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When acting as an engineering expert I’m often called upon to investigate incidents where energy converts from one form to another, a phenomenon that James Prescott Joule observed when he built his apparatus and performed his experiments with electricity. Today we’ll apply Joule’s findings to our own experiment with a coffee mug when we convert its kinetic energy into electrical energy and see how the units used to express that energy also change. We had previously calculated the kinetic energy contained within our falling coffee mug to be 4.9 kg • meter2/second2, also known as 4.9 Joules of energy, by using de Coriolis’ Kinetic Energy Formula. Now most of us don’t speak in terms of Joules of energy, but that’s easily addressed. As we learned in a previous blog on The Law of Conservation of Energy, all forms of energy are equivalent and energy can be converted from one form to another, and when it does, the unit of energy used to express it also changes. Let’s say we want to put our mug’s 4.9 Joules of kinetic energy to good use and power an electric light bulb. First we must first find a way of converting the mug’s kinetic energy into electrical energy. To do so, we’ll combine Joule’s apparatus with his dynamo, and connect the mug to this hybrid device with a string.
Converting Kinetic Energy to Electrical Energy As the mug falls its weight tugs on the string, causing the winding drum to rotate. When the drum rotates, the dynamo’s magnet spins, creating electrical energy. That’s right, all that’s required to produce electricity is a spinning magnet and coils of wire, as explained in my previous blog, Coal Power Plant Fundamentals – The Generator. Now we’ll connect a 5 Watt bulb to the dynamo’s external wires. The Watt is a unit of electrical energy named in honor of James Watt, a pioneer in the development of steam engines in the late 18th Century. Now it just so happens that 1 Watt of electricity is equal to 1 Joule of energy per a specified period of time, say a second. This relationship is expressed as Watt • second. Stated another way, 4.9 Joules converts to 4.9 Watt • seconds of electrical energy. Let’s see how long we can keep that 5 Watt bulb lit with this amount of energy. Mathematically this is expressed as, Lighting Time = (4.9 Watt • seconds) ÷ (5 Watts) = 0.98 seconds This means that if the mug’s kinetic energy was totally converted into electrical energy, it would provide enough power to light a 5 Watt bulb for almost 1 second. Next time we’ll see what happens to the 4.9 Joules of kinetic energy in our coffee mug when it hits the floor and becomes yet another form of energy. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |
Converting Kinetic Energy to Electrical Energy
November 3rd, 2015
Joule’s Dynamo – The Joule Heating Effect
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 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 ____________________________________ |
Joule’s Experiment With Electricity
October 16th, 2015|
In my work as an engineering expert I’ve dealt with all forms of energy, just as we’ve watched James Prescott Joule do. He constructed his Joule Apparatus specifically to demonstrate the connection between different forms of energy. Today we’ll see how he furthered his discoveries by building a prototype power plant capable of producing electricity, a device which came to be known as Joule’s Experiment With Electricity.
Joule’s Experiment With Electricity As the son of a wealthy brewer, Joule had been fascinated by electricity and the possibility of using it to power his family’s brewery and thereby boost production. To explore the possibilities, he went beyond the Apparatus he had built earlier and built a device which utilized electricity to power its components. The setup for Joule’s experiment with electricity is shown here. Coal was used to bring water inside a boiler to boiling point, which produced steam. The steam’s heat energy then flowed to a steam engine, which in turn spun a dynamo, a type of electrical generator. Tracing the device’s energy conversions back to their roots, we see that chemical energy contained within coal was converted into heat energy when the coal was burned. Heat energy from the burning coal caused the water inside the boiler to rise, producing steam. The steam, which contained abundant amounts of heat energy, was supplied to a steam engine, which then converted the steam’s heat energy into mechanical energy to set the engine’s parts into motion. The engine’s moving parts were coupled to a dynamo by a drive belt, which in turn caused the dynamo to spin. Next time we’ll take a look inside the dynamo and see how it created electricity and led to another of Joule’s discoveries being named after him. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |
James Prescott Joule and the Joule Apparatus
October 6th, 2015|
As an engineering expert I’ve often witnessed energy change forms, something our example coffee mug has been experiencing as it moves from a shelf to the floor. The mug’s various energies were proven to be mathematically equivalent, expressed as, 4.9 kg•meter2 /second2 , which is read as, “kilogram meter squared per second squared.” This mouthful led to the renaming of the measurement to the Joule, in honor of James Prescott Joule, a scientist who successfully demonstrated the interrelationship between different forms of energy. We’ll focus on one of his experiments, the Joule Apparatus, today. Back in the 1840s Joule built his Apparatus, a device which demonstrated the interrelationship between different forms of energy.
