# Homework Help: Rotational Mechanics

1. Sep 22, 2004

### Parth Dave

I have a physics lab to do. Now, I want to make sure that I am on the right track (I don't want to go completely in the wrong direction). Essentially what we have for our lab is two cans of soup (both with the same dimensions and similar mass) which we roll down a ramp and let it roll until it stops. The objective is to determine which will one go farther and why it does so. The biggest difference between the two is the contents. In one of them, we have a broth (very thin and liquidy) and in the other creme of chicken soup (very creamy and thick).

Now, my hypothesis is that the creme of chicken soup will go farther. The can has two kinds of kinetic energy (rotational and translational). Is if safe for me to assume that the creme of chicken soup willhave more rotatioanl kinetic energy than the broth because more energy is needed to get it rotating? That being true is the basis for my hypothesis.

The can only slows down and stops because of friction. Another assumption im making is that friction has a greater effect on translational motion than it does on rotational. This assumption seems a little more valid than the other one. Is it also true? a fair estimate? or completely wrong?

If my two assumptions are true, than i can say that friction will add on the two cans in a very similar fashion. However, when one of the cans runs out of translational kinetic energy it will run purely on rotational kinetic energy. Thus the can with greater rotational kinetic energy will go farther.

This is because the two cans kinetic energy will decrease at a similar rate. However, one can will run out of translational kinetic energy before the other can. At that the net decrease in kinetic energy for it will have reduced (since friction is only acting on the rotational kinetic energy and we assumed earlier that friction has a markedly lower effect on rotational kinetic energy).

Are my assumptions correct? If they aren't dont tell me what is the correct method. I would much rather discover that on my own.

2. Sep 22, 2004

### Tide

Can you clarify the objective a little bit? How are the cans set in motion, for example?

3. Sep 22, 2004

### Parth Dave

They are on a ramp and are simply just released. Than they are allowed to roll freely off the ramp and onto the ground until they stop. (about a 15 degree angle and the ramp being ~1m long)

4. Sep 22, 2004

### Sirus

I think the main difference between the cans is the distribution of the mass. Assuming they are of identical mass, the can containing the less dense soup will have more mass concentrated in the outer surface of the can, whereas the can containing the denser soup will have more evenly distributed mass (more of the can's mass will be found on the inside). I think this is something to consider.

5. Sep 22, 2004

### faust9

I'd say the fluid dynamics would play the biggest role. The cream soup is essentially a solid while the broth is a contained fluid. The bulk of the broth will not begine to rotate for some time while the entirety of the cream soup will rotate almost immediatly. I'd venture a guess and say the broth will have less rotational KE at the bottom of the ramp because the fluid within will not all rotate with the same angular velocity; moreover, the broth's angular velocity will probably be significantly less than the can's housing the broth.

My guess is that the broth will convert a lot more of the original PE to heat energy than the cream soup will thus the broth will not roll as far. Just a guess.

6. Sep 24, 2004

### faust9

So, what's the verdict?

7. Sep 24, 2004

### Sirus

Looks like you'll have to find out in the lab! :)

8. Sep 24, 2004

### Parth Dave

I'll let you know in a week.

9. Sep 24, 2004

### vsage

"I think the main difference between the cans is the distribution of the mass. Assuming they are of identical mass, the can containing the less dense soup will have more mass concentrated in the outer surface of the can, whereas the can containing the denser soup will have more evenly distributed mass (more of the can's mass will be found on the inside). I think this is something to consider."

I think what is being implied here is that the can of broth has a larger rotiational inertia which would make it harder to move (to oversimplify it). Because the broth is not moving entirely uniformly (it would be a little chaotic), the forces acting at some points inside the fluid of the broth will be cancelling out other forces and therefore there's a less resultant motion in a particular direction. I think the energy dissipated as by such things as sound and heat are irrelevant given the overall energy being given by rolling it down a ramp. Just my two cents.

10. Sep 30, 2004

### Parth Dave

The final results:

The broth would get to the bottom of the ramp quicker. It would also have a higher velocity at the bottom of the ramp. However, the cream would always go a farther distance.