Tuesday Sept. 4, 2007

An iron bar was passed around class at the beginning of class.  Students were asked to guess how much it weighed. 

Air in Tucson dried out dramatically over the weekend.  Dew points, which had been in the 60s since the start of the summer monsoon in early July dropped into the upper 30s.  Tropical moisture from the remains of Hurricane Henriette are expected to move into Arizona by mid week and should increase our chances of rain.  You can track the progress of Hurricane Henriette and also Hurricane Felix (which made landfall on the east coast of Central America this morning) at the National Hurricane Center website.  The latest forecast for Tucson and Southern Arizona can be found at the National Weather Service Tucson Forecast Office website

I forgot to mention that the first of this semester's 1S1P assignments is now online.  I will discuss this in class before the Practice Quiz this coming Thursday. 

A copy of the Practice Quiz Study Guide was handed out in class.  Reviews are scheduled for Tue. and Wed. afternoon from 4 - 5 pm in FCS 225.


There's a lot of information in this figure.  The atmosphere that surrounds the earth has mass.  Gravity pulls downward on the air giving it weight.  Galileo used a simple demonstration to prove that air has weight.

Pressure is defined as force divided by area; in this case the weight of the atmosphere divided by area.  Atmospheric pressure is determined by and tells you something about the weight of the air overhead.

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.  That is the same as the steel bar that was passed around class (many people think it is heavier than 14.7 pounds).  Normal atmospheric pressure at sea level is 14.7 pounds per square inch (psi).  Psi are the pressure units you use when you fill up your car or bike tires with air.

We will mostly use millibar (mb) units in this course.  Standard atmospheric pressure is about 1000 mb or 30 inches of mercury.  The second value refers to the reading from a mercury barometer.  1000 millibars is also equal to 1 bar or 1 atmosphere.



As you move upward through the atmosphere there is less and less air left overhead.  The pressure at any level in the atmosphere is determined by the weight of the air remaining overhead. Thus pressure decreases with increasing altitude.

Pressure changes much more quickly when you move in a vertical direction than it does when you move horizontally.  This will be important when we cover surface weather maps.  Meterologists attempt to map out small horizontal changes or differences in pressure on weather maps.  These small changes are what cause the wind to blow and produce weather.

Pressure increases even more rapidly as you descend into the ocean.  The pressure at some level in the ocean is determined by the atmospheric pressure plus the pressure produced by the weight of the water above you.  Water is much denser than air, so the extra weight builds up quickly. The submarine in the lower left hand corner of the figure above would experience a pressure of 2000 mb at 30 feet in the ocean, twice what it would feel at the surface of the ocean.  Only 30 feet of water has produced the same pressure as the entire atmosphere.


As you move upward from the ground pressure decreases by 100 mb in both layers in the figure above.  Both layers contain the same amount of air (if you refer back to the previous figure you will find the a 100 mb drop when you go from sea level to Tucson - 10% of the air in the atmosphere lies between sea level and 3000 ft altitude in Tucson).  That air is found in a smaller volume in the figure at left (the layer is thinner).  This means the air at left is denser than the air at right.  The drop in air pressure in the layer at left occurs in a shorter vertical distance than in the air layer at right.  That is a more rapid rate of pressure decrease with distance than in the layer at right.

The rate of pressure decrease with altitude is higher in the dense air at left than in the lower density air at right.

This is a fairly subtle but important concept.  We will use this concept later in the semester when we try to understand the intensification of hurricanes.
The following discussion of Newton's Law of Universal Gravitation wasn't covered in class.


The gravitational attraction between two objects depends first of all on the distance separating the objects.  The  gravitational force becomes weaker the further away the two objects are from each other.  In the bottom picture above and the top figure below we see that the attractive force also depends on the masses of the two objects.

The complete formula is shown in the middle of the page above.  G is a constant.  On the surface of the earth G, M, and R don't change.  The gravitational acceleration, g, is just G times Mearth divided by ( Rearth )2 .  To determine the weight (on the earth's surface) of an object with mass m you simply multiply m x g. 

