Tuesday Sep. 5, 2006

A copy of the Practice Quiz Study Guide was handed out in class.  Still no word on the location of the Tuesday and Wednesday afternoon reviews.  You'll find the locations posted on the class web page as soon as they are known.

The link to the Sample 1S1P Report is now working correctly.  The Assignment #1 1S1P reports are due next Tuesday, Sep. 12.


Mass is just a measure of how much of a particular material you have.   It is really not the same as volume, two objects (different materials) could have the same volume but different masses.  Similarly two objects (different materials) could have the same total number of atoms or molecules and still have different masses.  The picture below attempts to make clearer the meaning of inertia or resistance to change in motion which are sometimes used to define mass.


A Cadillac and a volkswagen have both stalled in an intersection.  Both cars are made of steel.  The Cadillac is larger and has more steel, more stuff, more mass.  The Cadillac is also much harder to get moving, it has a larger inertia (it would also be harder to slow down if it were already moving).


We generally don't distinquish between weight and mass.  This is because the strength of the gravitational force exerted on a mass and produces its weight is always the same on the surface of the earth.

A mass of 1 kg will always have a weight of 2.2 pounds (lbs).  Similarly an object that has a weight of 2.2 pounds will, no matter what its size or composition, have a mass of 1 kg. 

You would need to be more careful if you compared objects on the earth and the moon.  This is because the gravitational attractive forces on the earth and moon are different.



An object with a mass of 1 kg on the earth does not contain the same amount of stuff as an object that weighs 2.2 pounds on the moon (the object on the moon would need to have a mass of a little over 6 kg in order to weigh 2.2 pounds because of the weaker lunar gravity)


Now just to add to the confusion (we didn't spend much time on this figure in class).  The course instructor weighs around 160 pounds (actually a little less at the end of the summer bicycling season).  Pounds are units of weight in the English units system.  The instructor has a mass of 73 kilograms (kilograms are metric system units for mass). 

To determine the instructor's weight in metric units you would need to multiply the mass by g, the acceleration of gravity on the earth (9.8 m/sec2).  You would obtain 715 Newtons (metric units of force or weight).

To determine the instructor's mass in English units you would need to divide the weight by the acceleration of gravity (32 ft/sec2).  You obtain 5 slugs (believe it or not, slugs are English units of mass).

The gravitational acceleration on the moon 5.2 ft/sec2, about 1/6 of what it is on the earth.  On the moon, the instructor would still have a mass of 5 slugs but a weight of only 26 pounds.

The sketch on the right edge of the page above gives you an idea of what g, the gravitational acceleration, really represents.  You drop an object.  After 1 second it will have fallen 16 feet and will be falling at a speed of 32 ft/sec.  At the end of 2 seconds it will be falling 64 ft/sec, after 3 seconds at 96 ft/sec.  The speed of the falling object is increasing by 32 feet/sec per second.  Rate of change of speed is acceleration.  If gravity were the only force acting on the falling object (and it usually is not) it wouldn't matter how big or how heavy the object was, it's speed would increase 32 ft/sec per second.  A small light weight object and a larger heavier object would both fall at the same speed and reach the ground at the same time.
Bottles containing equal volumes of water and mercury were passed around class (thanks for being careful with the mercury). 

What explains the large difference in masses?  Part of the answer is that the mercury atoms are packed together more tightly than are the water molecules.  A more important difference is that the water molecules and mercury atoms contain very different numbers of protoms and neutrons.


Gravity pulls downward on the air surrounding the earth producing weight (people didn't really realize that air had mass and weight and didn't devise ways of measuring air pressure until the 1600s).  Air pressure is determined by and tells you something about the weight of the air overhead.  This is one way of trying to understand atmospheric pressure.

A one inch by one inch column of air extending from sea level to the top of the atmosphere would, under average conditions, weigh 14.7 pounds (the same as a 4 foot long iron bar that was passed around in class).  Pressure is defined as force divided by area, in this case weight divided by area.  So a typical sea level pressure would be 14.7 pounds per square inch or psi.  These are the same units used when filling an automobile tire with air.  You usually put about 30 psi into car tires.

We will mostly use millibar (mb) units in our 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 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; pressure has doubled to 2000 mb when you are only about 30 feet deep in the ocean.
The following two pages from the photocopied Class Notes weren't covered in class
Isaac Newton was one of the greatest scientists that ever lived.  Among his accomplishments was the formulation of a law describing the gravitational attraction between two objects.  With a picture or two and some thought you can understand the roles that the various variables in the equation play.


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 (we assume the two objects are spherical).  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 .
Down at the bottom of the page are the Metric and English units of mass and weight.

As you move upward from the ground pressure decreases by 100 mb in both figures.  Both layers contain the same amount of air (10% of the air in the atmosphere).  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 it when we try to understand the intensification of hurricanes later in the semester.
You'll find the following material discussed on p. 29 in the photocopied notes.  In 3 simple steps you can understand how a barometer works.  It is probably worth mentioning that barometers are used to measure pressure (atmospheric pressure).  It is not coincidence that the word bar that appears in barometer is the same bar that appears in millibars.  We will be learning about weather maps next week and will come across isobars, contours of pressure.


A manometer can be used to measure pressure difference.  The manometer is just a u-shaped tube usually made of glass so that you can see the liquid that is inside.  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.

In this picture the fact that the liquid levels are the same in the right and left tubes means P1 and P2 are the same (note you really don't know what P1 and P2 are, just that they are equal).



Now the situation is a little different, the liquid levels are no longer equal.  The orange shaded portion of the liquid is the balance that we had in the previous picture.  The pressures at the levels of the two blue arrows are equal (the red shaded fluid is the balance).  P2 is not able by itself to balance P1, P2 is lower than P1.  P1 plus the pressure produced by the column of extra liquid on the right balances P1.  The height of the column of extra liquid provides a measure of the difference between P1 and P2.


We have changed the manometer by lengthening the right tube and sealing it off at the top.  Air pressure can't get into the right tube any more.  The balance is again shaded in orange at the bottom of the barometer.  Pressures at the two blue arrows indicated are equal.  Pair is equal to the pressure produced by the column h inches tall on the right.  If Pair changes, h will change.  You now a way of measuring and monitoring 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 in class a week or so ago).  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.


Under normal conditions sea level pressure is about 1000 mb (about 30 inches of mercury).  It can be higher and lower than this but usually falls in the range 950 mb to 1050 mb.  Record high and low sea level pressure values are shown in the chart.  Note the record low values have all be observed in hurricanes.

Hurricane Wilma set a new low sea level pressure reading (882 mb) last year for the Atlantic.  At the time the winds were 185 MPH.