Our last discussion entertained expansion of steel rails for a railroad due to the addition of heat. So did our railroad engineer design the rail system correctly, or does this person need a refresher in physics? Well, there was 2.5 millimeters between the rails. Unfortunately, the linear expansion for the steel used was given at 1.2*10^-5 C^-1 and the original length of the rails were 12 meters long. A 50 degree change in temperature could lead to linear expansion of .0072 meters or 7.2 millimeters; our engineer may have just cost his company quite a bit of money and should probably look forward to a physics refresher.
Monday, July 9, 2012
Thursday, June 14, 2012
Thermodynamics, Railroading and Linear Expansion
My last post entertained briefly the First Law of Thermodynamics. Such a concept permeates most all systems including what is often referred to as a closed system. Within a closed system, matter can not cross a set boundary - enter or leave. Most textbooks refer only to energy as being able to cross the set boundary within a closed system. We demonstrated from earlier posts that work and energy were in fact synonomous, and as such, we can include work as being able to cross the set boundary of the system; this validates both th qualitative and quantitative definitions of the law: 1. conservation of energy; 2. delta U= Q-W - change in internal energy is equal to energy/heat added to the system minus the work done on the system. Let's discuss why most solids expand when energy/heat is added.
As a child, I can remember my grandmother running hot water over the lids of jars to help open them. This practice is based on the concept of linear expansion. When energy/heat is added to most solids the molecules of the material speed up their interactions, push outward and the solid expands. Quantitatively, and from a linear perspective, this is given by delta L = «a»L delta T - change in length is equal to the coefficient of linear expansion times the original length times the change in temperature. This «a» or coefficient of linear expansion will almost always be given in a stated problem. For a good list of coefficients of this type you can go to www.engineeringtoolbox.com and search for coefficient of linear expansion for materials. Here is a railroad example.
You are reviewing some specifications on a newly constructed railroad. As you are examining the 12 meter long rails, you notice there is 2.5 millimeter gap between the rails. The coefficient of linear expansion for the steel used in the rail is 1.2*10^-5 C^-1; the units for coefficient of linear expansion are 1/C or C^-1. You check the almanac and find that the normal temperature can increase as much as 50 degrees Celsius on a hot day. Did the chief engineer wisely design the rail system or should he retake high school physics?
Next time, we will.check the answer to this and tackle some other thermodynamic issues with rail transport.
Monday, June 4, 2012
Clearcutting Controversy
Here is a link to an interesting article from Clemson University which discusses the controversy surrounding clearcutting. As with most pursuits of humankind, rarely if ever can we deal in absolutes.
Tree Identification
Tree identification will be an important part our project. I have chosen to link to a business named Industrial Timber and Lumber. This group has several locations. Yet, what pulled me to them was that they have two major sawmill operations in Vinton County, Ohio only about 45 minutes from my home, and a huge kiln drying operation in Marlington, WV. I believe this is close to Elkins, WV. I plan on visiting the sawmills
inthe next few days and hope we can stop at the Marlington location during our trip.
Their site offers great deal of information on various species. This includes tree identification by leaf, charted information about relative working properties for each wood, sample grade photos, and an overview of each species. Incidently, information about each location's production offers some good insight into the productivity of our region.
First Law of Thermodynamics and Steam Locomotives
Recently, we have discussed work and energy concepts. Let us now build upon those concepts within a basic steam locomotive.
We know from previous posts that there is more than one way to define work. I am going to now offer another definition. Work equals force times distance - W=Fd, is our most common definition. We also know this is equal to a change in energy. Yet, if we consider pressure is equal to force divided by area - P=F/A, a common concept learned at least by middle school. An easy manipulation tells us that F=PA. Substituting this into our equation yields work equals pressure times area times distance - W=PAd. But, area times distance is a definition of volume. So work is equal to pressure times a change in volume - W=PdeltaV. This concept of changing volume at constant pressure to move a piston is precisely the mechanism behind basic steam locomotive operation and owes its origination to the 1st Law of Thermodynamics; the change in the internal energy of a system is equal to the heat added to a system minus the work done on the system - delta U=Q- W.
Our locomotive burns coal or oil to heat water. The water eventually changes to high pressure steam which increases its volume and expands pushing a piston within a cylnder. This explains why locomotives must take on water periodically as its water supply is constantly be turned to steam. The piston is connected to a rod apparatus which connects to coupling rods which move the wheels. Incidently, the steam exaust is simply released by a valve under great pressure which accounts for the "choo choo choo choo" we hear and, the piston returns to its original position ready to be pushed again by pressure and volume expansion.
We now should begin to recognize some basic relationships among work, energy, power, and force with a locomotive.
Tuesday, May 22, 2012
Energy Follow-Up
My good friend Steve Beckelhimer posed an interesting question as to whether I could relate a problem on the energy concept I spoke of last time to rail and timber transport. Absolutely! If we consider a train in motion on a track, an important engineering principle is continuous tractive force. This is a force applied by an object pushing or pulling on another causing a change in velocity. This tractive force is inversely proportional to the velocity of the train. As the train speeds up, more fluid resistance
impedes the tractive force of the train. How can we quantify this continuous tractive force? Power is needed to propel the train. Power is the transfer or use of our good friend energy during a rate of time. Since energy and work are synonymous (demonstrated in the last blog entry) we arrive at the traditional definition of power=work/time -P=W/t. But we also know work is equal to force times distance on object moves - W=Fd. So, power is also equal to force times distance divided by time - P=Fd/t. Distance divided by time is velocity, which was being solved for on the physics question in the last posting. Now, we have arrived at power is equal to force times velocity - P=Fv or F=P/v. This is the equation engineers use to calculate the continuous tractive force for a train and it is derived from the concept of energy and its partner work.
Saturday, May 19, 2012
Question from Physics Final
Energy is a very robust and powerful concept. Most early concepts in a physics deal with Newtonian Mechanics (motions, forces etc.). However, when we start to look at the world of Quantum Mechanics, we must surrender some of our most dear and cherished understandings that have served us so well. Early experiments at the sub-atomic level raised some interesting questions. One was that there seemed to be a loss of energy in some fission experiments. Niels Bohr, the father of the atom, proposed that maybe the law of conservation of energy did not hold up at the sub-atomic level. Wolfgang Pauli put forth that he would place his money on the conservation of energy and postulated that there was some particle that was not seen which accounted for the mass/energy. Today, we know that Pauli was correct and the neutrino (similar to an electron without a charge) is a fascinating particle which accounted for the energy in those experiments. As such, it is important for our students to have firm understanding of the concpet of energy and for that matter its relationship to work.
Here is a question I offered my seniors on their final to asses their consolidation of energy and work: A freight train with a mass of 4*10^7 kg experiences a net force of 6.8*10^7 N and moves a distance of 110 meters. If its initial velocity is 5.5 m/s, what is its final velocity? How we define work and energy solves this problem. W=Fd, F=ma and d=vt this is average velocity vf +vi/2. Now remember that acceleration is change in velocity divided by change in time. This together gives us W=m (vf-vi/t )*(vf+vi)t/2. The t's cancel and dividing by 2 is like multiplying by 1/2. This yields W=1/2mvf^2 - 1/2mvi^2. 1/2mv^2 is the definition of kinetic energy. Thus, work is the change in kinetic energy.
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