The Joule Apparatus The Joule Apparatus consisted of a weight suspended by string over a pulley, which in turn was wound around a winding drum. As long as the drum remained stationary, the weight remained motionlessly suspended. While motionless, the weight’s potential energy lay latent within it, just as it had in our example coffee mug resting on a shelf. But when the pressure keeping the winding drum stationary was released, the weight was set free to fall, and its potential energy began converting to kinetic. In the process, the string the weight was attached to unwound from the drum, which caused the drum to turn and along with it the paddle wheel it was attached to. Joule’s Apparatus followed energy through many forms. From the quiet of potential energy to the kinetic energy demonstrated by the falling weight. The kinetic energy in turn was converted into mechanical energy, made manifest by the interaction between the moving drum and paddle wheel. The rotating paddles agitated the water, causing its temperature to rise. Observing this, Joule concluded that the mechanical energy of the spinning paddle wheel had been converted into heat energy, which temperature measurement proved was transferred into the water. Joule’s experiment thus proved the link between potential, kinetic, mechanical, and heat energies. Joule’s work paved the way to make possible the later development of a host of modern mechanical devices that also converted heat energy into mechanical energy, or vice versa. These devices include a car’s engine and your kitchen’s refrigerator. Next time we’ll see how Joule demonstrated a link between electrical and other forms of energy, including mechanical and heat. We’ll then use his discoveries to convert our falling coffee mug’s kinetic energy into yet another form. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog
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Calculating Velocity — de Coriolis’ Kinetic Energy Formula
September 28th, 2015|
Last time we introduced Gaspard-Gustave de Coriolis’ formula to compute kinetic energy. Today we’ll use it to determine the speed of descent, or velocity, of the coffee mug we’ve been watching closely in the last few blogs. To calculate the mug’s velocity, we must bear in mind physicist Julius Robert von Mayer’s assertion that all forms of energy are interrelated, and in fact interchangeable, because energy can neither be created nor destroyed, it can only change forms. For a refresher, see The Law of Conservation of Energy. Let’s now put a practical spin on this concept and apply it to our coffee mug’s free fall to the floor. Once again, de Coriolis’ formula, KE = ½ × m × v2 (1) where m is the mass of our falling object and v its velocity. The ½ is an unchanging, constant term that’s present due to the mathematical Rules of Integration governing integral calculus. Calculus and its derivations are beyond the scope of this blog, but if you’re interested in pursuing this, follow this link to, The Physics Hypertextbook – Kinetic Energy. According to von Mayer’s Law, at the precise instant before the mug hits the floor its kinetic energy, KE, is equal to the potential energy, PE, it possessed when it rested passively on the shelf. Stated another way, the instant before the mug makes contact with the floor, all its potential energy will have been converted into kinetic. The mug’s PE was calculated previously to be equal to 4.9 kg • meter2/second2. See Computing Potential Energy for a review. Knowing this, the mathematical relationship between the mug’s potential and kinetic energies is expressed as, PE = KE = 4.9 kg • meter2/second2 (2) By substituting this mathematical representation for KE into equation (1) we arrive at, 4.9 kg • meter2/second2 = ½ × m × v2 (3) We also know the mug’s mass, m, to be equal to 2.6 kilograms, so integrating that into the right side of equation (3) it becomes, 4.9 kg • meter2/second2 = ½ × ( 0.25kg) × v2 (4) That leaves the mug’s velocity, v2, as the only remaining unknown term. We’ll use algebra to isolate this variable by dividing both sides of equation (4) by ½ × ( 0.25kg). (4.9 kg • meter2/second2) ÷ [½ × ( 0.25kg)] = v2 39.20 meter2/second2 = v2 Finally, we’ll take the square root of the equation to place it in terms of v. 6.26 meters/second = v The mug’s velocity an instant before impact equates to 6.26 meters/second, or almost 21 feet per second.
