Why do water bottle oscillations grow on a sloping surface?

[DuncanM]

Hi, folks.

I am looking for some help to understand the physics of a water pendulum (in fact, I don’t even know if my terminology is correct). It has been several years since I left school and my math/physics tools are rusty.

Here’s the set up:
Whenever I come back from the beach with a partially-empty soda pop bottle and balance it on the roof of my car, it always seems to oscillate back and forth and the oscillations grow until the bottle finally falls over. Now I am wondering why the oscillations grow; as far as I can tell, nothing nearby is feeding it energy (there is no railway, etc. nearby to create a resonance vibration. I am not touching it, breathing on it, etc.).

What I am now considering doing is creating a science project for my son (in elementary school) based on this phenomenom. The equipment is simple and inexpensive: a plastic 2 Litre pop bottle partially filled with water and set on a convex surface.

I was planning to tell my son the oscillations grow because the water keeps changing its center of gravity, much like a person adjusts their body position on a playground swing when they want to go higher.

But first, I want to make sure I am correct.

Do the water bottle’s oscillations, indeed, grow because of the changing center of gravity? Or is another force at work (i.e. - lunar/tidal, or some other force)?




Duncan

 

[luke]

does this phenomenon occur no matter how much water you put in the water bottle? I feel like there but be a certain amount of water where this phenomenon would be more pronounced.

I haven't thought about your problem long and I am not positive I understand exactly the phenomenon that is occurring but here is a stab in the dark.

Idea 1:
That the time it takes the water to slosh from one side of the bottle to another corresponds with the period of oscillation of the bottle + water as an inverse pendulum. So any fluctuations in the the water are amplified since the water bottle is in a unstable equilibrium.

Idea 2:
This idea hinges on you giving the water bottle an initial push (since I am a little unsure how the phenomenon starts). So maybe if you give the water bottle a push but not enough to knock it over the water and the bottle will oscillate out of phase so that the bottle will remaining standing. But it would make sense that they would back into phase with each other and once that happens the water would knock the bottle over. This idea assumes that the system starts with all the energy it needs to knock the bottle over and it was just a phase difference in bottle & water oscillations that kept it up for some time.

I think I might go gives this a try tomorrow and see if it get the same behavior. I would like to see how the water oscillates with the bottle. I think idea 1 is most like what you are referring to.

 

[astrokreng]

Hello Duncan,

The phenomenon you are describing is known as a water pendulum or a sloshing pendulum. It occurs when a partially filled container is set in motion on a curved surface, such as the roof of your car. The oscillations of the water inside the bottle are caused by the shifting of the water's center of mass as the bottle moves back and forth. This is similar to the way a person adjusts their body on a swing to maintain the swinging motion.

The reason the oscillations grow is due to a principle in physics known as resonance. When a system is subjected to a periodic force, such as the motion of the car, it will start to oscillate at its natural frequency. In this case, the natural frequency of the water pendulum is determined by the amount of water in the bottle, the shape of the bottle, and the curvature of the surface it is resting on.

As the oscillations continue, the water's center of mass reaches its maximum displacement, causing the bottle to tip over. This is because the natural frequency of the pendulum is no longer in sync with the periodic force of the car's motion, leading to destructive interference and the eventual collapse of the oscillations.

In summary, the oscillations of the water pendulum are caused by the shifting of the water's center of mass and are amplified by the principle of resonance. I hope this helps with your science project and encourages your son's interest in physics. Keep exploring and asking questions!