# Does a bottle of water or a bottle of ice roll downhill faster? [Video]

• MrPennywhistl
In summary: Frozen water does not expand and so the bottle will be bigger. Since water has no internal viscosity, the bottle will not rotate. The bottle of water will roll down the slope faster than the bottle of ice.
MrPennywhistl
Before you watch the video, give your answer here... and why you think it's correct.

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I think the bottle of ice will roll down faster. Water expands upon freezing, so the bottle will be bigger, so it will roll faster.

Edit:Ok, I thought it was a drinking bottle of water being rolled, so what I said is void.

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I think the bottle of water will roll faster, because the water in it doesn't have to rotate when it starts rolling.

I agree with willem2, in the ideal case; I don't know if the video would help.

I would think the ice rolls faster. If the bottles are both completely filled, the bottle of water will be heavier as water is denser than ice, and hence the water bottle should feel a greater force of friction and so move slower. Probably a lot more to it than that though, to do with fluid dynamics of the water and whatnot.

When you drop objects in free fall, what is the guiding principle? [Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate.]

So they should roll equally fast.

Naty1 said:
When you drop objects in free fall, what is the guiding principle? [Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate.]

So they should roll equally fast.

You're ignoring the fact that the water is a fluid, and thus, doesn't have to rotate at the same speed as the container.

(The correct answer is that it depends)

If the slope is very gentle, then the water would act approximately like a non-viscous fluid. Therefore, it wouldn't rotate, only the plastic bottle would. Therefore the bottle of water will go down the slope faster than the bottle of ice. (since it takes energy to make the ice rotate).
But if the slope is steep enough that the water acts like a viscous fluid, friction of the water would cause the bottle to rotate less quickly. Then one of two things could happen: 1) the bottle start sliding instead of rolling, in which case it speeds up. 2) it keeps rolling, but the rotation is slower, so it goes slower.
I think the viscosity of water will be too low, so the bottle with water will go faster.

cjl said:
You're ignoring the fact that the water is a fluid, and thus, doesn't have to rotate at the same speed as the container.

(The correct answer is that it depends)

The last word there: depends.

I want to assume we pretend all kinds of things are not happening. Freezing water does not expand: and it does not burst the bottle. That the bottle is not plastic and grows wider. That water has no internal viscosity (so I prefer a cryostat of liquid helium and frozen helium, which is hard to come by).

The liquid water will be sloshing around in the bottle. The friction of the sloshing around will slow it down. Alot. That's how you can tell if an egg is raw or hard-boiled: by spinning it.

Frozen-water bottle should should roll down faster.

## 1. Does the weight of the bottle affect its speed rolling downhill?

Yes, the weight of the bottle does affect its speed rolling downhill. Objects with more mass have more inertia, which means they are harder to start or stop moving. Therefore, a heavier bottle will have a slower speed rolling downhill compared to a lighter bottle.

## 2. Does the shape of the bottle impact its speed rolling downhill?

Yes, the shape of the bottle can impact its speed rolling downhill. Objects with a streamlined shape, such as a water bottle, experience less air resistance and therefore can reach higher speeds compared to objects with a bulkier shape, such as an ice bottle.

## 3. Is the speed of the bottle affected by the surface it is rolling on?

Yes, the surface the bottle is rolling on can affect its speed. A smoother surface will allow the bottle to roll faster, while a rougher surface will cause more friction and slow down the bottle's speed.

## 4. Does the temperature of the bottle affect its speed rolling downhill?

Yes, the temperature of the bottle can affect its speed rolling downhill. A bottle of ice will melt as it rolls downhill, which can create a layer of water between the bottle and the surface, reducing friction and allowing the bottle to roll faster.

## 5. Can the angle of the slope impact the speed of the rolling bottle?

Yes, the angle of the slope can impact the speed of the rolling bottle. A steeper slope will result in a faster descent for the bottle, while a flatter slope will slow down the bottle's speed.

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