Monday April 12, 2010
click here to download today's notes in a more printer friendly format.

A failed attempt to show some bicycle racing before class today.  I'll try again on Wednesday.  The video shows part of a stage from the 2000 Tour de France up the infamous Mont Ventoux.  I hoping to go there with my own bicycle this coming summer.

Grade summaries were handed out in class today.  You'll find some discussion of this at the end of today's notes.

I think we started by finishing up the last couple of pages from the handout distributed in class last Friday.  Specifically we looked at why surface winds blow across the contour line toward low pressure (upper level winds blow parallel to the contour lines).


The top figure shows upper level winds blowing parallel to straight contours.  The PGF and CF point in opposite directions and have the same strength.  The net force is zero.  The winds would blow in a straight line at constant speed.

We add friction in the second picture.  It points in a direction opposite the wind and can only slow the wind down.  The strength of the frictional force depends on wind speed (no frictional force if the wind is calm) and the surface the wind is blowing over (less friction over the ocean than when the wind is blowing over the land).

Slowing the wind weakens the CF and it can no longer balance the PGF (3rd figure).  The stronger PGF causes the wind to turn and blow across the contours toward Low.  This is shown in the 4th figure.  Eventually the CF and Frictional force, working together, can balance out the PGF.

Now the transition from the straight contours above to the circular contours below might be a little abrupt.  But if you zero in on a very small part of a larger circular pattern the contours look straight.  The important thing to remember is that surface winds will always blow across the contours toward low. 


The winds are spiralling inward in the top and bottom examples (1 and 3).  These must be surface centers of low pressure.  The winds are spiraling outward from the centers of high pressure (2 and 4).

Now you probably don't want to figure out which of these are northern and which are southern hemisphere pictures.  It is probably best to remember one of the pictures.  Remember in 1, for example, that surface winds spin counterclockwise and spiral inward around centers of low pressure in the northern hemisphere (something we learned early in the semester).  Then remember that winds spin in the other direction and blow outward around high pressure in the northern hemisphere (2).  The spinning directions of the winds reverse when you move from the northern to the southern hemisphere.  Thus you find clockwise spinning winds and inward motion around low pressure (3) and counterclockwise and outward spiraling winds around high pressure in the southern hemisphere.

Converging winds cause air to rise.  Rising air expands and cools and can cause clouds to form.  Clouds and stormy weather are associated with surface low pressure in both hemispheres.  Diverging winds created sinking wind motions and result in clear skies.

Next we had a short look at the cause of the Coriolis force.  Most of what follows can be found on p. 122c in the photocopied ClassNotes.

Imagine something flies over Tucson.  It travels straight from west to east at constant speed.  The next figure shows the path that the object followed as it passed over the city.  You would, more or less subconciously,  plot its path relative to
reference points on the ground.



It would appear to be moving in a straight line at constant speed.  You would conclude there was zero net force acting on the moving object (Newton's first law of motion).


In this second picture the object flies by overhead just as it did in the previous picture.  In this picture, however, the ground is moving (don't worry about what might be causing the ground to move).


This is the path that you would see relative to the ground in this case.  Even though the object flew from west to east it appears to have been traveling from the NW toward the SE because the ground was moving as the object passed overhead.  Because the motion is still in a straight line at constant speed, you would conclude the net force acting on the object was zero.


In this last figure the object flies by again from west to east.  In this case however the ground is rotating.

Now the path of the object plotted on the ground appears to be curved.  If you ignore the fact that the ground is moving then there must have been a force causing the moving object to follow the curved path.  The needed force would be perpendicular to the direction of motion and to the right in this case.

At most locations on the earth the ground IS rotating (we're just not aware of it).  This is most easily seen at the poles.

Imagine a piece of paper glued to the top of a globe.  As the globe spins the piece of paper will rotate.  A piece of paper glued to the globe at the equator won't spin, it will flip over.  At points in between the paper would spin and flip, the motion gets complicated.

The easiest thing for us to do is to ignore the fact that the ground on which we are standing is rotating.  However, if we do that we need to account for the curved paths that moving objects will take when they move relative to the earth's surface.  That is what the Coriolis force does.

It seemed appropriate at this point to look at a common misconception involving the Coriolis force.  You might already have heard that water spins in a different direction when it drains from a sink or a toilet bowl in the southern hemisphere than it does in the northern hemisphere.  You might also have heard that this is due to the Coriolis force or the Coriolis effect. 

The Coriolis force does cause winds to spin in opposite directions around high and low pressure centers in the northern and southern hemisphere.  The PGF starts the air moving (in toward low, out and away from high pressure) then the Coriolis force bends the wind to the right (N. hemisphere) or to the left (S. hemisphere).
Here's what you end up with in the case of low pressure (you'll find these figures on p. 130 in the photocopied ClassNotes):



Air starts to move inward toward low pressure.  Then the Coriolis force causes it to turn to the right or left depending on which hemisphere you're in.  You should be able to identify the northern hemisphere and the southern hemisphere picture above.




The same kind of idea applies to high pressure except that the air starts moving outward.  The Coriolis force then turns it to the right or left.

There are situations where the PGF is much stronger than the CF and the CF can be ignored.  A tornado is an example.  Winds can blow around Low pressure because the PGF points inward.


The wind can spin in either direction in either hemisphere.


 Without the CF winds can't spin around High pressure because there is nothing to provide the needed inward force.


What about water draining from sinks, buckets, toilets etc.


There's just an inward pointing PGF, no CF.  Water can spin in either direction in either hemisphere.

Now we watched a short video segment that seemed to show otherwise.  Don't believe everything you see on video.  The gentleman in the video, who apparently makes a living demonstrating the Coriolis effect, was just very good at getting the draining water to spin one direction or another as he moved on opposite sides of the equator.  Probably the most difficult part would be to get the water draining without spinning, which is what he was able to do when standing right on the equator.

Also, the CF is zero at the Equator.  You would have to move a 100 miles or more to one side or the other before the CF becomes significant.  The CF is zero at the Equator and is still zero a few to one side or the other of the Equator.


Here is one of my favorite optional assignments of the semester.
Finally here is an example of the grade summaries that were handed out in class today.  The grade summaries will give you a pretty accurate idea of how you're doing in this class and will allow you to check to be sure the grade information recorded for you is correct.  The numbers on the grade summary below are averages for this section of the class.

1. 
The scores you have received on each of this semester's quizzes and the percentage grades. 
2. 
The total number of extra credit points you have earned on the optional assignments.
3.
The score you received on an experiment/book/scientific paper report.  A zero means you haven't turn one in or it hasn't been graded yet.  Even if you haven't turn in a report, an average grade was used by the computer to show the effect that the writing grade has on your overall average.  If you don't turn in a report by the end of the semester, you will receive a zero and that will have a damaging effect on your overall average.
4. 
This shows the number of 1S1P pts you have earned so far.  This includes all of the Bonus Assignments and Assignment #1.  Any Assignment #2 reports you may have turned in haven't been graded yet and aren't included in this total.

5.
The writing percentage grade is determined using the experiment report and 1S1P reports points totals.  This is averaged together with your quizzes to determine your overall average.

6.
This is your overall average without any quiz grades dropped.  This is the grade that must be 90.0 or above at the end of the semester in order to not have to take the final exam.

7.
This is your overall average grade with the lowest quiz score dropped.  At the end of the semester this grade together with your final exam grade will be used to determine the grade you receive in the class.