Friday Sept. 7, 2007

The Practice Quiz was returned in class today.  You'll find answers to the quiz questions here.

The first optional assignment is due one week from today.

There is also a new reading assignment.
We will sometimes "beat material to death" in this class.  Here's an example: we worked through the following figure in great detail in class. 

Point 1a - 1000 mb is a reasonable sea level pressure value.

Point 1b - The fact that the pressures are equal at the bottoms of both pictures means that the weight of the atmosphere at the bottom of the picture on the left is the same as the weight of the atmosphere at the bottom of the picture at right.  The only way this can be true is if there is the same total amount (mass) of air in both cases.

Point 2 - Moving upward from the ground we find that pressure decreases to 900 mb at the level of the dotted line in the picture at left.  This is what you expect, pressure decreases with increasing altitude. 

The pressure decreases to 900 mb in the picture at right, but you have to go to higher altitude before this occurs.

Point 3 - The most rapid rate of pressure decrease with increasing altitude is occurring in the picture at left.

Point 4 - Since there is a 100 mb drop in the layer at left and in the layer at right, both layers must contain the same amount (mass) of air.

Point 5 - The air in the picture at left is squeezed into a thinner layer than in the picture at right.  The air density in the left layer is higher than in the layer at right.

We used and analyzed this picture to prove to ourselves that the rate of pressure decrease with altitude is higher in dense air than in lower density air.

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.
We didn't work through the following figures at all (except for filling in the box at the bottom of p. 28 with the English and Metric units for mass and weight).


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.

The mass of a person would be the same on the earth and on the moon. The weight of a person depends on the person's mass and on the strength of gravity (the acceleration of gravity term, the g variable below).


(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 weighs 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.
Here's another topic that we'll beat into submission, trying to understand how a mercury barometer works (it's used to measure atmospheric pressure).  You'll find most of what follows on p. 29 in the photocopied Class Notes.


The instrument above ( a u-shaped glass tube filled with a liquid of some kind) is a manometer and can be used to measure pressure difference.  The two ends of the tube are open so that air can get inside and air pressure can press on the liquid.  Given that the liquid levels on the two sides of  the manometer are equal, what could you about PL and PR?

The liquid can slosh back and forth just like the pans on a balance can move up and down.  A manometer really behaves just like a pan balance.
PL and PR are equal (note you don't really know what either pressure is just that they are equal).
Now the situation is a little different, the liquid levels are no longer equal.  You probably realize that the air pressure on the left, PL, is a little higher than the air pressure on the right, PR.  PL is now being balanced by PR + P acting together.  P is the pressure produced by the extra fluid on the right hand side of the manometer (the fluid that lies above the dotted line).  The height of the column of extra liquid provides a measure of the difference between PL and PR.


Next we will go an extreme and close off the right hand side of the manometer.


Air pressure can't get into the right tube any more.  Now at the level of the dotted line the balance is between Pair and P (pressure by the extra liquid on the right).  If Pair changes, the height of the right column, h,  will change.  You now have a barometer, an instrument that can measure and monitor the atmospheric pressure.



Barometers like this are usually filled with mercury.  Mercury is a liquid.  You need a liquid that can slosh back and forth in response to changes in air pressure.  Mercury is also dense which means the barometer won't need to be as tall as if you used something like water.  A water barometer would need to be over 30 feet tall.  With mercury you will need only a 30 inch tall column to balance the weight of the atmosphere at sea level under normal conditions (remember the 30 inches of mercury pressure units mentioned earlier).  Mercury also has a low rate of evaporation so you don't have much mercury gas at the top of the right tube.


Finally here is a more conventional barometer design.  The bowl of mercury is usually covered in such a way that it can sense changes in pressure but not evaporate and fill the room with poisonous mercury vapor.

The figure above (p. 30 in the photocopied Class Notes) first shows average sea level pressure values (1000 mb or 30 inches of mercury are close enough in this class).  Sea level pressures usually fall between 950 mb and 1050 mb.  Record high sea level pressure values occur during cold weather.  Record low pressure values have all been set by intense hurricanes (the record setting low pressure is the reason these storms were so intense)

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 above 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.
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).