Does Shaking and Settling Affect the Weight of a Milk Bottle?

[Fruh2theline]

Homework Statement

An old fashioned non-homogenized milk bottle is shaken up so the cream and milk are uniformly mixed. The bottle is then placed down, and the cream and milk begin to separate. Does the bottle weigh more or less when it is being carried or just after it is put down? Estimate the difference if any.

Homework Equations

As far as I can see it's a purely qualitative problem.

The Attempt at a Solution

I think the answer may be that it weighs more when it is put down, as the milk has momentum as it separates downwards which is greater than the momentum of the cream upwards as the milk has greater mass and they are both separating at the same speed.
No idea how to estimate the difference in weight though...

Anyone have any ideas about this problem?

 

[Quinzio]

I can't really understand.
Is the bottle closed ? If so, nothing goes in, nothing comes out, how can it weight differently ?

 

[zorro]

I think it weighs more just after it is shaken than when it is put down.
The cream starts separating just after we stop shaking the bottle, cream being less denser than milk starts rising upwards thereby exerting a force downwards which adds upto the weight of the bottle for a moment.

 

[Quinzio]

Yeah, ok.
But the weight is just an acceleration (Weight = g*m)
(A hint for your solution)

As soon as the convective motion in the milk mass has stabilized (very soon I guess), there is no more acceleration, so the weight must be it's rest weight.

And when exist, the difference is really little.

 

[rwisz]

I would approach this problem by considering the physical principles at play. The separation of cream and milk in a bottle is due to the difference in density between the two substances. Cream, being less dense, rises to the top while milk, being more dense, sinks to the bottom.

When the bottle is shaken, the milk and cream are mixed and the total mass of the bottle remains the same. However, as the mixture settles, the cream will rise to the top and the milk will sink to the bottom. This separation process is driven by gravity, which will pull the denser milk downwards and the less dense cream upwards.

Therefore, when the bottle is being carried, the milk and cream are still in the process of separating and the bottle will weigh slightly more due to the downward force of the milk. Once the bottle is put down and the separation process is complete, the bottle will weigh the same as it did before it was shaken, as the total mass of the bottle has not changed.

Estimating the difference in weight may be difficult without knowing the specific dimensions and density of the milk and cream. However, we can estimate that the difference in weight would be small, as the density difference between milk and cream is not very large. Additionally, the separation process is relatively slow, so the weight difference would only be noticeable for a short period of time.