Down at the bottom of the page are the Metric and English units of mass and weight.
Here's another page from the photocopied Class Notes that we didn't cover in class.  The weight of a person on the earth and the moon is calculated in English and metric units.

(1) The course instructor weighs about 160 pounds.   In (2) we see that the gravitational acceleration is 32 ft/sec2 in English units.  The meaning of this value is shown in (3).  Gravity will cause a falling object to fall 32 ft/sec faster with every second it continues to fall.  Dividing the instructor's weight by the gravitation acceleration in (4) we obtain the instructor's mass, 5 slugs, in English units.

In metric units, the instructor has a mass of 73 kilograms (5).  The gravitation acceleration is 9.8 m/sec (6).  Multiplying these two values, in (7), we find that the instructor weigh 715 Newtons.

On the moon, the mass stays the same.  Gravity is weaker, so the value of g is smaller.  The instructor would weigh quite a bit less (117 Newtons or 26 pounds) on the moon compared to the earth.

Air pressure is a force that pushes downward, upward, and sideways.  If you fill a balloon with air and then push downward on it, you can feel the air in the balloon pushing back (pushing upward).  You'd see the air in the balloon pushing sideways as well.

The bottom person in the people pyramid below must push upward with enough force to support the other people.  The air in a layer at the bottom of the atmosphere must do the same thing.  It pushes upward with enough force to support the weight of all the air overhead. 

The air pressure in the four tires on your automobile push down on the road (that's something you would feel if the car ran over your foot) and push upward with enough force to keep the 1000 or 2000 pound vehicle off the road.

The person on the bottom of the "people pyramid" must support the weight of all the people above.  People in the middle don't have to support as much weight.


Three layers of air in the atmosphere are shown above (point b: each layer contains the same amount of air, 10% of the air in the atmosphere).  You can tell because you see the same pressure drop as you move upward through each layer (point a).  This picture reminds you that air pressure decreases with increasing altitude.

The layer at the ground and at the bottom of the atmosphere is "squished" by the weight of the air above.  Squeezing all of this air into a thin layer or small volume (point c) increases the air's density.  The highest air density is found at the bottom of the atmosphere.

The next layer up is also squished but not as much as the bottom layer.  The density of the air in the second layer is lower than in the bottom layer.  The air in the 3rd layer has even lower density.  It is fairly easy to understand that air density decreases with increasing altitude. 

Finally if you look closely at the figure you can see that pressure decreases most rapidly with increasing altitude in the dense air at the bottom of the atmosphere.
We finished class with a demonstration of the upward force caused by air pressure.

The demonstration is described on p. 35a in the photocopied Class Notes. 
The following more detailed look at what is going on in the demonstration wasn't covered in class .  First the case of a water balloon:

The figure at left shows air pressure (red arrows) pushing on all the sides of the balloon.  Because pressure decreases with increasing altitude, the pressure pushing downward on the top of the balloon is a little weaker (strength=14) than the pressure pushing upward at the bottom of the balloon (strength=15).  The two sideways forces cancel each other out.  The total effect of the pressure is a weak upward force (shown on the right figure, you might have heard this called a bouyant force).  Gravity exerts a downward force on the water balloon.  In the figure at right you can see that the gravity force (strength=10) is stronger than the upward pressure difference force (strength=1).  The balloon falls as a result. 


In the demonstration a wine glass is filled with water.  A small plastic lid is used to cover the wine glass.  You can then turn the glass upside down without the water falling out. 


All the same forces are shown again in the left most figure.  In the right two figures we separate this into two parts.  First the water inside the glass isn't feeling the downward and sideways pressure forces (because they're pushing on the glass).  Gravity still pulls downward on the water but the upward pressure force is able to overcome the downward pull of gravity.  The upward pointing pressure force is used to overcome gravity not to cancel out the downward pointing pressure force.

The demonstration was repeated using a 4 Liter flash (more than a gallon of water, more than 8 pounds of water).  The upward pressure force was still able to keep the water in the flask (much of the weight of the water is pushing against the sides of the flask which the instructor was supporting with his arms).