Next time we’ll discuss a metric unit used to measure energy known as the Joule and discover the man behind it. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |
Calculation of the Effect of Machines — How to Calculate Kinetic Energy
September 18th, 2015|
Last time we introduced kinetic energy as the energy of movement. Today we’ll see how to calculate it, using French mathematician Gaspard-Gustave de Coriolis’ formula as set out in his textbook, Calculation of the Effect of Machines. We’ll then apply his formula to our example of a coffee mug falling from its shelf. Gaspard-Gustave de Coriolis’ book presented physics concepts, specifically the study of mechanics, in an accessible manner, without a lot of highbrow theory and complicated mathematics. His insights made complicated subjects easy to understand, and they were immediately put to use by engineers of his time, who were busily designing mechanical devices like steam engines during the early stages of the Industrial Revolution. Within its pages the mathematics of kinetic energy was presented in the scientific form that persists to present day. That formula is, KE = ½ × m × v2 where m is the moving object’s mass and v its velocity. In the case of our coffee mug, its kinetic energy will be zero so long as it remains motionless on the shelf. A human arm had lifted it to its perch against the force of gravity, thereby investing it with gravitational potential energy. If the mug was sent freefalling to the ground by the mischievous kitty, its latent potential energy would be realized and converted into the kinetic energy of motion.
To illustrate, let’s say a mug with a mass equal to 0.25 kg rests on a shelf 2 meters above the floor. Its potential energy would then be equal to 4.9 kg • meter2/second2, as was computed in our previous blog, Computing Potential Energy. Once kitty nudges the mug from its perch and it begins to fall, its latent gravitational potential energy begins a conversion process from potential to kinetic energy. It will continue to convert into an amount of kinetic energy that’s precisely equal to the mug’s potential energy while at rest on the shelf, that is, 4.9 kg • meter2/second2. Upon impact with the floor, all the mug’s gravitational potential energy will have been converted into kinetic energy. Next time we’ll apply the Law of Conservation of Energy to the potential and kinetic energy formulas to calculate the mug’s velocity as it freefalls to the floor. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________
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Willem Gravesande’s Experimentation on Kinetic Energy
September 11th, 2015|
Last time we introduced The Law of Conservation of Energy, which holds that energy can neither be created nor destroyed. We then applied the concept to a mug resting on a shelf, brimming with latent gravitational potential energy. Today we’ll continue our discussion with a focus on kinetic energy and how Willem Gravesande’s experimentation contributed to our understanding of the subject. The concept of kinetic energy was first posited by mathematicians Gottfried Leibniz and Johann Bernoulli in the early 18th Century when they theorized that the energy of a moving object is a factor of its mass and speed. Their theory was later proven by Willem Gravesande, a Dutch lawyer, philosopher, and scientist. Gravesande conducted experiments in which he dropped identical brass balls into a soft clay block. See Figure 1.
Figure 1 Figure 1 shows the results obtained when balls of the same mass m are dropped from various heights, resulting in different velocities as they fall and different clay penetrations. The ball on the left falls at velocity v and penetrates to a depth d. The center ball falls at twice the left ball’s velocity, or 2v, and penetrates four times as deep, or 4d. The right ball falls at three times the left ball’s velocity, 3v, and it penetrates nine times deeper, 9d. The results indicate an exponential increase in clay penetration, dependent on the balls’ speed of travel. In fact, all the kinetic energy that the balls exhibited during freefall was converted into mechanical energy from the instant they impacted the clay until their movement within it stopped. This change in forms of energy from kinetic to mechanical demonstrates what Julius Robert von Mayer had in mind when he derived his Law of Conservation of Energy. For a refresher on the subject, see last week’s blog, The Law of Conservation of Energy. As a result of his experimentation, Gravesande was able to conclude that the kinetic energy of all falling objects is a factor of their mass multiplied by their velocity squared, or m × v2. We’ll see next time how Gravesande’s work paved the way for later scientists to devise the actual formula used to calculate kinetic energy and then we’ll apply it all to our coffee mug falling from the shelf. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________
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The Law of Conservation of Energy
September 2nd, 2015|
Last time we calculated the potential energy hidden within a coffee mug resting on a shelf. The concept of a passive object possessing energy may not be something all readers can identify with, but the secret behind that mug’s latent energy lies within The Law of Conservation of Energy, the topic we’ll be discussing today. Julius Robert von Mayer, a German physicist of the mid 19th Century, is the man behind the Law. He posited that energy cannot be created or destroyed, it can only be transferred from one object to another or converted from one form of energy to another. Forms of energy include potential, kinetic, heat, chemical, mechanical, and electrical, all of which have the ability to become another form of energy. Let’s take our coffee mug for example. Where did its potential energy come from? Ultimately, from the radiant energy emitted by the sun. The sun’s radiant energy was absorbed by plants and then converted to chemical energy through the process of photosynthesis, enabling them to grow. When they were later eaten by humans and other animals, the plants’ chemical energy became incorporated into their bodies’ cells, including the arm muscles used to lift the mug to the shelf. In the act of lifting the cup, the arm’s muscle cells converted their own chemical energy into mechanical energy. And because lifting a mug to a shelf is work, for some of us greater than others, some of the arm’s chemical energy became heat energy which was lost to the environment. Because of the elevated perch provided to the mug by the arm, which was in direct defiance of Earth’s gravitational pull, the arm muscles’ mechanical energy was transferred to the mug and converted to latent potential energy, because without that shelf to support it, the mug would fall to the ground. The mug’s potential energy would realize its full potential if it should be sent crashing to the floor, at which time it would become another form of energy. The mischievous orange kitty seems to have just that in mind.
