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Consider a cube of ice in a flat based container(the base is very broad).The temperature of the system is at first fixed at a minus Celsius temperature, but then the system is left on a table with the top open to atmosphere.
The ice starts melting, and finally there is only water, spread over the container's base(water doesn't touch walls of the container,so it looks like water spilled on the floor)
Here, the centre of mass of the $H_2O$-container system moves downward because of the lowering of height of water molecules.
But,this system experiences no net external force on it,all the time.Hence, the centre of mass of this system shouldn't accelerate at all!
How is this contradiction sorted out?I feel that since melting is very slow, the centre of mass might move only very slowly, but still that doesn't explain things.For example if the room was very hot, melting wouldn't have been slow, right?

Edit:Many people are probably getting confused regarding what perspective I'm taking.Let the container and water(solid/liquid) be a single system.We can think of them together as a point mass.This point mass is at equilibrium,and at rest,situated at the position of the centre of mass of ice+container system(let's say,at a height 'h' above the table.
There may be internal forces happening inside the point mass,but the net external force(resultant) is zero,all the time.Hence, according to Newton's first law,the point mass must remain at equilibrium and hence,at rest.But,when ice melts,the position of center of mass of ice+container system has moved down!
Hence the point mass has to move down, in the absence of any resultant external force.The gravitational force on ice+container is cancelled by normal reaction of table on container.

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What about gravity? –  Bernhard Dec 25 '13 at 12:53
    
There are lots of forces acting on it: a) Gravity, b) Contact with walls of container, c) Air pressure .. etc –  ja72 Dec 25 '13 at 15:21
    
The net external force of the water-container system is zero.the system is at rest on a table. –  scienceauror Dec 25 '13 at 18:40
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If there is no gravity, then the water resultant of the melting of the ice would not stay in the bottom... So either there is gravity, or you must prove that the center of mass would change. You cannot have it both ways. youtube.com/watch?v=gTqLQO3L4Ko –  SJuan76 Jun 7 at 12:20

3 Answers 3

For each molecule of water in the ice cube there are two forces to consider: the electromagnetic force and gravity. When the ice cube is frozen, the molecules have low kinetic energy so they stick to their rigid crystalline structure which is sufficient to counter the gravitational force. When they have a bit more kinetic energy (i.e. at higher temperature) they are able to break free of their crystalline structure and so are unable to counter the gravitational force.

The fact that the water molecules are accelerated is ok - there is additional energy added to the water molecules as they heat up.

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I'm not concerned about the internal forces in water,or between water and container.When both water and container are considered as a system on whole,they are at equilibrium already right? –  scienceauror Dec 25 '13 at 18:47
    
But, as you have observed, the water+container system isn't in equilibrium. This is because there is energy transfer from the surroundings to the system. –  jk88 Dec 25 '13 at 21:35
    
I had said that the water+container system is at equilibrium. –  scienceauror Dec 26 '13 at 11:43
    
How can energy transfer accelerate a system?? –  scienceauror Dec 26 '13 at 11:48
    
But the water+container system isn't in equilibrium- it is heating up. The temperature of a system is related to the kinetic energy of the particle in it (see this Wikipedia page). Therefore if you increase the temperature of a system you increase the average kinetic energy and hence the average speed of the particles in the system also increases (acceleration). –  jk88 Dec 26 '13 at 12:27

Simply put, the ice-container system is not closed; there are external gravitational forces.

If you consider the earth and container as one part, and the ice/liquid water as the other, of a new, closed system, as the water melts and drops down, the earth rises (a tiiiiiny bit) and the CofM of this system remains unchanged

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So do you mean to say that a system consisting of water and container is not at equilibrium?if yes,why? –  scienceauror Dec 25 '13 at 18:42
    
We're not talking about equilibrium, we're talking about closed. An exploding hand grenade is not at equilibrium until it's through exploding, but the center of mass the grenade stays unaccelerated throughout the explosion. –  User58220 Dec 25 '13 at 19:05
    
"An exploding hand grenade is not at equilibrium" --explain,because you just said "center of mass of grenade stays unaccelerated" –  scienceauror Dec 26 '13 at 11:54
    
If you explodes a stationary hand grenade in vaccuum in deep space, the parts will spread "evenly" in space, leaving the grenades center of mass intact. If an hypothetical ice-container was melting i a closed container in gravity free deep space and did not have surface tension (hypothetically!), the water would stay in cubic position. –  claj Dec 26 '13 at 13:53
    
Yea,that point is correct in case of gravity free space, but in this case,in the absence of a net external force, for the CofM of the system to remain at it's initial position,as water's CofM shifted down,the container must shift up!(with respect to the table).Hence, the container must go up in air!so is there something like for every infinitesimal time interval when a very small amount of ice has melted,the container goes up in air by a very small height,and then the gravity pulls them down??That must be like(looking in a very powerful microscope) the container moving up and down very fast!! –  scienceauror Dec 27 '13 at 10:57

You can no longer consider the ice block as a system once it starts melting, so it no longer remains a rigid body. Consequently, you cannot apply Newton's law on it. Peace ;)

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