Tuesday Sep. 10, 2013

Playing for Change: Stand By Me, Higher Ground, Gimme Shelter.  I also like "Groove in G".

The Practice Quiz is Thursday this week and the Study Guide has been updated to show the point totals from the various topics that we have covered.  Even though this is just a Practice Quiz and will have no effect on your grade there will be reviews Tuesday and Wednesday afternoons.  Both reviews will be held from 2 - 3:15 pm in Saguaro 225 (it probably won't take the full 75 minutes to cover the material on the study guide).

A new 1S1P Bonus Assignment ("Much more than you ever wanted to know about scattering of sunlight") is now available.  You can write up to 2 reports as part of Assignment #1 plus this Bonus Assignment if you want to.

Today's class was all about mass, weight, density, and especially pressure.  Weight is something you can feel so I passed an iron bar (it's sketched below) around class.  You were supposed to estimate it's weight.  The fact that it was 1" by 1" is significant.  More about the bar later in today's notes.


I also passed around a couple of small plastic bottles (below at left).  One contained some water the other an equal volume of mercury (here's the source of the nice photo of liquid mercury below at right).  I wanted you to appreciate how much heavier and denser mercury is than water. 




Thanks for being careful with the mercury.  A spill would have shut down at least ILC 150 and perhaps more of the ILC Building until the hazardous materials people could come in and clean it up.  It isn't so much the liquid mercury that is a hazard, but rather the mercury vapor.  Mercury vapor is used in fluorescent bulbs (including the new energy efficient CFL bulbs) which is why they need to be disposed of carefully.  That is something we'll mention again later in the class.

Something that wasn't passed around, three blocks of roughly equal shape and volume.   They were made of brick, lead, and wood but were wrapped in brown paper so that you couldn't see them. 

If you were asked to determine what was inside of each, without unwrapping them, probably the first thing you would do would be to lift each of them to see how heavy they were.  You might also squeeze them.



It would have been hard to guess exactly what was in each, but you could easily have arranged them in order from heaviest to lightest.



The lead (above at left) weighed about 15 pounds and was much heavier than the wood (at right and less than 1 pound) or the brick (in back, 5 pounds).

What exactly is weight?


The weight of an object depends on the object itself (how much of it there is) and on gravity.  We measure weight all the time.  What units do we use?  Usually pounds, but sometimes ounces or maybe tons. 

Why is lead heavier than wood or brick?  Lead has a higher density than wood or brick.  Here's a definition of density.

The lead was denser than the brick or wood even though its volume was about the same.  That must mean there was a lot more mass in the block of lead than in the other two blocks.

The term mass is a little hard to define.  Here's one definition (at the top of p. 23 in the ClassNotes).



Grams (g) and kilograms (kg) are commonly used units of mass (1 kg is 1000 g).  You could have equal volumes of two materials and still have different masses (which would result in different weights).  That was the case with the water and mercury making their way around the classroom.  You could also have equal numbers of atoms or molecules of different materials and still have different masses.

We'll be more concerned about air in this class than wood, brick, or lead.  In the first example below we have two equal volumes of air but the amount in each (the number of dots representing air molecules) is different.  Most everyone had no problem recognizing that the example on the right has higher density




The amounts of air (the masses) in the second example are the same but the volumes are different.  The left example with air squeezed into a smaller volume has the higher density. 

Now we can go back and make our definition of weight a little more precise.


Think of weight as being mass times gravity.  We tend to use weight and mass interchangeably (one kilogram equals 2.2 pounds) because we spend all our lives on earth where gravity never changes. 

On the earth's surface you determine the weight of an object by multiplying the object's mass by g.  As long as you're on the surface of the earth g has a constant value; it's called the gravitational acceleration. 

On the earth, two objects with the same masses would be multiplied by the same value of g and the weights of the two objects would be the same.  The moon is smaller than the earth and gravity on the moon is weaker than on the earth.  If you were to carry a brick to the moon the mass, volume, and density of the brick would stay the same but the brick would weigh less.



It would be the same brick in both cases and would have the same mass.  The gravitational force on the moon is weaker than on the earth and the value of the gravitational acceleration on the moon is about 1/6th the value on the earth.  So a 5 pound brick on the earth would weigh less than 1 pound on the moon.  The brick would weigh almost 12 pounds on the surface on Jupiter where gravity is stronger than on the earth.

Here's a little more information (not covered in class) about what determines the value of the gravitational acceleration (Newton's Law of Universal Gravitation).

What if we were in outer space and the three wrapped blocks of lead, wood, and brick were weightless (no gravitational attraction).  Could we tell them apart then?  They would still have very different densities and masses but we wouldn't be able to feel how heavy they were.

