Does Throwing Iron Overboard or Melting Ice Affect Water Levels?

[Saska]

1) You're sitting in a boat filled with iron, in a pool. What happens with the waterlevel in the pool when you throw out the iron in the pool. Why?

Really I don't get this. Either the level is constant, nothing changes, or the level rises? I had a discussion with some classmates and no one could figure it out! Help please?

2) Place icecubes in a glass and fill the glass with water to the brim. The ice will stick upp somewhat out of the glass. What happens to the waterlevel when the ice melts. why?
I don't get this either :O First I thought that the water level would decrease because ice has lower density, now I'm not so sure anymore.

 

[Shooting Star]

1) Level falls. The iron, being denser than water, displaces more than its volume of water when it's floating in the boat. When it's not floating any more but submerged completely, naturally it displaces less water.

2) Level remains same. The whole of the ice after melting takes up exactly the volume that the submerged portion of the ice was displacing.

 

[Saska]

The second answer confuses me. Isn't ice less denser than water ... So the level should rise?

 

[Shooting Star]

By Archimedes' principle, weight of water displaced by ice = weight of ice, which means that the vol of water equal to the vol of ice that is under water weighs as much as the whole ice piece.

After melting, the ice becomes water, so the vol of the melted ice should be exactly equal to the vol of water that it was displacing.

 

[stewartcs]

1) Level falls. The iron, being denser than water, displaces more than its volume of water when it's floating in the boat. When it's not floating any more but submerged completely, naturally it displaces less water.

Another way to say it is that when the lead is in the boat, it displaces its weight in water. When it's in the pool, it displaces only its volume.

 

[stewartcs]

The second answer confuses me. Isn't ice less denser than water ... So the level should rise?

The water level in the glass is dependent on the amount of water that is displaced by the ice (i.e. the mass of the ice).

Suppose the ice was enclosed in a waterproof sack (that had no mass). Would the total contents of the sack (mass) change when it melted?

 

[Saska]

-Suppose the ice was enclosed in a waterproof sack (that had no mass). Would the total contents of the sack (mass) change when it melted?-
yeah ... not the mass, but the volume would change.


-- After melting, the ice becomes water, so the vol of the melted ice should be exactly equal to the vol of water that it was displacing. --
But doesn't it depend on the temperature of the water, since the density of water changes depending on the temperature?

 

[Shooting Star]

I think density change of water with temp is being ignored here. This type of problem has more to do with teaching students about buoyancy etc.

But if the water is at, say 50 C, and the ice at -50 C, then for accurate calculations, the density of both have to be taken into account. In this problem, it’s assumed that the melted ice has exactly the density of the water it is in.