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.