Final Day and Reflection

The last day of our trip included a third and final water quality test of the Greenbrier River and a tour of a railroad museum in Clifton, Virginia.
The water testing indicated the water quality was "good" for all three locations of the Greenbrier River.  These tests were uniform in what was tested:  temperature, dissolved oxygen, turbidity, conductivity, and pH.
The tour of the C&O Railroad Museum in Clifton, Virginia was both informative and very enjoyable.  The staff were extremely helpful and even gave us a ride on a model train.

In the end, I hope this blog helps to serve us in our classroom.  The friends and experiences of the week will continue to play a role in our ongoing discussions.  Moreover, this blog was an attempt on my part to relate each of the major concept areas we cover to the experiences of the of this project.  Most physics texts cover Motion, Forces, Work and Energy, Momentum and Collisions, Impulses, Thermodynamics, Fluid Mechanics, Rotational Mechanics, Waves and Optics, Electrcity, Magnetism, and Modern Physics.  Of these, only Magnetism was not addressed through my experiences with this project and discussed in a blog entry; I alone bear the burden for not having it addressed.
I hope you have enjoyed this experience as much as I have.  I do look forward to our continued collaboration, for this good luck it's not good-bye.

The Mountains of West Virginia and Pascal's Principle

Some of the most memorable experiences of our trip were the breathtaking views at higher elevations.  We visited Bald Knob and Gaudineer Knob; both views were something to behold with respective elevations of roughly 4800 feet and 4430 feet above see level.  These views were remarkable, and the physics we can derive from them is paramount to developing a better understanding of fluid mechanics.  Specifically, we will entertain Pascal's Principle.
Pascal's Principle is usually stated as the pressure in a fluid is transmitted undiminished throughout the fluid.  Yet, this also tells us that the height or depth within the fluid also determines the absolute pressure exerted.  Quantitatively, this is written as P = «P» + pgh:  Pressure is equal to atmospheric pressure plus density of the fluid times gravity times height.  This height element is why our ears "pop" when ascending or descending heights quickly.  Our bodies are attmepting to equalize the pressure inside our body with the surroundings.  The trip up to Bald Knob was on a Shay Locomotive and took close to an hour and a half for a distance of eleven miles.  This rate of ascension was gradual and did not cause my ears to "pop, as they did when driving up to Cathedral State Park.
Here are a couple of questions to consider, each having its answer within the noted equation above:
1.  Why are there fewer air molecules with an increase in height?
2.  From the equation, why would "going down" equate to an increase in pressure?

Water Quality Testing and Archimedes Principle

Our group conducted water quality tests in the Greenbrier River today.  These tests included dissolved oxygen, conductivity, total dissolved solids and pH.  A fellow teacher made the mistake of asking why certain a rock would sink but a "larger" piece of wood would float; physics to the rescue.
Remember folks that fluid dynamics plays an important part of our daily life.  And for you AP students, fluid dynamics accounts for roughly 12% of the AP Physics B exam.  As such, let us entertain one of the key concepts of this study.
Archimedes principle simply states that an object is buoyed up by a force equal to the weight of the fluid it displaces.  Quantitatively this can be written as Fb = mgf (force buoyancy is equal to mass times gravity of displaced fluid).  However, we should remember that mass is equal to density times volume.  Thus, we can think of the buoyant force as being equal to the density of the fluid times gravity times volume.  The force the object applies downward is equal its mass times gravity (mg).  If the object floats, the buoyant force must be equal to the weight of the object (mg).  We can set theses forces equal and the density substitution and arrive at this: 
volume fluid     density of obj
___________  = ________________
volume obj       density of fluid
This equation will serve you well, as test writers routinely will as you to determine the volume of the object submerged.  It is equal to the volume of the dispaced fluid represented in this equation; I assure you this will be asked.  Let' see an example of what to expect.
A wooden cube  with a density of 650 kg/m^3 floats in fresh water.  If an edge of the cube is 200 cm, what level or height of the cube is submerged?
Wood clearly floats well due to its density.  It is no wonder most of us have seen logs travelling by way of water.  And, its nothing more than a little physics making our lives easier.

Shay 11 and Newton's 2nd Law

Our group had a wonderful experience today.  We rode a Shay Steam Locomotive to the top of Bald Knob, elevation 4730 feet.  One the more interesting physics concepts that jumped out at me was the instances when the train would begin its motion and come to a rest. 

With some scrutiny, you could recognize the coupling between the cars and hear a "clank, clank, clank" when starting and stopping.  This brought to my mind the essence of the great. Isaac Newton and his 2nd Law of Motion.  We are most certainly familiar with the notion that F=ma.  Yet, I think it is imporant to remind ourselves that this not exactly what Newton said in his masterpiece Principia.  More precisely he said that the sum of the impulses acting on a body is equal to the net change in the bodies momentum. We of course quantify this as F delta t = delta p.  This change in momentum for a train of course must huge, as mass is being increased with each additional car and with a change in the velocity.  The key to this is really a term we use often and is in our equation.  It begins with "t" and rhymes with "ime"; yes, it is time, time, time. 

A force applied during a greater period of time will equal a greater change in momentum and this is what is needed to start or or stop.  So, the next time you hear a train go "clank, clank, clank" I want you to think Newton and his 2nd Law of Motion.

Here is a sample. If a train with a weight of 800 tons wants to achieve a velocity of 10 km/hr, how much time must be allowed if the maximum tractive force of 16000 Newtons?  Mind your conversion and remember what weight is.