Here's another definition of mass.



This comes from Newton's 2nd law of motion, something we'll cover later in the semester.  I think the following illustration will help to understand inertia.




Two stopped cars.  They are the same size except one is made of wood and the other of lead.  Which would be hardest to get moving (a stopped car resists being put into motion).  It would take considerable force to get the lead car going.  Once the cars are moving they resist a change in that motion.  The lead car would be much harder to slow down and stop.

So you could distinguish between a brick and blocks of lead and wood.  You could give each of them a push.  It would take more effort to get the lead moving than the block of wood (more effort to slow the lead block down also).

Here's another question that was asked in class.





You can assume all three objects are sitting on the surface of the earth.  You'll find the answer to this question at the end of today's notes.

Before we change topics (and because I like lists), here are densities of some of the materials used in class today.   Sorry I wasn't able to bring nice samples of gold, platinum, iridium, or osmium to pass around class.
 
material
 density g/cc
air
 0.001
redwood
 0.45
water
 1.0
iron
 7.9
lead
 11.3
mercury
 13.6
gold
 19.3
platinum
 21.4
iridium
 22.4
osmium
 22.6

Don't worry about the units, but g/cc stands for grams per cubic centimeter.  A cubic centimeter is a volume about the size of a sugar cube.

Now we're ready to define (and hopefully understand) pressure.  It's a pretty important concept.  A lot of what happens in the atmosphere is caused by pressure differences.  Pressure differences cause wind.  Large pressure difference (such as you might find in a tornado or a hurricane) create powerful and destructive storms.  And we'll be using a couple of pages from the ClassNotes.



The air that surrounds the earth has mass.  Gravity pulls downward on the atmosphere giving it weight.  Galileo conducted (in the 1600s) a simple experiment to prove that air has weight.  The experiment wasn't mentioned in class.

Atmospheric pressure depends on, is determined by, the weight of the air overhead.  This is one way, a sort of large scale representation, of understanding air pressure.

Pressure is defined as force divided by area.  In the case of atmospheric pressure the weight of a column of air divided by the area at the bottom of the column (as illustrated above). 

Under normal conditions a 1 inch by 1 inch column of air stretching from sea level to the top of the atmosphere will weigh 14.7 pounds.  Normal atmospheric pressure at sea level is 14.7 pounds per square inch (psi, the units you use when you fill up your car or bike tires with air).

Now back to the iron bar.  It was a little hard to tell but I think that a lot of people felt it weighed more than 30 pounds, others maybe between 20 and 30 pounds.  The bar actually weighs 14.7 pounds.  When you stand the bar on end, the pressure at the bottom would be 14.7 psi.



So the weight of a 1" x 1" steel bar 52 inches long is the same as a 1" x 1" column of air that extends from sea level to the top of the atmosphere 100 or 200 miles (or more) high.  The pressure at the bottom of both would be 14.7 psi.

Psi are perfectly good pressure units, but they aren't the ones that most meteorologists used.




Typical sea level pressure is 14.7 psi or about 1000 millibars (the units used by meteorologists and the units that we will use in this class most of the time) or about 30 inches of mercury.    Milli means 1/1000 th.  So 1000 millibars is the same as 1 bar.  You sometimes see typical sea level pressure written as 1 atmosphere.

Inches of mercury refers to the reading on a mercury barometer.  Mercury (13.6 grams/cm3)  is denser than steel ( about 7.9 grams/cm3 ) so it would only take about a 30 inch tall column of mercury to equal the weight or pressure of the atmosphere.


Each of these columns would weigh 14.7 pounds.  The pressure at the base of each would be the same. 

A mercury barometer used to measure pressure is, we'll find, just a balance.  You balance the weight of a very tall column of air with the weight of a much shorter column of mercury.

You never know whether something you learn in ATMO 170A1 will turn up.  I lived and worked for a short time in France (a very enjoyable and interesting period in my life).  Here's a picture of a car I owned when I was there (this one is in mint condition, mine was in far worse shape)



It's a Peugeot 404.  After buying it I took it to the service station to fill it with gas and to check the air pressure in the tires.  I was a little confused by the air compressor though, the scale only ran from 0 to 3.  I'm used to putting 30 psi or so in my car tires (about 90 psi in my bike tires).  After staring at the scale for a while I finally realized the numbers were pressures in "bars" not "psi".  Since 14.7 psi is equivalent to 1 bar, 30 psi would be about 2 bars.  So I filled up all the tires and carefully drove off (one thing I quickly learned was you have to watch out for in France is the "Priority to the right" rule). 


You can learn a lot from bricks. 

