Posts Tagged ‘de Coriolis’

The Math Behind the Work-Energy Theorem

Friday, January 1st, 2016

    As an engineering expert I’ve applied the Work-Energy Theorem to diverse situations, but none as unique as its most recent application, the progress of Santa’s sleigh.   Last week we saw how Santa and his reindeer team encountered a wind gust which generated enough force to slow them from an initial velocity of v1 to a final velocity, v2, over a distance, d.   Today we’ll begin using the Work-Energy Theorem to see if Santa was able to keep to his Christmas delivery schedule and get all the good boys and girls their gifts in time.

Santa and the Work Energy Theorem

    Before we can work with the Work-Energy Theorem, we must first revisit the formula it’s predicated upon, de Coriolis’ formula for kinetic energy,

KE = ½ × m × v2                            (1)

where, KE is kinetic energy, m is the moving object’s mass, and v its velocity.

    The equation behind the Work-Energy Theorem is,

W = KE2 KE1                                    (2)

where W is the work performed, KE1 is the moving object’s initial kinetic energy and KE2 its final kinetic energy after it has slowed or stopped.   In cases where the object has come to a complete stop KE2 is equal to zero, since the velocity of a stationary object is zero.

    In order to work with equation (2) we must first expand it into a more useful format that quantifies an object’s mass and initial and final velocities.   We’ll do that by substituting equation (1) into equation (2).   The result of that term substitution is,

W =× m × v22 ] – [½ × m × v12]      (3)

    Factoring out like terms, equation (3) is simplified to,

W = ½ × m × [v22v12]                        (4)

    Now according to de Coriolis, work is equal to force, F, times distance, d.   So substituting these terms for W in equation (4), the expanded version of the Work-Energy Theorem becomes,

F × d = ½ × m × [v22v12]                 (5)

    Next time we’ll apply equation (5) to Santa’s delivery flight to calculate the strength of that gust of wind slowing him down.

Copyright 2015 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog



Joule’s Dynamo – The Joule Heating Effect

Saturday, October 24th, 2015

      As an engineering expert with 14 years’ electric utility experience, I’ve dealt with all types of electrical power generators, including many similar to the dynamo that James Prescott Joule used in his Experiment With Electricity.   Today we’ll look inside Joule’s dynamo and see how it contributed to creating electricity as well as another of Joule’s discoveries, the Joule Heating Effect.

Dynamo-Circa Early 19th Century

Dynamo-Circa Early 19th Century

      In Joule’s Experiment With Electricity, the dynamo was powered by a steam engine, which enabled the dynamo’s shaft to spin.    As it spun, the magnet located inside the dynamo also spun, thus creating a rotating magnetic field that surrounded the dynamo’s internal copper wire coils.

      The interaction between the magnetic field and wire produced electric current which flowed inside the coils.   The current ultimately made its way out of the dynamo by way of external wires, to which any number of devices could be powered when attached.   The net result was the engine’s mechanical energy had been converted into electrical.   To learn more about the process of producing electricity with magnets see my blog on, Coal Power Plant Fundamentals – The Generator.

      As electrical energy flowed through the dynamo’s wiring, some of it was converted into heat energy.   This was due to resistance posed by impurities present in the makeup of the wire, impurities which served to impede the overall flow of electric current.   When electrons flowing through the wire collided with these impediments, they caused heat to build up inside the wire, a phenomenon which came to be known as the Joule Heating Effect.   To read more on electrical resistance and Joule heating go to my blog, Wire Size and Electric Current.

      The net result of Joule’s Experiment With Electricity was to further prove the link between chemical, heat, mechanical and electrical energies as set out in the Law of Conservation of Energy.   And I suspect that knowledge was later put to use by Joule’s family for the betterment of their brewery business.

      Next time we’ll use Joule’s experimental findings in conjunction with de Coriolis’ Kinetic Energy Formula to quantify the energy of the falling coffee mug we’ve been watching.

Copyright 2015 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog