Wednesday Jan. 27, 2016

Mariachi Flor de Toloache NPR Music Tiny Desk Concert (20:28).  "Let Down" (0:00 - ~5:00), "Dicen" (5:15 - 9:30), "Blue Skies" (9:30 - 11:10 - 15:30), "Guadalajara" (16:00 - 20:00)

 Mass, weight, density, and pressure.

Weight is something you can feel.  I'll pass an iron bar around in class (it's sketched below) - try to guess or estimate 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 than 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 be very expensive.  So this semester I'll pass around a smaller, much safer, sample of mercury so that you can at least see what 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 carefully.  That is something we'll mention again later in the class.

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 (there are a total of 7) to help with organization.  There's also a summary at the end of today's notes.

1. weight
This is a good place to start because we are most familiar with this term.  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.  A student mentioned 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




Grams (g) and kilograms (kg) are commonly used units of mass (1 kg is 1000 g).

3.  gravitational acceleration
On the surface on 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 I feel they should be available 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, 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.



Any idea what the English units for mass and the Metric units for weight (force) are?   "Slugs" if you can believe it are the English units for mass.  The metric units for weight (force) are dynes (if mass is in grams) or Newtons (for mass in kilograms)


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

I wish I could 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 we were in outer space with the three wrapped blocks of lead, wood, and brick.  They'd be weightless.
Could we 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 didn't mention it in class, but this concept of inertia comes from Newton's 2nd law of motion
F = m a
F is force, m is mass, and a is 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.  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).  The experiment wasn't mentioned in class.







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, 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 the weight by the area it 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 p. 24 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 most meteorologists use.


Typical sea level pressure is 14.7 psi or about 1000 millibars (the units used by meteorologists and the units that we will use in this class most of the time) or about 30 inches of mercury.    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.

Inches of mercury refers to the reading on a mercury barometer.  This seems like unusual units for pressure.  But if you remember the chart earlier, Mercury (13.6 grams/cm3)  is denser than steel ( about 7.9 grams/cm3 ).  If we could some how construct a 1" x 1" bar of mercury it would only need to be 30 inches long to equal the weight or the iron bar or the weight of a tall column of air.




Each of these columns would weigh 14.7 pounds.  The pressure at the base of each would be the same. 

A mercury barometer is, we'll find, just a balance. 
You balance the weight of a very tall column of air with the weight of a much shorter column of (liquid) mercury.

 This is as far as we got in class today.  I was worried that we wouldn't finish all of this material but we did and actually finished a little early. 

As promised, here's a short summary of the main points from the mass, weight, density, and pressure section.