Posts Tagged ‘kinetic energy’

Calculation of the Effect of Machines — How to Calculate Kinetic Energy

Friday, 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.

mechanical engineering expert witness

      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

Friday, 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.

Gravesande's Experiment

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

Wednesday, 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.

engineering expert witness falling objects

      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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Coal Power Plant Fundamentals – The Steam Turbine

Sunday, February 20th, 2011

     When I was a kid I didn’t have video games or cable TV to help me occupy my time.  Back then parents tended to be frugal, and the few games I had were cheap to buy and simple in operation, like the plastic toy windmill I’d play with for hours on end.  All I had to do to make it spin was take a deep breath, pucker my lips together, fill my cheeks with breath, then blow hard into the windmill blades.  Its spin was fascinating to watch.  Little did I know that as an adult I would come to work with a much larger and complex version of it, in the form of a power plant’s steam turbine.

     You see, when you trap breath within bulging cheeks and then squeeze your cheek muscles together, you actually create a pressurized environment.  This air pressure buildup transfers energy from your mouth muscles into the trapped breath within your mouth, so that when you open your lips to release the breath through your puckered lips, the pressurized energy is converted into kinetic energy, a/k/a the energy of movement.  The breath molecules flow at high speed from your lips to the toy windmill’s blades, and as they come into contact with the blades their energy is transferred to them, causing the blades to move.  A similar process takes place in the coal power plant, where steam from a boiler takes the place of pressurized breath and a steam turbine takes the place of the toy windmill.

     If you recall from my previous article, the heat energy released by burning coal is transferred to water in the boiler, turning it to steam.   This steam leaves the boiler under great pressure, causing it to travel through pipe to the steam turbine, as shown in Figure 1.

Figure 1 – A Basic Steam Turbine and Generator In A Coal Fired Power Plant

     At its most basic level the inside of a steam turbine looks much like our toy windmill, of course on a much larger scale, and it is very appropriately called a “wheel.”  See Figure 2.  

Figure 2 – A Very Basic Steam Turbine Wheel

     The wheel is mounted on a shaft and has numerous blades.  It makes use of the pressurized steam that has made its way to it from the boiler.  This steam has ultimately passed through a nozzle in the turbine that is directed towards the blades on the wheel.  This is the point at which heat energy in the steam is converted into kinetic energy.  The steam shoots out of the nozzle at high speed, coming into contact with the blades and transferring energy to them, which causes the turbine shaft to spin.  The turbine shaft is connected to a generator, so the generator spins as well.  Finally, the spinning generator converts the mechanical energy from the turbine into electrical energy.

     In actuality, most coal power plant steam turbines have more than one wheel and there are many nozzles.  The blades are also more numerous and complex in shape in order to maximize the energy transfer from the steam to the wheels.  My Coal Power Plant Fundamentals seminar goes into far greater detail on this and other aspects of steam turbines, but what I have shared with you above will give you a basic understanding of how they operate. 

     So to sum it all up, the steam turbine’s job is to convert the heat energy of steam into mechanical energy capable of spinning the electrical generator.  Next time we’ll see how the generator works to complete the last step in the energy conversion process, that is, conversion of mechanical energy into electrical energy.

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Diesel Locomotive Brakes

Sunday, June 6th, 2010

     In the past few weeks we’ve taken a look at both mechanical and dynamic brakes.  Now it’s time to bring the two together for unparalleled stopping performance.

     Have you ever wandered along a railroad track, hopping from tie to tie, daring a train to come roaring along and wondering if you could jump to safety in time?  Many have, and many have lost the bet.  That’s because a train, once set into motion, is one of the hardest things on Earth to bring to a stop.  In this discussion, let’s focus on the locomotive.  A large, six-axle variety is shown in Figure 1.

Figure 1 – A Six-Axle Diesel-Electric Locomotive

     These massive iron horses are known in the industry as diesel-electric locomotives, and here’s why.  As Figure 2 shows, diesel-electric locomotives are powered by huge diesel engines.  Their engine spins an electrical generator which effectively converts mechanical energy into electrical energy.  That electrical energy is then sent from the generator through wires to electric traction motors which are in turn connected to the locomotive’s wheels by a series of gears.  In the case of a six-axle locomotive, there are six traction motors all working together to make the locomotive move.  So how do you get this beast to stop?

