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.

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.

Clear Cutting?

Greetings!  I was wondering if any of my fellow bloggers could tell if these pictures offer an example of clear cutting?  I must admit the pictures are not from WV, but from Ohio.  I was driving north on Route 7 in Gallia County when I came upon this site.  Lushes and green and then boom, nothing.  It looks like the area which goes way back over the hill has been carpet bombed.  Is this a common practice?  I suppose if you wanted a biologic which needed massive amounts of sunlight to grow in abundance this might be viable.  I just don't know.  If you have any ideas, post back.  I will try to get some more photos today.

K and M Current Photos

Here are some current photos of the railbridge near Pt. Pleasant.  There are several factors that go into bridge design and have a direct relationship with physical science.  Students should remember that Newton's 2nd and 3rd Laws must always be accounted for together when analyzing a situation.  Consider a train moving over the railbridge.  The train exerts a force on the bridge, its weight: F=ma (acceleration is gravity).  The bridge is in equilibrium, it is not falling or accelerating down.  Newton's 3rd Law helps to explain that the bridge must be appyling a force equal to and opposite in direction of the force the train applies and, their net force must be 0 so we say - Fnet = Ftr +Fbr = 0.  The acceleration due to gravity should have a negative sign for indication of direction.  This would be very appropriate for 9th graders.  11th and 12th graders could up the game by incorporating Hooke' Law: F = -kx and Young's Modulus: E = Stress/Strain.  I will discuss those on my next blog posting.