Physics Puzzlers- Class In Session!

[John James]

........ I'm going with "They will not move".

I'm going to get an aspirin!

 

[toxcrusadr]

I know of no force that would 'draw the bubbles together' under such conditions. In the homogeneous steady-state water universe, we can assume no temperature gradients, no currents, no energy sources of any kind, so basically nothing is happening, except random collisions between molecules. I would expect these to gradually dissolve the air bubbles and disperse the air molecules evenly (in time) throughout the water universe, through Brownian motion. However, we're told that's not going to happen. Instead I guess we can assume that all molecular effects are equal on all sides of the bubbles, so everything cancels out and nothing happens.

Now the presence of the two bubbles would have a gravitational effect. The homogenous water universe creates an unchanging and equal gravitational flux in all directions, except on the axis of the two bubbles. For each bubble, there is less density, and thus less gravity, in the direction of the other. So the stronger attraction of the rest of the universe might cause the bubbles to move directly apart from each other. But we are talking two bubbles in an infinite universe. The difference would likely be too small to overcome the inertia of the bubbles in their medium. And if the bubbles were of significant enough size and close enough together for this not to be the case, they would find the gravitational difference lessening the further they moved apart, and eventually it would become too weak to overcome the physical resistance of the medium, and motion would cease.

So I see this universe attaining a totally steady state, if it doesn't start in one, in which the two bubbles remain, unchanging and unmoving, a certain distance apart.

I was about to make an argument here but after further review, I think this the correct answer. If they each have less gravity on them in the direction of the other bubble, they will drift apart ('upward' if you will) until that effect is negligible, and then the universe reaches a steady state.

 

[cubby01]

If the temperature of space were such that H2O was in liquid form then I think the two air bubbles would come together to form a single sphere giving the least amount of 'surface area' to the water.

But being the temperature of space is such that H2O would be a solid, I don't think the air bubbles would do anything.

 

[toxcrusadr]

If the temperature of space were such that H2O was in liquid form then I think the two air bubbles would come together to form a single sphere giving the least amount of 'surface area' to the water.

But being the temperature of space is such that H2O would be a solid, I don't think the air bubbles would do anything.

The universe in the question is defined however the question defines it. Although temperature is not mentioned, I assume it was liquid because it was called 'water' and not 'ice'.

Getting back to your first point, assuming one sphere would have lower surface area than two, I agree. But what would make them come together in the first place? They are 'nearby' each other and not gravitationally attracted - quite the opposite.

 

[tybrad]

on this one!

 

[cubby01]

The universe in the question is defined however the question defines it. Although temperature is not mentioned, I assume it was liquid because it was called 'water' and not 'ice'.

Getting back to your first point, assuming one sphere would have lower surface area than two, I agree. But what would make them come together in the first place? They are 'nearby' each other and not gravitationally attracted - quite the opposite.

Hmmm, The 'air' spheres are less dense than the water and each have a negative mass relative to the water (space as it were). The two negative masses attract gravitationally just as two positive masses attract in the reverse situation.

 

[old_tv_nut]

In the news recently, the rate of Big Ben was adjusted by adding a coin or two to the pile on top of the pendulum bob (this has been done many times before).

My question is, how does this work? By changing the mass of the pendulum, or by changing its center of gravity? [I think a simple thought experiment will give the answer.]

 

[finnbow]

In the news recently, the rate of Big Ben was adjusted by adding a coin or two to the pile on top of the pendulum bob (this has been done many times before).

My question is, how does this work? By changing the mass of the pendulum, or by changing its center of gravity? [I think a simple thought experiment will give the answer.]

It would raise the CG, thereby speeding up the pendulum's swing.

 

[toxcrusadr]

The period of a pendulum is directly proportional to the length of the string and the mass hanging at the end of it. The gravitational constant is in there somewhere too.

 

[Fisherdude]

The period of a simple pendulum is based on the length. There is no "m" in the equation. So, adding weight to the top of the bob would indeed move the CG slightly upward, effectively shortening the length, and very slightly decreasing the period.

T= 2pi sqrt(L/g), where g is the acceleration due to gravity.

The unknown here is the weight of the rod. If it is not negligible with respect to the weight of the bob, then this is not a trivial calculation. It now involves a torque and a moment of inertia, and the expression inside the square root does indeed include the mass, in the denominator. So, while the calculation is still complex, if the mass increases the period will get smaller.

 

[old_tv_nut]

OK - here's the thought experiment: put two identical pendulums side by side, swinging together at exactly the same rate. Now move them closer and closer together until they are touching and furthermore until they are stuck to each other and are one - no change in rate will occur, so changing the mass by a factor of even 2x won't change the rate. So yes, it must be the center of gravity. If the mass of the rod is significant, then it seems the C of G could move downward when mass is added to the top of the bob.