 

Figure 2 – The Propulsion System In A Six-Axle Diesel-Electric Locomotive

     You probably noticed in Figure 2 that there are resistor grids and cooling fans.  As long as you’re powering a locomotive’s traction motors to move a train, these grids and fans won’t come into play.  It’s when you want to stop the train that they become important.  That’s when the locomotive’s controls will act to disconnect the traction motor wires running from the electrical generator and reconnect them to the resistor grids as shown in Figure 3 below.

Figure 3 – The Dynamic Braking System In A Six-Axle Diesel Electric Locomotive

     The traction motors now become generators in a dynamic braking system.  These motors take on the properties of a generator, converting the moving train’s mechanical, or kinetic, energy into electrical.  The electrical energy is then moved by wires to the resistor grids where it is converted to heat energy.  This heat energy is removed by powerful cooling fans and released into the atmosphere.  In the process the train is robbed of its kinetic energy, causing it to slow down.

     Now you may be thinking that dynamic brakes do all the work, and this is pretty much true, up to a point.  Although dynamic brakes may be extremely effective in slowing a fast-moving train, they become increasingly ineffective as the train’s speed decreases.  That’s because as speed decreases, the traction motors spin more slowly, and they convert less kinetic energy into electrical energy.  In fact, below speeds of about 10 miles per hour dynamic brakes are essentially useless.  It is at this point that the mechanical braking system comes into play to bring the train to a complete stop.

     Let’s see how this switch from dynamic to mechanical dominance takes place.  A basic mechanical braking system for locomotive wheels is shown in Figure 4.  This system, also known as a pneumatic braking system, is powered by compressed air that is produced by the locomotive’s air pump.  A similar system is used in the train’s railcars, employing hoses to move the compressed air from the locomotive to each car. 

Figure 4 – Locomotive Pneumatic Braking System

     In the locomotive pneumatic braking system, pressurized air enters an air cylinder.  Once inside, the air bears against a spring-loaded piston, as shown in Figure 4(a).  The piston moves, causing brake rods to pivot and clamp the brake shoes to the locomotive’s wheel with great force, slowing the locomotive.  When you want to get the locomotive moving again, you vent the air out of the cylinder as shown in Figure 4(b).  This takes the pressure off the piston, releasing the force from the brake shoes.  The spring in the cylinder is now free to move the shoes away from the wheel so they can turn freely.  We have now returned to the situation present in Figure 2, and the locomotive starts moving again.

     Next week we’ll talk about regenerative braking, a variation on the dynamic braking concept used in railway vehicles like electric locomotives and subway trains.

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Dynamic Brakes

Monday, May 31st, 2010

     Last week we looked at how a mechanical brake stopped a rotating wheel by converting its mechanical energy, namely kinetic energy, into heat energy.  This week, we’ll see how a dynamic brake works.

     Chances are you have directly benefited by a dynamic braking system the last time you rode in an elevator.  But, to understand the basic principle behind an elevator’s dynamic brake system, let’s first take a look at the electric braking system in Figure 1 below. 

Figure 1 – A Simple Electric Braking System

     Here the brake consists of an electric generator wired via an open switch to an electrical component called a resistor.  The weight is attached to a cable that is wound around a pulley on the generator’s shaft.   As the weight freefalls, the cable unwinds on the pulley, causing the pulley to turn the generator’s shaft.

     Unlike last week’s mechanical brake which required a good deal of effort to employ, a dynamic braking system requires very little.  All that needs to be done is to close a switch as shown in Figure 2 below.  When the switch is closed, an electrical circuit is created where the resistor gets connected to the generator.  The resistor does as its name implies: it resists (but doesn’t stop) the electrical current flowing through it from the generator.  As the electrical current fights its way through the resistor to get back to the generator, the resistor gets hot like an electric heater.  This heat is dissipated to the cooler surrounding air.  At the same time, the weight begins to slow down in its descent.  But how is this happening?