Colonial Millworks and the Physics of a Laser

Today we visited Colonial Millworks in Beverly, West Virginia.  This plant focused its energy on floor mouldings and cabinet mouldings.  Though the plant revealed many physics concepts we will encounter in class, there was one concept that caught my attention more so than the traditional mechanics applications we would typically discuss - LASER.  Yes friends, the plant incorporates lasers at various saw-stations for alignment in the process of making the most accurate cut.  But, what really is a laser?

LASER is an acronym which stands for Light Amplification by Stimulated Emmission of Radiation.  If an atom absorbs energy it will enter an excited state.  The atom, however is like most thinks in nature and desperatly wants to stay in comfortable equilibrium and so return to its natural ground state.  To do this, it will emmit light energy in the form of a photon. We should remember from chemistry that the energy of a photon is equal to Planck's Contant times the frequency of the photon:  E = hv.  A laser plays on this emmission of energy.

Stimulated emmission of a photon is the essence of what we "see" as a laser.  When an emmitted photon strikes an atom in an excited state (absorbed energy) two photons can be released to strike two more excited atoms.  This process can continue to grow and replicate itself.  It is important to note that these photons are all in phase; they have the same wavelength and frequency causing a large amplification of the light/radiation, and now we have a laser.  Since they do have the same wavelength and frequency the laser appears monochromatic or of only one color; this will usually be red or green like the lasers seen at Colonial Mills. 

A point of interest is the timing of this blog post.  I just received an email last night from a friend who pointed me to a story where at Lawrence Livermoore a new laser generated 500 terawatts which would be about 1000 times more power than the entire US would use at any given moment.  It also generated 1.85 megajoules of enegy; this is 100 times more than any previous laser. The scientist are attempting to use the laser to master clean nuclear fusion which would solve all future energy problems; it takes an enormous amount of energy to overcome the repulsive force between positive nuclei.

So, from trying to solve our dependency on fossil fuels, to making sure your cabinets line up correctly, physics is constantly changing the world in which we live.  Can you think of any other applications of a laser?  I think you will be surprised just how dependent we are on Light Amplification by Stimulated Emmission of Radiation.

Physics at Hamer Pellet Fuel

This morning we visited Hamer Pellet Fuel in Elkins, West Virginia.  This facility solely produces wood pellets common for wood pellet stoves.  This was an excellent opportunity to see several of the physics concepts we examine in application.

Let's begin by examining the blue cylinder seen in the picture section which turns and helps dry the saw dust used in the making process.  Our guide informed us the drum cylnder weighs approximately 110,000 lbs.  The estimated radius of the cylinder is 20 ft.  If the cylinder has an angular speed of 1.57 radians per second.  This speed must be maintained in order to complete the drying process.  The cylinder is rotated by four trunion wheels.  What total torque does the cylinder experience due to the rotating trunion wheels? This is an AP level question folks.  Remember to think of how we define torque.  The moment of inertia (I) for the cylinder is given by I = 1/2MR^2.

Now let us look at the dreaded incline plane. The picture section shows an incline with rollers used to move pallets loaded with bagged pellets at a weight of two thousand lbs.  With angle of the incline being rougly 15 degrees what is the final velocity of the pallet if it takes four seconds to move down the incline? The pallet is at rest initially.  The operators are using the incline, gravity, the pallets own mass and the rollers (eliminate friction) to move the pallet unassisted over a specific distance where the pallet is picked up by a forklift and deposited elsewhere. No man, no electical or computerized element are used.  Only a simple machine and physics.

Day One of Trip

Greetings folks!  Today was the first day of our excursion throughout West Virginia studying the timber and rail industries.  We spent the bulk of our time at Cathedral State Park. 

This is a remarkable sight which is in fact considered virgin timber; it has never had an ax brought against it.  Specifically, this area is predominantly composed of Hemlock.  Hemlock is an Evergreen tree that grows between 18 and 21 meters in height and makes its habitat in soils that are acidic; this is described as having a pH (Power of Hydrogen) below 7; alkaline describes a pH level above 7.  The numerical values can be determined by the equation pH = -log 10base [H+]. Qualitatively, pH canbe desribed as the molar concentration of hydrogen ions present.  The insturment typically used for this test consists of a a wire coated in silver chloride within a diluted hydrocloric acid solution surrounded by a glass membrane.  This membrane seperates the solution from what is being tested and determines the potential devoloped across the glass.  This can be shown to be proportional to the hydrogen ion concentration on the two surfaces.  Soil sample tests were conducted using a Vernier Labquest and were confirmed at a pH of roughly 4.1.

In addition to soil testing with pH confirmation, we worked in teams to determine the board feet of a tree.  Board feet is an industry term which estimates the amount of "usable" wood from a tree.  This proces includes using basic geometry and angle studies to determine the volume of a tree.  Volume is equal to area  times height.  We found the area by measuring the circumferene of the tree and used this to determine the radius.  With the radius known the area at chest level was determined.  A clinometer and the tangent function of the corresponding angle made and a distance of 66 feet from the tree were used to calculate the height.  The tree we measured was estimated at 1441 board feet.

This was a great first day.  Actually seeing a sight that had never been logged was exciting.  Yet, what struck me the most was the acid level of the soil and lack of life therein.  There really was not much living in this area aside from specific trees, mostly Hemlock, and ferns.  Cellular functions can only take within certain pH parameters and my best hypothesis is that a combination of reduced sun, a major canopy exists here, and acidic soil make this ecosystem limited in the number and types  of species it can sustain.

Take care, and I will bring you up to date on day two tomorrow.