Wednesday, Jan. 23, 2019

Sia: "California Dreamin' " (3:37), "Chandelier" (4:14), "Chandelier" (4:05), "Midnight Decisions" (3:44), "Breathe Me" (4:55),  "The Girl You Lost to Cocaine" (3:58)

We'll be using page 23a, page 23b, page 23c, page 23d, page 24a, and perhaps page 29 today from the ClassNotes.

An Optional (Extra Credit) Assignment was handed out in class today and collected at the end of class.  If you weren't in class, you can download the assignment and turn it in at the beginning of class on Friday.

Mass, weight, density, and pressure.

Pressure is a pretty important concept, that's what we'll be working on today.   Differences in atmospheric pressure create winds which can then cause storms.  To better understand pressure we need to first review mass and weight.

 Weight is something you can feel.  I'll pass an iron bar around in class (it's sketched below) - lift it and try to guess it's weight.  The fact that it is a 1" by 1" is significant.  More about the bar later in today's notes.


I used to pass around a couple of small plastic bottles (see below).  One contained some water, the other an equal volume of mercury (here's the source of the nice photo of liquid mercury below at right).  I wanted you to appreciate how much heavier and denser mercury is compared to water.   But the plastic bottles have a way of getting brittle with time and if the mercury were to spill in the classroom the hazardous material people would need to come in and clean it up.  That would probably take a few days, would be very expensive, and I would get into a lot of trouble.  So this semester I'll pass around a smaller, much safer, sample of mercury so that you can at least see what mercury it looks like (it's a recent purchase from a company in London).  I'll keep the plastic bottles of mercury up at the front of the room just in case you want to see how heavy the stuff is.


It isn't so much the liquid mercury that is a hazard, but rather the mercury vapor.  Mercury vapor is used in fluorescent bulbs (including the new energy efficient CFL bulbs) which is why they need to be disposed of properly (you shouldn't just throw them in the dumpster).  That is a topic that will come up again later in the class.  Mercury and bromine are the only two elements that are found naturally in liquid form.  All the other elements are either gases or solids.

I am hoping that you will remember and understand the following statement


atmospheric pressure at any level in the atmosphere
depends on (is determined by)
the weight of the air overhead


We'll first review the concepts of mass, weight, and density but understanding pressure is our main goal.  I've numbered the various sections  to help with organization.  There's a summary at the end of today's notes.

1. weight
This is a good place to start because this is something we are pretty familiar with.  We can feel weight and we routinely measure weight.
 
 


A person's weight also depends on something else.


In outer space away from the pull of the earth's gravity people are weightless.  Weight depends on the person and on the pull of gravity.


 



We measure weight all the time.  What units do we use?  Usually pounds, but sometimes ounces or maybe tons.  Students sometimes mention Newtons, those are metric units of weight (force).

2. mass
Rather than just saying the amount of something it is probably better to use the word mass




It would be possible to have equal volumes of different materials or the same total number of atoms or molecules of two different materials, and still have different masses.

Grams (g) and kilograms (kg) are commonly used units of mass (1 kg is 1000 g).  They're metric units (slugs are the units of mass in the English (American) system of units).

3.  gravitational acceleration
On the surface of the earth, weight is mass times a constant, g,  known as the gravitational acceleration.  The value of g is what tells us about the strength of gravity on the earth; it is determined by the size and mass of the earth.  On another planet the value of g would be different.  If you click here you'll find a little (actually a lot) more information about Newton's Law of Universal Gravitation.  You'll see how the value of g is determined and why it is called the gravitational acceleration.  These aren't details you need to worry about but they're there just in case you're curious.
Here's a question to test your understanding.



The masses are all the same.  On the earth's surface the masses would all be multiplied by the same value of g.  The weights would all be equal.  If all 3 objects had a mass of 1 kg, they'd all have a weight of 2.2 pounds.  That's why we can use kilograms and pounds interchangeably.

The following figure show a situation where two objects with the same mass would have different weights.