For example the photo below (taken in my messy office) shows two of the bricks from class.  One is sitting flat, the other is sitting on its end.  Each brick weighs about 5 pounds.  Would the pressure at the base of each brick be the same or different in this kind of situation? 



Pressure is determined by (depends on) weight so you might think the pressures would be equal.  But pressure is weight divided by area.  In this case the weights are the same but the areas are different.  In the situation at left the 5 pounds must be divided by an area of about 4 inches by 8 inches = 32 inches.  That works out to be about 0.15 psi.  Atmospheric pressure is 14.7 psi almost 15 psi.  You would need a stack of 100 bricks to equal atmospheric pressure.

In the other case the 5 pounds should be divided by a smaller area, 4 inches by 2 inches = 8 inches.  That's a pressure of 0.6 psi, 4 times higher.  Notice also these pressures are much less the 14.7 psi sea level atmospheric pressure.

The main reason I brought the bricks was so that you could understand what happens to pressure with increasing altitude.  Here's a drawing of the 5 bricks stacked on top of each other (I used 4 bricks in class).

At the bottom of the pile you would measure a weight of 25 pounds (if you wanted to find the pressure you'd divide 25 lbs by the 32 square inch area on the bottom of the brick).  If you moved up a brick you would measure a weight of 20 pounds, the weight of the four bricks that are still above.  The pressure would be less.  Weight and pressure will decrease as you move up the pile.

The atmosphere is really no different.  Pressure at any level is determined by the weight of the air still overhead.  Pressure decreases with increasing altitude because there is less and less air remaining overhead. 



At sea level altitude, at Point 1, the pressure is normally about 1000 mb.  That is determined by the weight of all (100%) of the air in the atmosphere.

Some parts of Tucson, at Point 2, are 3000 feet above sea level (most of central Tucson is a little lower than that around 2500 feet).  At 3000 ft. about 10% of the air is below, 90% is still overhead.  It is the weight of the 90% that is still above that determines the atmospheric pressure in Tucson.  If 100% of the atmosphere produces a pressure of 1000 mb, then 90% will produce a pressure of 900 mb. 

Pressure is typically about 700 mb at the summit of Mt. Lemmon (9000 ft. altitude at Point 3) because 70% of the atmosphere is overhead..

Pressure decreases rapidly with increasing altitude.  We will find that pressure changes more slowly if you move horizontally.  Pressure changes about 1 mb for every 10 meters of elevation change.  Pressure changes much more slowly normally if you move horizontally: about 1 mb in 100 km.  Still the small horizontal changes are what cause the wind to blow and what cause storms to form.

Point 4 shows a submarine at a depth of about 30 ft. or so.  The pressure there is determined by the weight of the air and the weight of the water overhead.  Water is much denser and much heavier than air.  At 30 ft., the pressure is already twice what it would be at the surface of the ocean (2000 mb instead of 1000 mb).


The next and final figure (p. 26 in the ClassNotes) explores why the rate of pressure change as you move or down in the atmosphere depends on air density.  In particular air pressure will decrease more quickly when you move upward through high density air than if you move upward through low density air.


There's a lot going on in this picture, we'll examine it step by step.

1.The sea level pressure is the same, 1000 mb, in both pictures.  Since pressure is determined by the weight of the air overhead, the weight of the air overhead in the left picture is the same as in the right picture.  The amount (mass) of air above sea level in both pictures is the same.

2.  There is a 100 mb drop in pressure in both air layers.  Pressure has decreased because air that was overhead (the air between the ground the level of the dotted line) is now underneath.  Because the pressure change is the same in both pictures the weight of the air layers are the same.  The thin layer at left has the same weight as the thicker layer at right.  Both layers contain the same amount (mass) of air.

3.  Both layers contain the same amount (mass) of air.  The air in the layer at left is thinner.  The air is squeezed into a smaller volume.  The air in the layer at left is denser than the air in the layer at right.

4.  To determine the rate of pressure decrease you divide the pressure change (100 mb for both layers) by the distance over which that change occurs.  The 100 mb change takes place in a shorter distance in the layer at left than in the layer at right.  The left layer has the highest rate of pressure decrease with increasing altitude.

So both the most rapid rate of pressure decrease with altitude and the densest air are found in Layer A.

The fact that the rate of pressure decrease with increasing altitude depends on air density is a fairly subtle but important concept.  This concept will come up 2 or 3 more times later in the semester.  For example, we will need this concept to explain why hurricanes can intensify and get as strong as they do. 


Here's the answer to the earlier question about the weights of three different objects that all have the same mass.
Because you're multiplying the same value of mass by the constant value of g (constant as long as you remain on the surface of the earth), you'll get the same value of weight.