# A magic can

1. Sep 20, 2006

### Jeno

Imagine that now i have a can. I poke a hole at the centers of both the bottom and the cover of the can. Then i tie a rubber band onto the holes that it goes across the tin from the hole at the bottom to the hole on the cover. After that i stick some plasticine onto the rubber band. When i roll the can, it will stop and come back to me. What is the mechanism inside the can that make it stops and comes back? Thank you for answering my question.

2. Sep 20, 2006

### HallsofIvy

I think I made one of those when I was in cub scouts!

There is a heavy washer or other weight attached to the rubber band. As the can rolls, the weight causes the rubber band to wind up. When the can comes to a halt, the rubber band unwinds, sending the can back the other way.

3. Sep 20, 2006

### Jeno

Thank you for answering my question. But the problem is when the can rolls, the rubber band is twisted and the inner mass will also roll. thus, when the can stops, the inner mass will gain a angular velocity. it will continue to roll and this will unwind the rubber band as well. therefore, there will no any angular momentum that rolls the can back. this is, however, not match with the reality where the can really rolls back. so, can you explain why? thank you. -Jeno-

4. Sep 20, 2006

### LURCH

If the innner mass rolls untill the rubber band unwinds, the can will not return.

5. Sep 20, 2006

### DaveC426913

The inner mass does not roll. It hangs from the rubber band, causing the mass and central portion of the rubber band to not roll, thus winding the rubber band up.

6. Sep 20, 2006

### Jeno

But in the experiment, the can really rolls back. So can you explain this?

But when the can is rolling and winding up the rubber band, the rubber band will unwind at the same time, with a smaller rate. Therefore, it will give both the can and the rubber band a torque in opposite direction, just like the action and reaction forces mentioned in Newton's third law. Thus, i think that the mass will roll at the same time the can rolls. Besides that, in my experiment, when i roll the can, the can will stop at a distance from me and then rolls back. but it didn't stop at the point where i roll it. it will continue rolling until a point behind me (assume that i am facing the direction where i first roll the can to). After that, it will stop at the point there and won't come back anymore. If the inner mass does not roll, then we can think that it is a simple harmonic motion where the equilibrium point is the place i start rolling the can. so the can suppose to oscillate and stop at that point finally. But it didn't match with the result of the experiment. The can just go and back one time and stop at a distance from where it start to roll. can you explain this? thank you.

Last edited: Sep 20, 2006
7. Sep 21, 2006

### Danger

Why don't we just prove this empirically? Use a transparent plastic tube instead of a can, and watch what happens inside.

8. Sep 21, 2006

### zoobyshoe

I'm not sure there's any big mystery to this. Isn't any SHM just being damped by the rolling friction and the friction of the rubber band against itself as it twists up?

9. Sep 21, 2006

### Jeno

Ya, i think this is a good way, but i cant find any suitable transparent tube to do this experiment.
i think even though it is a damped oscillation, it will finally stop at the equilibrium point, except those overdamped oscillation. but the can can come back to the equilibrium point once, that means that it is not a overdamped oscillation. so why don't it stop at the equilibrium point?

10. Sep 21, 2006

### Danger

You could do a quick and dirty version by sticking one end of the rubber band to the bottom of a glass jar with chewing gum or Plasticene and running the other end through a hole in the lid.

11. Sep 21, 2006

### zoobyshoe

I had to think about this a bit. Your set up is something like an imperfect set up for SHM. Suppose you clamped a metal rod in a vise then pulled the rod back and let it go. It would oscillate with SHM. But now suppose your vise was not attached to a bench, only sitting on it. The only things preventing the vise from moving is its inertia. If you now set the rod into motion the rod will oscillate but also exert force on the vise and move it. The SHM will come to a halt very quickly and since the vise has been moved it will not be at the original position of equilibrium.

12. Sep 21, 2006

### DaveC426913

I think there is a misunderstanding of this experiment.

You let the can roll a few feet until it is about to change direction, then you can grab it, and pick it up (gently).
You get distracted by the TV for a few minutes, and then return to your experiment, which you have been holding in your hands.
You set the can back down on the ground. The can will, of its own accord, roll backwards several feet.

The rubber band acts as a storage device whose potential can be released immediately, or at an arbitrary time later.

Are we agreed?

13. Sep 21, 2006

### DaveC426913

Thusly:
10 char

Last edited: Jul 20, 2007