On the earth a brick has a mass of about 2.3 kg and weighs 5 pounds.  If you were to travel to the moon the mass of the brick wouldn't change (it's the same brick, the same amount of stuff).  Gravity on the moon is weaker (about 6 times weaker) than on the earth because the moon is smaller and it has less mass, the value of g on the moon is different than on the earth.  The brick would only weigh 0.8 pounds on the moon.  The brick would weigh almost 12 pounds on the surface on Jupiter where gravity is stronger than on the earth.  On the moon, a brick would have the same mass, the same volume, the same density, but a different weight as(than) it would on the earth.



The three objects below were not passed around class (one of them is pretty heavy).  The three objects all have about the same volumes.  One is a piece of wood, another a brick, and the third is something else. 





The easiest way to determine which is which is to lift each one.  One of them weighed about 1 pound (wood), the 2nd about 5 pounds (a brick) and the last one was 15 pounds (a block of lead).

The point of all this was to get you thinking about density.  Here we had three objects of about the same size with very different weights.  Different weights means the objects have different masses (since weight depends on mass).   The three different masses, were squeezed into roughly the same volume producing objects of very different densities. 

4. density






The brick is in the back, the lead on the left, and the piece of wood (redwood) on the right.

The wood is less dense than water (see the table below) and will float when thrown in water.  The brick and the lead are denser than water and would sink in water.
We'll be more concerned with air in this class than wood, brick, or lead.
In the first example below we have two equal volumes of air but the amount (mass) of air squeezed into each volume is different (the dots represent air molecules). 



The amounts of air (the masses) in the second example are the same but the volumes are different.  The left example with air squeezed into a smaller volume has the higher density.
material
 density g/cc
air
 0.001
redwood
 0.45
water
 1.0
iron
 7.9
lead
 11.3
mercury
 13.6
gold
 19.3
platinum
 21.4
iridium
 22.4
osmium
 22.6


g/cc = grams per cubic centimeter
cubic centimeters are units of volume - one cubic centimeter is about the size of a sugar cube
1 cubic centimeter is also 1 milliliter (mL)

I would sure like to get my hands on a brick-size piece of iridium or osmium just to be able to feel how heavy it would be - it's about 2 times denser than lead.

Here's a more subtle concept.  What if you were in outer space with the three wrapped blocks of lead, wood, and brick?  They'd be weightless.
Could you tell them apart then?  They would still have very different densities and masses but we wouldn't be able to feel how heavy they were.

5. inertia






I think the following illustration will help you to understand inertia.






Two stopped cars.  They are the same size except one is made of wood and the other of lead.  Which would be hardest to get moving (a stopped car resists being put into motion).  It would take considerable force to get the lead car going.  Once the cars are moving they resist a change in that motion.  The lead car would be much harder to slow down and stop.

This is the way you could try to distinguish between blocks of lead, wood, and brick in outer space.  Give them each a push.  The wood would begin moving more rapidly than the block of lead even if  both are given the same strength push.

I usually don't mention in class that this concept of inertia comes from Newton's 2nd law of motion
F = m a
force = mass x acceleration

We can rewrite the equation
a = F/m

This shows cause and effect more clearly.  If you exert a force (cause) on an object it will accelerate (effect).  Acceleration can be a change in speed or a change in direction (or both).  Because the mass is in the denominator, the acceleration will be less when mass (inertia) is large.



Here's where we're at


From left to right the brick, the iron bar, the piece of wood, and the lead block. They're all standing on end.   The weight of the iron bar is still unknown.

Now we're close to being ready to define (and hopefully understand) pressure.  It's a pretty important concept.  A lot of what happens in the atmosphere is caused by pressure differences.  Pressure differences cause wind.  Large pressure differences (such as you might find in a tornado or a hurricane) can create strong and destructive storms.


The air that surrounds the earth has mass.  Gravity pulls downward on the atmosphere giving it weight.  Galileo conducted a simple experiment to prove that air has weight (in the 1600s).






We could add a very tall 1 inch x 1 inch column of air to the picture.  Other than being a gas, being invisible, and having much lower density, it's really no different from the other objects.

 
6. pressure



Atmospheric pressure at any level in the atmosphere
depends on (is determined by)
the weight of the air overhead 

This is one way, a sort of large scale, atmosphere size scale, way of understanding air pressure.

