Mon., Jan. 22, 2007

The first Optional (Extra Credit) Homework Assignment was handed out today.  It will be due at the beginning of class next Monday (Jan. 29).  Optional assignments should be ready to be turned in when you come to class.  Don't let the instructor see you finishing an optional assignment or working with a friend in the last few minutes before the start of class (he is likely to take your unfinished assignment and that of your friend and give you either partial credit or no credit at all).

The first 1S1P Assignment was also made.  Those reports are due in two weeks on Monday, Feb. 5.
A steel bar was passed around class.  You were supposed to guess how much it weighed. 

The answer to the question about the bar's weight will relate to something covered later in the class period today.

Before we can learn about atmospheric pressure, we need to review the terms mass and weight.  In some textbooks you'll find mass defined at the "amount of stuff."  Other books will define mass as inertia or as resistance to change in motion.  The next picture illustrates both these definitions.  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).


It is possible to have two objects with the same volume but very different masses.  Here's an example:


Bottles containing equal volumes of water and mercury were passed around in class (thanks for being careful with the bottles of mercury).  The bottle of mercury was quite a bit heavier than the bottle of water.


Weight is a force and depends on both the mass of an object and the strength of gravity. 

We tend to use weight and mass interchangeably because we spend all our lives on earth where gravity never changes. 


  Any three objects that all have the same mass would necessarily have the same weight.  Conversely

Three objects with the same weight would have the same mass.

The difference between mass and weight is clearer (perhaps) if you compare the situation on the earth and on the moon.

If you carry an object from the earth to the moon, the mass remains the same (its the same object, the same amount of stuff) but the weight changes because gravity on the moon is weaker than on the earth.

Here's a little detour we took concerning values and units of weight of someone on the earth and on the moon.


(1) The course instructor weighs about 160 pounds (after putting on a little weight over the winter).  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.
Now back to the bottles of water and mercury.

Mercury atoms are built up of many more protons and neutrons than a water molecule (also more electrons but they don't have nearly as much mass as protons and neutrons).  The mercury atoms have 11.1 times as much mass as the water molecule.  This doesn't quite account for the 13.6 difference in density.  Despite the fact that they contain more protons and neutrons, the mercury atoms must also be packed closer together than the molecules in water.


Definition and illustrations of high and low density.


This ended up being a very busy figure.  Basically the air that surrounds the earth has mass.  Gravity pulls downward on the atmosphere giving it weight.  Galileo proved that air has weight using the following demonstration.

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 (the same as the steel bar passed around in class).  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).

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, 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.
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 .
Down at the bottom of the page are the Metric and English units of mass and weight.