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.