Pressure depends on, is determined by, the weight of the air overhead.  To determine the pressure you need to divide by the area the weight is resting on.
 
and here we'll apply the definition to a column of air stretching from sea level to the top of the atmosphere (the figure below is on page 23d in the ClassNotes)


Pressure is defined as force divided by area.  Atmospheric pressure is the weight of the air column divided by the area at the bottom of the column (as illustrated above). 

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.  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).

Now back to the iron bar.  The bar actually weighs 14.7 pounds (many people I suspect think it's heavier than that).  When you stand the bar on end, the pressure at the bottom would be 14.7 psi.




The weight of the 52 inch long 1" x 1" steel bar is the same as a 1" x 1" column of air that extends from sea level to the top of the atmosphere 100 or 200 miles (or more) high.  The pressure at the bottom of both would be 14.7 psi.

7. pressure units

Pounds per square inch, psi, are perfectly good pressure units, but they aren't the ones that meteorologists use most of the time.


Typical sea level pressure is 14.7 psi or about 1000 millibars (the units used by meteorologists and the units that we will probably mostly use in this class) or about 30 inches of mercury (refers to the reading on a mercury barometer).    Milli means 1/1000 th.  So 1000 millibars is the same as 1 bar.  You sometimes see typical sea level pressure written as 1 atmosphere.


Summary


Average and record setting sea level pressure values

Sea level pressure averages about 1000 mb but it changes and can be higher or lower than that.

The simple figure above at left contains just the essential information.  Focus on and try to remember that.  A lot more information and details have been added to the figure at right.

Sea level pressure values usually fall between 950 mb and 1050 mb.

Record HIGH level sea pressure values occur during cold winter weather.  The TV weather forecast will often associate hot weather with high pressure.  This might seem contradictory but they are generally referring to upper level high pressure (high pressure at some level above the ground) rather than surface pressure.  You'll sometimes hear this upper level high pressure referred to as a ridge, we'll learn more about this later in the semester.

Record setting LOW sea level pressure values are found in the centers of strong hurricanes. 

Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic, 882 mb.  Hurricane Katrina earlier in the same year had a pressure of 902 mb.  The table below lists some information on intense hurricanes.  2005 was a very unusual year, 3 of the 10 strongest N. Atlantic hurricanes ever occurred in 2005.  There were also a record number of Atlantic hurricanes in 2005.  The strongest Atlantic hurricanes from 2017 have been added.  2017 was the costliest hurricane season on record in the United States and the deadliest since 2005.

Hurricane Patricia off the west coast of Mexico in fall 2015 set a new surface low pressure record for the Western Hemisphere - 872 mb and very close to the world record.  Sustained winds of 200 MPH were observed in that storm. 


Most Intense North Atlantic Hurricanes
 Most Intense Hurricanes
to hit the US Mainland
Wilma (2005) 882 mb
Gilbert (1988) 888 mb
1935 Labor Day 892 mb
Rita (2005) 895 mb
Allen (1980) 899
Katrina (2005) 902
 1935 Labor Day 892 mb
Camille (1969) 909 mb
Katrina (2005) 920 mb
Andrew (1992) 922 mb
1886 Indianola (Tx) 925 mb

strong 2017 hurricanes
Harvey 937 mb
Irma 914 mb
Jose 938 mb
Maria 908 mb


What makes hurricane winds so strong is the pressure gradient, i.e. how quickly pressure changes with distance (horizontal distance).  Pressure can drop from near average values (1000 mb) at the edges of the storm to the low values shown above at the center of the storm.

Low pressure is also found in the centers of tornadoes.  A surface pressure value of 850 mb was measured in 2003 inside a strong tornado in Manchester, South Dakota (https://www.weather.gov/fsd/20030624-tornadosamaras).  This is a very difficult (and very dangerous) thing to try to do.  Not only must the instruments be built to survive a tornado but they must also be placed on the ground ahead of an approaching tornado and the tornado must then pass over the instruments (also the person placing the instrument needs to get out of the way of the approaching tornado).

You can experience pressure values much lower than that (roughly 700 mb) by simply driving up to Mt. Lemmon.  Pressure changes much more quickly if you move vertically in the atmosphere than if you move sideways.  Very strong vertical changes in pressure are usually almost balanced exactly by gravity.