations I need to use for which parts.

 

[Katy96]

so in part b I know I need to use

 

[PeroK]

so in part b I know I need to use View attachment 86958

Yes, you've got the KE now and you're given $\omega$ (although you need to watch the units again), so you should be able to calculate $I$.

 

[Katy96]

which is ω?

 

[PeroK]

which is ω?

Read the question.

 

[Katy96]

Read the question.

I have, I can't figure it out and by that I mean how do I change it to something I can use units wise

 

[PeroK]

I have, I can't figure it out

$\omega$ is "angular velocity", which must be used in radians per second. The question gives you it, however, in revolutions per something. Just as an aside, you seem to have truncated most of the units when quoting the question.

 

[Katy96]

yes its given in revolutions per min, and I am unsure of how to change it from revolutions per min to radians per second once I do that I know how to do part b)

 

[PeroK]

yes its given in revolutions per min, and I am unsure of how to change it from revolutions per min to radians per second once I do that I know how to do part b)

How many radians are in a revolution?

 

[Katy96]

2Pi/60?

 

[PeroK]

2Pi/60?

A poor guess. It's $2\pi$. You could always have googled that!

 

[SammyS]

so how do I change 48km/h into m/s? never mind I got it now!

Is editing a response as you type it a lost skill?

I see this so often it's ridiculous !

 

[Katy96]

A poor guess. It's $2\pi$. You could always have googled that!

okay well do I just divide by 2pi? because I thought you would do 16000X2pi/60

 

[PeroK]

okay well do I just divide by 2pi? because I thought you would do 16000X2pi/60

I see what you did. There are $2\pi$ radians in a revolution, so yes it's $2\pi /60$ to convert from revs per minute to radians per second.

 

[Katy96]

I see what you did. There are $2\pi$ radians in a revolution, so yes it's $2\pi /60$ to convert from revs per minute to radians per second.

when I did that I got the right answer so in part c do I use v_max=rω_max or do I use I=0.606mr²

 

[PeroK]

when I did that I got the right answer so in part c do I use v_max=rω_max or do I use I=0.606mr²

Does that give the right answer?

I'm going offline now. Good luck with the rest of it.

 

[Katy96]

Does that give the right answer?

I'm going offline now. Good luck with the rest of it.

thanks.

 

[Katy96]

Its just part e I'm struggling on now

 

[jbriggs444]

e) Determine also the

Its just part e I'm struggling on now

Yes. It is quite the conundrum.

 

[Katy96]

Yes. It is quite the conundrum.

sorry it meant to say Determine also the mean frictional torque causing the slowing down in the two minute stop.

 

[jbriggs444]

You know how much energy it had at the beginning of the two minute stop. You have already used that to calculate its angular velocity at that time.

The question tells you what fraction of the starting energy it has at the end of the two minute stop. How much energy is that? How fast does that mean that it must be rotating at the end of the two minutes?

 

[Katy96]

this is what I know, i need to use the change in the KE to find the final angular speed, and hence the angular deceleration, using the equations of angular motion and torque Important to show answer is negative, as result of deceleration
The force providing the centripetal acceleration acts towards the axis so cannot have a torque about it.and flywheel does not stop during the 2 mins.

 

[jbriggs444]

this is what I know, i need to use the change in the KE to find the final angular speed

Then there is a starting point. What is the change in KE?

 

[Katy96]

Then there is a starting point. What is the change in KE?

that's where I get stuck

 

[jbriggs444]

The problem statement says that four fifths of the flywheel's energy remains after two minutes.