Thursday, Sep. 13, 2018

Brandi Carlile "It's Over" (3:58), "Touching the Ground" (3:38), "Losing Heart" (3:35), "That Wasn't Me" (3:50), "The Story" ( ~ 4:25)

The material below on Archimedes Principle can be found on page 54a and page 54b in the ClassNotes.

Hurricane Florence has weakened to a Category 2 hurricane and is expected to make landfall along the Carolina coast late tonight or early tomorrow.

The Expt. #1 reports are due next Tuesday.  If you haven't yet returned the materials, you can still come by my office in Harshbarger 220 and do that.  You will then have an opportunity to pick up the Supplementary Information handout which will help with the analysis portion of your report.  There's a box just outside my office door where you can leave the materials and copies of the Suppl. Info. handout are nearby.  The building should be open all day Friday and Monday, you don't necessarily need to stop by during office hours.

A new 1S1P Assignment is now available.  See the 1S1P Assignments & Topics page for more details.

 Free convection
Free convection is one way of causing rising air motions in the atmosphere.  We will soon see that rising air is important because it can lead to cloud and storm formation.



Sunlight shines through the atmosphere.  Once it reaches the ground at (1) it is absorbed and warms the ground.  This in turns warms air in contact with the ground (2)  As this air warms, its expands and its density starts to decrease (pressure is staying constant).  When the density of the warm air is low enough (lower than the surrounding air), small "blobs" of air separate from the air layer at the ground and begin to rise, these are called "thermals."  (3) Rising air expands and cools (we've haven't covered this yet and it might sound a little contradictory).  If it cools enough (to the dew point) a cloud will become visible as shown at Point 4.  This whole process is called convection; many of our summer thunderstorms start this way.


Archimedes' principle
Here's another way of trying to understand why warm air rises and cold air sinks - Archimedes Law or Principle (see pps 54a & 54b in the ClassNotes).  It's perhaps a simpler way of understanding the topic.  A gallon bottle of water can help you to visualize the law.



A gallon of water weighs about 8 pounds (lbs).  I wouldn't want to carry that much water on a hike unless I thought I would really need it.

Here's something that is kind of surprising.
If  you submerge the gallon of water in a swimming pool, the jug becomes, for all intents and purposes, weightless.  The weight of the water (the downward gravity force) doesn't just go away.  Once the jug is immersed, there must be an upward force of some kind, one that can cancel out gravity.  Archimedes' recognized that this would happen and was able to determine how strong the upward force would be.


The strength of the upward buoyant force is the weight of the fluid displaced by the bottle.  In this case the 1 gallon bottle will displace 1 gallon of pool water.  One gallon of pool water weighs 8 pounds.  The upward buoyant force will be 8 pounds, the same as the downward force.  The two forces are equal and opposite.

What Archimedes law doesn't really tell you is what causes the upward buoyant force.  You should know what the force is - it's the upward pressure difference force.





We've poured out the water and filled the 1 gallon jug with air.  Air is much less dense than water; compared to water,  the jug will weigh practically nothing.  But it still displaces a gallon of water and experiences the 8 lb. upward buoyant force.  The bottle of air would rise (actually it shoots) up to the top of the pool. The density of the material inside and outside the bottle are the same. A bottle filled with water is weightless. 

Next we'll fill the bottle with something denser than water (I wish I had a gallon of mercury)
Sand is about 50% denser than water.  The weight of a gallon of sand is more than a gallon of water.  The downward force is greater than the upward force and the bottle of sand sinks.


You can sum all of this up by saying anything that is less dense than water will float in water, anything that is more dense than water will sink in water.




Most types of wood will float (ebony and ironwood will sink).  Most rocks sink (pumice is an exception).

The fluid an object is immersed in doesn't have to be water, or even a liquid for that matter.  You could immerse an object in air.  So we can apply Archimedes Law to parcels of atmospheric air. 



Air that is less dense (warmer) than the air around it will rise.  Air that is more dense (colder) than the air around it will sink.

Here's a little more information about Archimedes.

I want to show one last application of some of what we have been learning - a Galileo thermometer.  That's assuming it survives the trip from my office to ILC 150.  It's a fairly new acquisition of mine and is fragile. 






The left figure above comes from an interesting and informative article in Wikipedia.  The right figure is a closeup view of the thermometer I brought to class.

Here's an explanation of how the thermometers work.  It requires some time to process.

The fluid in the thermometer will expand slightly if it warms.  It will shrink when it cools.



The changes in the volume of the fluid will change the fluid's density.  The graph above shows how the fluid density might change depending on temperature.  Note lower densities are found near the top of the graph (the fluid expands as it warms).


The colored balls in the thermometer all have slightly different densities.  They also have little temperature tags.  The 60 F ball has a density equal to the density of  the fluid at 60 F.  The 64 F ball has a slightly lower density, the density of the fluid when it has warmed to 64 , and so on.  The densities of the floats don't change.






In use the density of the fluid in the thermometer will change depending on the temperature.  The densities of the balls remain constant.  As an example we will that the fluid in the thermometer has a temperature of 74 F.  The 60, 64, 68, and 72 F balls will all have densities higher than the fluid (they lie below the 74F line in the graph above) and will sink.  The remaining balls have densities lower than the fluid and will float.

The lower most floating ball in the illustration has a 76 F temperature tag.  The uppermost of the balls that have sunk reads 72 F.  The temperature is something between 72 F and 76 F.  With this thermometer you can only determine temperature to the nearest 4 F.  Also the thermometer takes quite a while (maybe an hour or two) to respond to a change in temperature.

The material on air temperature changes with altitude, the troposphere & stratosphere has been moved to a separate Supplementary Reading section.  An Optional Assignment is included with that material.