Frankly Physical...Displacement and Density
Regarding my discussion with El Franko about displacement of water in an April 8th blog entry i.e.
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Phill has met up with icebergs at some 'high up' lakes at the foot of glaciers, and so have I for that matter. During one of our regular 'scrabbulations'...Phill floated the question:
As the ice melts, what does that do to the water level in the lake?
Does it go up, down, sideways or what?
Are you willing to stick your neck out and make a prediction?
Please do give reasons for your answers!
I'll post my own thoughts regarding this question in a week.
Frank Weichman | Resident Mathematical Mind at SecretSpot.net
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...here are some musings from Frank:
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Start with the basic facts
1. Ice floats
2. Ice turns into water
3. How much water does ice turn into?
4. How much water does ice, or any other material, displace when put in the water?
5. What if there are bubbles (or salt) in the ice?
Instead of ice, let us start with a solid hunk of iron and a pail of water. It has a volume which we will call V. Iron is denser than water, therefore it will sink and the height of the water in the pail will rise exactly as much as it would if we had poured in a volume V of water.
Iron can be shaped. Suppose we made a cup out of the hunk of iron. That cup, if carefully placed in the water, would float. Why? An object floats when it can displace more weight of the liquid (water in our case) than the weight of the object itself. By clever shape change you can even push down on the cup, say by putting lead pellets into it, and it will still float. The rise in water level will correspond exactly to the volume of water pushed aside, and, according to Archimedes's Principle, the weight of that volume of water is exactly equal to the weight of the iron cup, with or without the lead pellets. Before we shaped the hunk of iron, its volume was too small to push aside ('displace') its total weight.
What about ice? Ice is less dense than water, so it will float by displacing just enough water. Specifically, one kilogram of ice will displace one kilogram of water as it floats. The rest of the ice, roughly 1/10th, will stick up above the surface (FYI, the density of ice is 0.917 compared to water as 1.000). Suppose now that half the ice melts. We need to displace only half a kilogram of water to keep the rest afloat. We have half a kilogram of volume to spare, and the water level could go down by half a kilogram's worth of water. Isn't it strange that just that half a kilogram's worth of water has just melted and kept the level the same. The remaining half kilogram of water would do the exact same thing as it melts.
Do the test. Put some ice cubes in a glass and then fill the glass to the top with water. Will the water dribble over the edge as the ice melts?
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If a person was dull...they might ask , 'Who cares?!".
To learn at least a new thing every single day is vital.
Enough said.
The next question that Frank posed is along the same lines and deals with density:
>>>>>>>>>>
Phill has met up with icebergs at some 'high up' lakes at the foot of glaciers, and so have I for that matter. During one of our regular 'scrabbulations'...Phill floated the question:
As the ice melts, what does that do to the water level in the lake?
Does it go up, down, sideways or what?
Are you willing to stick your neck out and make a prediction?
Please do give reasons for your answers!
I'll post my own thoughts regarding this question in a week.
Frank Weichman | Resident Mathematical Mind at SecretSpot.net
>>>>>>>>>>
...here are some musings from Frank:
>>>>>>>>>>
Start with the basic facts
1. Ice floats
2. Ice turns into water
3. How much water does ice turn into?
4. How much water does ice, or any other material, displace when put in the water?
5. What if there are bubbles (or salt) in the ice?
Instead of ice, let us start with a solid hunk of iron and a pail of water. It has a volume which we will call V. Iron is denser than water, therefore it will sink and the height of the water in the pail will rise exactly as much as it would if we had poured in a volume V of water.
Iron can be shaped. Suppose we made a cup out of the hunk of iron. That cup, if carefully placed in the water, would float. Why? An object floats when it can displace more weight of the liquid (water in our case) than the weight of the object itself. By clever shape change you can even push down on the cup, say by putting lead pellets into it, and it will still float. The rise in water level will correspond exactly to the volume of water pushed aside, and, according to Archimedes's Principle, the weight of that volume of water is exactly equal to the weight of the iron cup, with or without the lead pellets. Before we shaped the hunk of iron, its volume was too small to push aside ('displace') its total weight.
What about ice? Ice is less dense than water, so it will float by displacing just enough water. Specifically, one kilogram of ice will displace one kilogram of water as it floats. The rest of the ice, roughly 1/10th, will stick up above the surface (FYI, the density of ice is 0.917 compared to water as 1.000). Suppose now that half the ice melts. We need to displace only half a kilogram of water to keep the rest afloat. We have half a kilogram of volume to spare, and the water level could go down by half a kilogram's worth of water. Isn't it strange that just that half a kilogram's worth of water has just melted and kept the level the same. The remaining half kilogram of water would do the exact same thing as it melts.
Do the test. Put some ice cubes in a glass and then fill the glass to the top with water. Will the water dribble over the edge as the ice melts?
>>>>>>>>>>
If a person was dull...they might ask , 'Who cares?!".
To learn at least a new thing every single day is vital.
Enough said.
The next question that Frank posed is along the same lines and deals with density:
Based on the above arguments, would you care to predict what would happen if you poured Khukri Rum, instead of water, in the glass with ice cubes, or, for that matter, if you poured in very salty water? Alcohol is less dense than water, and salt water is more dense that water.
Dawa knows the answers to those questions! =^P
Do you?!
Until Soon
Phill =^)
PHILL MICHAEL | Expedition Leader and Summit Climber
Everest Freestyle Expedition/Secret Spot Seven Summits
Dawa knows the answers to those questions! =^P
Do you?!
Until Soon
Phill =^)
PHILL MICHAEL | Expedition Leader and Summit Climber
Everest Freestyle Expedition/Secret Spot Seven Summits
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