 

[Fisherdude]

...If the mass of the rod is significant, then it seems the C of G could move downward when mass is added to the top of the bob.

Agreed.

 

[tybrad]

Oops! I realized that I have been neglectful in the thread- sorry guys.

The bubbles in a water universe answer is....
...
...
they will move toward one another. Imagine it this way-

If you have an air bubble and a water bubble (both in the water universe) near each other and place a particle between them, it would move away from the air bubble and toward the water bubble. It is almost like the air bubble repelled the particle (but not really).

Since particles (objects) and bubbles move opposite one another (rocks sink, bubbles rise- both are gravitational arguments), a bubble of air placed near another bubble of air will be attracted to one another- not repelled.


If a cubic meter of air is decreased, then its temperature must be
a- increasing
b- decreasing
c- you can't determine


By the way- I liked the improv Q/A'ing on the pendulum. Clay is correct that a so-called physical pendulum needs a moment of inertia and COM argument

 

[Hyperion]

Oops! I realized that I have been neglectful in the thread- sorry guys.

The bubbles in a water universe answer is....
...
...
they will move toward one another. Imagine it this way-

If you have an air bubble and a water bubble (both in the water universe) near each other and place a particle between them, it would move away from the air bubble and toward the water bubble. It is almost like the air bubble repelled the particle (but not really).

Since particles (objects) and bubbles move opposite one another (rocks sink, bubbles rise- both are gravitational arguments), a bubble of air placed near another bubble of air will be attracted to one another- not repelled.


If a cubic meter of air is decreased, then its temperature must be
a- increasing
b- decreasing
c- you can't determine


By the way- I liked the improv Q/A'ing on the pendulum. Clay is correct that a so-called physical pendulum needs a moment of inertia and COM argument

What do you mean decreased? compressed? lowered in pressure? be MUCH more specific here. :yes:

 

[toxcrusadr]

Yes this is a vague question. If VOLUME is decreased, i.e. the air is compressed, pressure and temperature will increase.

 

[old_tv_nut]

You can't determine from the statement; depends on method of decreasing.

Decreasing by applying pressure, pressure and temperature increase.
Decreasing by cooling, pressure and temperature decrease.

I have to note the question is deliberately vague, in order to make (c) correct. I seem to recall questions on "intelligence" tests that could garner "incorrect" answers because certain assumptions were expected.

For example: how many spaces are there between 10 telephone poles?
Well, if you picture them in the assumed usual linear arrangement, the answer is 9. But what if you picture them in a circle?

 

[toxcrusadr]

Then you'd have a really dumb telephone company.

 

[cubby01]

The bubbles in a water universe answer is....
...
...
they will move toward one another. Imagine it this way-

If you have an air bubble and a water bubble (both in the water universe) near each other and place a particle between them, it would move away from the air bubble and toward the water bubble. It is almost like the air bubble repelled the particle (but not really).

Since particles (objects) and bubbles move opposite one another (rocks sink, bubbles rise- both are gravitational arguments), a bubble of air placed near another bubble of air will be attracted to one another- not repelled.

Now wait a minute. I agree the two air bubbles attract (for the reason I stated earlier) but what is a bubble of water within a water universe? That's a bit counterintuitive at first.

If that particle you place between them is polypropylene would it not move toward the air bubble?

Now what about a water universe with an air bubble and a bubble of oil? Wouldn't they too be attracted? Actually with the oil eventually encasing the bubble?

That's the way my thought experiment goes anyway.

 

[DonQuixote99]

Oops! I realized that I have been neglectful in the thread- sorry guys.

The bubbles in a water universe answer is....
...
...
they will move toward one another. Imagine it this way-

If you have an air bubble and a water bubble (both in the water universe) near each other and place a particle between them, it would move away from the air bubble and toward the water bubble. It is almost like the air bubble repelled the particle (but not really).

Since particles (objects) and bubbles move opposite one another (rocks sink, bubbles rise- both are gravitational arguments), a bubble of air placed near another bubble of air will be attracted to one another- not repelled.

I need to think about this more. I see no difference between an air bubble and a rock, except one is made out of rock and one is made out of air. I mean, the one made out of gas is less solid than the solid, but they both are made out of normal matter, right? So they both create and respond to normal gravity.

I don't see what the buoyancy of an air bubble in water, in a gravity field like the Earth's, has to do with the question. There's no Earth in the water universe.

This may clarify thing a little. If we do the water universe experiment, but replace the air bubbles with solid spheres, made of some material that is less dense than water (some plastic, say), does anything change?

 

[cubby01]

This may clarify thing a little. If we do the water universe experiment, but replace the air bubbles with solid spheres, made of some material that is less dense than water (some plastic, say), does anything change?

They attract. That's why I used polypropylene in the posed the question just above. The specific gravity is less than water.