Happy Holidays from EngineeringExpert.net, LLC and the Engineering Expert Witness Blog. Pulleys Make Santa’s Job Easier
Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ 
Happy Holidays from EngineeringExpert.net, LLC and the Engineering Expert Witness Blog. Pulleys Make Santa’s Job Easier
Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ 
Humans have been battling the force of friction since the first cave man built the wheel. Chances are his primitive tools produced a pretty crude wheel that first goaround and the wheel’s surfaces were anything but smooth, making its usefulness less than optimal. As an engineering expert, I encounter these same dynamics when designing modern devices. What held true for the cave man holds true for modern man, friction is often a counterproductive force which design engineers must work to minimize. Today we’ll learn about frictional force and see how it impacts our example broken coffee mug’s scattering pieces, and we’ll introduce the man behind friction’s discovery, CharlesAugustin de Coulomb. CharlesAugustin de Coulomb
Last time we learned that the work required to shatter our mug was transformed into the kinetic energy which propelled its broken pieces across a rough concrete floor. The broken pieces’ energetic transformation will continue as the propelling force of kinetic energy held within them is transmuted back into the work that will bring each one to an eventual stop a distance from the point of impact. This last source of work is due to the force of friction. In 1785 CharlesAugustin de Coulomb, a French physicist, discovered that friction results when two surfaces make contact with one another, and that friction is of two types, static or dynamic. Although Leonardo Da Vinci had studied friction hundreds of years before him, it is Coulomb who is attributed with doing the ground work that later enabled scientists to derive the formula to calculate the effects of friction. Our example scenario illustrates dynamic friction, that is to say, the friction is caused by one of the surfaces being in motion, namely the mug’s ceramic pieces which skid across a stationary concrete floor. While in motion, each of the mug’s broken pieces has its own unique velocity and mass and therefore a unique amount of kinetic energy. The weight of each piece acts as a vertical force pushing the piece down “into” the floor, this due to the influence of Earth’s gravitational pull, that is, the force of gravity. Friction is created by a combination of factors, including the ceramic pieces’ weights and the surface roughness of both the pieces themselves and the concrete floor they skid across. At first glance the floor and ceramic mug’s surfaces may appear slippery smooth, but when viewed under magnification it’s a whole different story. Next time we’ll examine the situation under magnification and we’ll introduce the formula used to calculate friction along with a rather odd sounding variable, mu. Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ 
My work as an engineering expert sometimes involves computations of energy expended, as when I must determine how much energy is required to move something. But sometimes the opposite needs to be calculated, that is, how much energy is required to stop something already in motion. That’s the subject of today’s discussion, which we’ll approach by way of the WorkEnergy Theorem. The WorkEnergy Theorem states that the work required to slow or stop a moving object is equal to the change in energy the object experiences while in motion, that is, how its kinetic energy is reduced or completely exhausted. Although we don’t know who to attribute the Theorem to specifically, we do know it’s based on the previous work of Gaspard Gustave de Coriolis and James Prescott Joule, whose work in turn built upon that of Isaac Newton’s Second Law of Motion. Consider the example shown here. A ball of mass m moves unimpeded through space at a velocity of v_{1 }until it is met by an opposing force, F. This force acts upon the ball over a travel distance d, resulting in the ball’s slowing to a velocity of v_{2}. The Work – Energy Theorem Illustrated
Does the illustration make clear the WorkEnergy Theorem dynamics at play? If not, return for the second part of this blog, where we’ll clarify things by getting into the math behind the action. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ 
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 ____________________________________ 
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•meter^{2 }/second^{2 }, 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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Last time we introduced kinetic energy as the energy of movement. Today we’ll see how to calculate it, using French mathematician GaspardGustave 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. GaspardGustave 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 × v^{2} 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 • meter^{2}/second^{2}, 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 • meter^{2}/second^{2}. 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 ____________________________________

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 ____________________________________

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, PE_{gravitational} = 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/second^{2}. The mug’s gravitational potential energy would then be expressed as, PE_{gravitational} = (0.25 kg) × (9.8 meters/second^{2}) × (2 meters) PE_{gravitational} = 4.9 kg • meter^{2}/second^{2}
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 ____________________________________

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, PE_{gravitational} = m × g × h This equation states that the mug’s gravitational potential energy, PE_{gravitational}, 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/second^{2}. 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 ____________________________________

Last time we calculated the sun’s force of gravity acting upon Earth. It was the final unknown quantity within Newton’s equation to determine the mass of the sun, an equation we’ve been working with for some time now. Today we’re set to discover just how big the sun is. Newton’s formula, introduced in a past blog in this series entitled, Gravity and the Mass of the Sun is again, M = (F_{g} × r^{2}) ÷ (m × G) where G is the universal gravitational constant as determined by Henry Cavendish and discussed in our blog, How Big is the Earth? and is equal to, G = 6.67 × 10^{11} meters per kilogram • second^{2} As discussed in last week’s blog, The Sun’s Gravitational Force, Earth’s mass, m, its distance from the sun, r, and the force of the sun’s gravity acting upon Earth, F_{g} , are respectively, m = 5.96 × 10^{24} kilograms r = 149,000,000,000 meters F_{g} = 3.52 × 10^{22} Newtons Inserting these values into Newton’s equation to determine the mass, M, of the sun we get: M = [(3.52 × 10^{22}) × (149,000,000,000)^{2}] ÷ [(5.96 × 10^{24}) × (6.67 × 10^{11})] M = 1.96 × 10^{30} kilograms So how big is 1.96 × 10^{30} kilograms? To get a better idea, let’s divide the sun’s mass, M, by the Earth’s mass, m, (1.96 × 10^{30} kilograms) ÷ (5.96 × 10^{24} kilograms) = 328,859.06 That’s a big number, and it translates to the sun being over 300,000 times more massive than Earth. The picture below displays this comparison in stunning visual terms. Once 19th Century scientists had calculated the mass of the sun, they went on to calculate the masses of other heavenly bodies in our solar system and the gravitational forces at play on each of them. Armed with this information mankind was able to subsequently build exploratory probes capable of extending their reach into the far unknowns of our solar system and beyond. This ends our discussion on gravity within our solar system. Next time we’ll return to Earth and begin exploring the physics behind falling objects.
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