Roller Coaster Calculation Errors: Round Marble vs. Sliding

[JimmyRay]

Hi we're doing a project in class where we make roller coasters and we test them out by sending a marble down them.

As a bonus question my teacher asked why there would be an error in the calculations we do (finding speed at different locations of the roller coaster) if we're using a marble...

Well I guess it has to do with the fact that the marble is round, and it is not sliding down the roller coaster it is rolling?

Would it change the conversation of energy formula? or Ek formula? In our class so far we havnt studied anything rolling... can someone help me out?

 

[ponjavic]

What is everyone assuming when doing energy calculations?
That there is no...

 

[JimmyRay]

fricttionnnnn ?

Yeah, friction would slow it down, but we're not going to include friction. X_X
But I still do not how rolling motion differs from sliding... when sliding you have to measure co effecient of sliding friction, is there a co effecient for rolling friction?

 

[ponjavic]

Heh you shouldn't have to include the friction I just think that your teacher wanted you to figure out that friction effects the results you will get since you are looking at the roller coaster at a conservation of energy perspective (i presume)
Rolling friction will be a lot less due to the fact that a much smaller area is in contact between the two "reagents" (sorry for my Swedish =)) But you will still have air friction.

Yeah, friction would slow it down, but we're not going to include friction. X_X

This is why you will have an error, this is the easy answer I bet your teacher is looking for. Since you are not supposed to include the friction you are supposed to get an erroneus result, thus the reason for the error margin is the friction, along with other less important things.

Well I guess it has to do with the fact that the marble is round, and it is not sliding down the roller coaster it is rolling?

There will still be some kind of friction as you yourself stated in an earlier post. It is not like the calculations would be correct if you used a cube instead of the marble, both would still give false results.

 

[JimmyRay]

you're right, friction is an easy answer, but its not what my teacher is looking for... because we are IGNORNING friction for this assignment, so BESIDES friction he said, what is wrong.. Which I am saying is that the marble is round, so it's rotational motion... correct? I think he wants us to calculate rotational motion? but i don't know it :/. My teacher said the perfect answer for the bonus question is at first year university physics... I'm in grade 11...

 

[ponjavic]

Even though I may be way over my head here I'd call your teacher a dumbstrut (if that is an English word)
Energy = Ep+Ek
If the ball rolls from one top to another using the conservation of energy as you still haven't said you aren't using
Energy(left)=Ep+Ek-Ef(energy loss from friction)
If you are totally ignoring friction even as an answer for the bonus question the only other answer I could guess is the fact that if the ball is at a higher point the gravity is different thus the conservation of energy laws wouldn't be directly applicable, but the effect this has on the results is ridiculous.

Again:
Using energy laws if there is no friction (or other sources of energy loss) a balls velocity will always be the same at a certain height.

If you want to play around with intertia and moment of inertia rolling work and so on run to google and do it, I have no idea why your teacher tries to impose university material on grade 11 students.

Have you verified that using the conservation of energy formulas is wrong/right?

 

[JimmyRay]

Yes we are using the conversation of energy formula without friction (EK+EG=ET), meaning we will find the velocity of the marble at different heights (for example at the top of a loop, bottom, max height) ...

... I understand what you're saying, the energy formula remains the same, regardless of what type of motion it is, right?

I will talk to him about it tommorow.

 

[Doc Al]

I suspect what your teacher is looking for is the fact that since the marble rolls, it has rotational KE as well as translational KE: The total mechanical energy at any point is the sum of:

gravitational PE
translational KE
rotational KE​

Thus, something that rolls down a hill will end up moving slower (lower translational speed of its center of gravity) than something that slides down since some of the potential energy is transformed to rotational energy. (Of course, this is ignoring energy losses due to friction.)

 

[ponjavic]

Crap, I'll have to read up on my energy too I guess =)
sry JimmyRay

 

[JimmyRay]

Yeah that is exactly what my teacher is looking for, I asked him today. No problem ponjavic.

Ok well it goes slower down the hill then something that is sliding because? I didnt understand your explanation Doc Al...

 

[Doc Al]

It's just conservation of energy. At the top of the hill you start off with a certain amount of potential energy. If the object only slides down, then all of that PE transforms to ordinary translational KE ($1/2 m v^2$). But if the object rolls down, then that same PE gets transformed into both ordinary KE and rotational KE. Which means there's less ordinary KE, so it goes slower. Make some sense?

 

[JimmyRay]

OHHHHHHHHHHHHHHHHHH yess it does make sense

So basically it takes energy for the ball to roll, and that takes away from the speed? (because it's EK is split in half?)

 

[Doc Al]

So basically it takes energy for the ball to roll, and that takes away from the speed?

Right.

(because it's EK is split in half?)

The kinetic energy is divided between translational and rotational, but not necessarily in half.

 

[JimmyRay]

Yeah sorry, not neccesairly in half lol, what am I thinking...


Ok so just to review, something sliding would have a higher speed then something rolling when going down a hill, but if we include friction into our calculation, wouldn't the rolling object move faster? I am just guessing. Our teacher doesn't want us to include friction, but I am just asking...

 

[Doc Al]

Ok so just to review, something sliding would have a higher speed then something rolling when going down a hill, but if we include friction into our calculation, wouldn't the rolling object move faster?

Right. It depends on the amount of friction of course, but most likely yes. Friction losses for rolling are generally much less than for sliding.

Here's something else to think about: Without friction, the marble wouldn't roll. Static friction is required to get the marble rolling.

 

[JimmyRay]

hmm... static friction is needed to get the marble rolling?

We're not going to calculate friction... But we know it will be there and our we'll say that our calculations will be off because of it...but why is friction needed for the marble to roll?

 

[ponjavic]

The marble has rotational energy, and angular velocity. Were there no friction at the point of contact between the marble and the table the marble would just rotate, since there is friction it will work against the marble trying to rotate thus there will be a forward thrust.

  __
 /  \
 |  | |
 \__/|/_
------
   --->

 

[Doc Al]

but why is friction needed for the marble to roll?

If the marble started from rest on a frictionless track, it would just slide down the track without rolling. To get it rolling, a torque must be exerted on the marble. Friction supplies that torque.

 

[JimmyRay]

I see...

Well I think my teacher wants me to use the equation for rotational motion in my calculations. Is there any extra math (grade 11 math right now) or physics I have to know for it? Well obviously some more physics lol but what exactly...

 

[ponjavic]

http://en.wikipedia.org/wiki/Kinetic_energy
I used this to solve my calculations for a similar project, I doubt you'll have to learn any new math.
Yes it is wikipedia but this is very well known not some personal thoughts.
BTW the moment of inertia is different for every kind of object so you will have to look up the moment of inertia for a sphere which should be there if you click the moment of inertia link, happy reading! =)

 

[JimmyRay]

thanks guys :)