Rolling Cans: Hypothesizing the action inside

[shoukisuke]

Hi peeps of this forum. I'm having trouble analyzing the results of an experiment, and it'd be great if I could get some pointers. Thnx :)

The experiment:
There are two cans. One is broth, aka viscosity is very low. One is cream soup, aka viscosity is very high. The two cans have the same dimensions, volume, and weight. Both cans are filled to about 5/6 of the can. Situation A: two cans roll down a ramp with slight slope so that once the cans reach flat surface, the broth can roll further until it stops. Situation B: two cans roll down a ramp with large slope so that once the cans reach flat surface, the cream can roll further until it stops.

We placed a motion detector at the top of the ramp angled to follow the slope of the ramp. We rolled down the cans individually once we found the ideal angles. And using the motion detector, we recorded the velocity of the cans for each of the slope.

The result of the experiment
The velocity of the broth can at the bottom of the ramp was higher for both angles compared to the cream can. But it was found to slow down faster compared to the cream soup can at the large slope, therefore resulting in the cream can going a farther distance.

Problem
Originally before the experiment, our group hypothesized that the cream can would go further because it has a higher velocity at the bottom of the ramp.

We hypothesized this mainly due to the moment of inertia. We thought, that once the cream can starts rolling and reaches a high enough speed, it'd have a similar inertia as a solid cylinder, which is (1/2)MR². Since the broth can has a small inside friction resulted from the liquid, our group treated it as a cylindrical shell, which is MR².

Since the cans have the same dimensions, from these two equations, it meant that the broth can would have a greater moment of inertia. This meant, to us, that the broth can would have a greater rotational kinetic energy, and thus less translational kinetic energy, which we took it to mean that the cream can went further.

However, the results of the experiment showed that the broth can had a higher velocity at the bottom of the ramp. As well, it seems that the cream can goes further due to the broth can slowing down faster.

We are confused. Very.
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Does this mean that our assumption of the cans being solid cylinder and cylindrical shell is wrong, and cream always has a higher rotational kinetic energy?

And to clarify, the higher the translational kinetic energy, does it indicate the farther an object will travel?

As well, if it is safe to assume the broth can to have an inertia of a cylindrical shell, should its mass be the mass of the can AND the liquid, or simply the mass of the empty can?

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[Kendappa]

The velocities must be the same.

Therefore,

http://www.jeffareid.net/misc/marbles.jpg

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[hmvb]

Figure this out yourselves, guys.

 

[willem2]

If there's very little friction in the broth can, the broth shouldn't start to rotate, so the mass of the broth doesn't contribute to the rotational inertia. The rotational inertia will be lower than that of the cream soup can, which explains that it accelerates slower on the slope.

The nature of the friction of a 5/6 filled soup can is complex. If the inside rotates fast enough, the empty space could be in the middle and there would be very liitle internal friction. This might happen sooner with the cream soup can..

 

[alexsb92]

Guys, trust me, the internet is smart, but unfortunately it is not smart enough to have the answers to VB's labs.

 

[nnnm4]

I'm going to try to shed some light on this in a more technical way than you really want, but I'll try to keep it fairly straight forward.

The true analysis of this problem, if one were to solve it rigorously, requires a hydrodynamic calculation regarding the motion of the fluid inside. The very outer layer of the fluid can be thought to couple to the can precisely, so the outer layer moves with the can. How far this movement continues on toward the centere of the fluid is dependent on the viscosity.

So for example if you had a zero-viscosity fluid (which exist by the way) it wouldn't move with the can at all and wouldn't contribute to the effective moment of inertia. However a really viscous fluid is sticky enough so that the outer layer of the fluid moving with the can sticks to the rest of the fluid (or a large portion of it) and moves around, so it's effectively a solid body moving with can. So that explains why the acceleration of the broth was higher at the end.

However, this imperfect coupling of the broth with the can adds dissipation to the system. A lot of energy is going into viscous heat loss in the broth because it's constantly rubbing back and forth against itself. But since the soup moves as a solid body, even though it's viscosity is higher, there's less "rubbing back and forth" and thus less dissipation

...I hope this was helpful and not too complex.