We’ll talk more about the mug’s potential energy being converted to other forms next time. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________
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Computing Potential Energy
August 25th, 2015|
Last week we discovered that objects acquire potential energy as it relates to gravity based on the height those objects are elevated above the ground. We also introduced an equation to calculate the potential energy of a coffee mug perched on a shelf. We’ll work with that equation today and compute the latent energy that’s hidden within that mug. Here again is the equation to determine potential energy, put in terms relating to gravity, PEgravitational = m × g × h where m is the mass of the mug, h is the height it’s been elevated above the floor, and g is the Earth’s acceleration of gravity factor, as explained in my previous blog entitled, Sir Isaac Newton and the Acceleration of Gravity. The equation above can be solved using either English or metric units. In the US it’s generally standard practice to perform calculations using English units, such as feet and pounds. But when measuring mass a less familiar English unit, the slug, comes into play. If you’re interested in learning more about this unit, go to a previous blog article entitled, The Force of Gravity. The kilogram is the metric equivalent of a slug. Since it’s the unit of mass most commonly used throughout the world, we’ll use it to perform our calculation.
Let’s say our mug has a mass of 0.25 kilograms, the shelf it’s resting on is 2 meters above the floor, and g is 9.8 meters/second2. The mug’s gravitational potential energy would then be expressed as, PEgravitational = (0.25 kg) × (9.8 meters/second2) × (2 meters) PEgravitational = 4.9 kg • meter2/second2
Next time we’ll expand on our discussion of potential energy and discuss the Law behind the phenomenon and the fact that energy can only be converted from one form to another. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________
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Gravitational Potential Energy on Earth
August 17th, 2015|
Last week we concluded our discussion on the force of gravity within our solar system. Today we’ll turn our attention to the subject of gravity on Earth and exploring the physics behind falling objects. We’ll start off by discussing potential energy as it relates to gravity, or the latent energy acquired by an object when it’s been elevated above ground level. Potential energy was the term adopted by 19th Century Scottish scientist William Rankine to represent the latent, or masked, energy hidden within objects. As an example, let’s say you’ve placed your favorite coffee mug in its designated spot on the kitchen shelf. Sitting there so still you wouldn’t dream it was brimming with gravitational potential energy, but if your cat came along and brushed against it, sending it freefalling to the floor, your mug would quickly become a projectile, gaining speed at a uniform rate as it accelerated towards ground level. Where did that once passive little cup acquire its mounting energy? Simply by virtue of the fact it had been lifted by your arm and placed in an elevated position. You see, Earth’s gravitational pull is forever exerting its invisible tug on objects. It was tugging at the mug as you lifted it, and the higher you lifted it, the more gravitational potential energy the mug received. Once perched on the shelf it bridled with latent energy, only to be set free when the cat caused it to lose its support. To illustrate the relationship between the coffee mug, the shelf, and Earth’s gravitational pull, we’ll employ the equation used to compute potential energy, notated in terms of gravity, PEgravitational = m × g × h This equation states that the mug’s gravitational potential energy, PEgravitational, is a factor of its mass, m, Earth’s gravitational pull, g, and the mug’s height above ground level, h. Within the scientific community g is referred to as Earth’s acceleration of gravity, a phenomenon commonly accepted to be the uniform accelerating rate at which an object falls on Earth, equal to 9.8 meters per second per second, or meters/second2. It represents a rate of constant acceleration, which happens to be precisely the same whether the object falling is a brick, feather, or coffee mug. Next time we’ll work with the potential energy equation which will enable us to see how the curious orange kitty sets loose the latent power held within that mug.
Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________
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