Wednesday Feb. 5, 2014

Exotic music and dance from Beats Antique: "Egyptic" and "Caterpillar".

If you missed the Practice Quiz you'll can download it here.  I would encourage you to have a look at it if only to become familiar with the quiz format.  Try answering the questions.  Here are the answers so that you can check and see how you would have done.

I'll try to get all the quizzes graded in time to return on Friday.  But I have to grade them all (both sections) myself.  My TAs are out of town. 

Here's another way of trying to understand why warm air rises and cold air sinks - Archimedes Law or Principle.  It's a perhaps simpler way of understanding the topic.  A 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.

If you submerge the gallon jug of water in a swimming pool, the jug becomes, for all intents and purposes, weightless.  That seems kind of amazing - 8 pounds suddenly doesn't weigh anything.  Archimedes' Law (see figure below, from p. 53a in the ClassNotes) explains why this is true.





Archimedes first of all tells you that the surrounding fluid will exert an upward pointing buoyant force on the submerged water bottle.  That upward force is strong enough to make the submerged jug become weightless. 

Archimedes law also tells you how to figure out how strong the buoyant force will be.  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.

Now we imagine pouring out all the water and filling the 1 gallon jug with air.  Air is about 1000 times less dense than water; compared to water,  the jug will weigh practically nothing.




If you submerge the jug of air in a pool it will still displace 1 gallon of water and the 8 pound upward buoyant force will still be there.  Since there is no downward force the jug will float (the bottle of air would shoot up to the surface of the pool).

One gallon of sand (which is about 1.5 times denser than water) weighs 12 pounds.



The jug of sand will sink because the downward force is greater than the upward force.

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 same reasoning applies to air in the atmosphere though it's harder to appreciate because air is invisible.

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 that I didn't mention in class.

There's a colorful demonstration that shows how small differences in density can determine whether an object floats or sinks.

A can of regular Pepsi was placed in a beaker of water.  The can sank.  A can of Diet Pepsi on the other hand floated.

Both cans are made of aluminum which has a density almost three times higher than water; aluminum by itself would sink.  The drink itself is largely water.  The regular soda also has a lot of high-fructose corn syrup, the diet soda doesn't.  The mixture of water and corn syrup has a density greater than plain water.  There is also a little air (or perhaps carbon dioxide gas) in each can (the diet soda probably wouldn't float if it weren't for the gas in the can.

The average density of the can of regular soda (water & corn syrup + aluminum + air) ends up being slightly greater than the density of water.  The average density of the can of diet soda (water + aluminum + air) is slightly less than the density of water.

In some respects people in swimming pools are like cans of regular and diet soda.  Some people float (they're a little less dense than water), other people sink (slightly more dense than water). 

Many people can fill their lungs with air and make themselves float, or they can empty their lungs and make themselves sink.  People have an average density that is about the same as water.  That makes sense because we are largely made up of water (water makes up about 60% of human males and 55% of human females according to this source)