     The electric braking system can be thought of as an energy conversion process.  We start out with the kinetic, or motion energy, of the freefalling weight.  This kinetic energy is transmitted to the electrical generator by the cable, which spins the generator’s shaft as the cable unwinds.  Electrical generators are machines that convert kinetic energy into electrical energy.  This energy travels from the electric generator through wires and a closed switch to the resistor.  In the process the resistor converts the electrical energy into heat energy.  So, kinetic energy is drawn from the falling weight through the conversion process and leaves the process in the form of heat.  As the falling weight is drained of kinetic energy, it slows down. 

 Figure 2 – Applying the Electric Brake   

     Okay, now let’s get back to dynamic brakes on elevators.  An elevator is attached by a cable to a hoist that is powered by an electric motor.  When it’s time to stop at the desired floor, the automatic control system disconnects the elevator’s electric motor from its power source and turns the motor into a generator.  The generator is then automatically connected to a resistor like the one shown in the electric brake above.  The kinetic energy of the moving elevator is converted by the generator into electrical energy.  The resistor converts the electrical energy into heat energy which is then dissipated into the surrounding environment.  The elevator slows down in the process because it’s being robbed of kinetic energy.  When the dynamic brake slows the elevator down enough, a mechanical brake is introduced, taking over to bring the elevator to a complete stop.  This two-fold process serves to reduce wear and tear on the mechanical brake’s parts, lengthening the operational lifespan of the system as a whole.

     Next time, we’ll tie everything together and show how mechanical and dynamic brakes work together in a diesel locomotive.

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Brakes and Braking Systems

Sunday, May 23rd, 2010

     Imagine driving in your car, you’re traveling at a speed of 65 mph and you’re coming up on a curve.  You depress your brake pedal to negotiate the turn, and nothing happens…

     Scenarios just like this one have been in the news quite often lately, brakes which just aren’t operating correctly.  We’ve heard the tales of terror, recounted by those unfortunate individuals who have been placed in this situation, but have we reflected on just why their brakes might have failed?

     Put most simply, a brake is a device whose purpose is to stop a body in motion.  This important task is accomplished by converting the kinetic energy (energy of motion) into heat energy.  This can be accomplished by either of two methods, mechanically or electrically.  In today’s blog we’ll focus on the mechanical aspect.

     A simple mechanical brake is shown in Figure 1 below.  In this arrangement kinetic energy is converted into heat energy when force is applied to a lever, causing a brake shoe to meet up with a rotating wheel.  The brake shoe has a pad attached to its surface that makes direct contact with the wheel, and when the two come together great friction is produced.  It’s this friction that will ultimately stop the object in motion.  Friction turns the kinetic energy into heat energy.

Figure 1 – A Simple Mechanical Brake

     Friction at its simplest is a mechanical resistance to movement.  Whenever two materials in motion come into contact with each other there is always some degree of friction.  The extent to which friction is produced by their meeting is referred to as the “coefficient of friction.” 

     The coefficient of friction varies according to the surface character of the materials coming in contact.  For example, the coefficient of friction for the leather sole of your shoe on smooth ice is very low.  This means you’ll do a lot of slipping when you’re trying to walk, and that’s because ice presents little friction to resist a smoothly soled shoe.  But take this same shoe and apply it to the rough surface of concrete, and you’ll be walking quickly and efficiently.  Coefficients of friction between different materials have been duly measured in laboratories and are tabulated for easy access in engineering reference books.

     Based on our simple example above, one would easily come to the conclusion that a high coefficient of friction is desirable when talking about brake shoes, specifically the one represented in Figure 1 above.  The higher the coefficient of friction, the more the pad wants to grab the wheel, and the less force you will need to apply to the brake shoe to successfully come to a stop.

     That’s mechanical braking in a nutshell.  Next time, we’ll focus on an electrical braking system known as a “dynamic brake.”

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Centrifugal Pumps

Sunday, May 16th, 2010

     Last week we focused on various types of positive displacement pumps.  Today we’ll take a look at centrifugal pumps.  See Figure 1.

Figure 1 – A Centrifugal Pump

     Just like the positive displacement pumps we talked about last week, centrifugal pumps have rotating parts as well, but that’s where their similarities end.  Unlike positive displacement pumps that take “bites” out of liquid before trapping it between moving parts, centrifugal pumps rely on kinetic energy to move liquid in a continuous stream.  Kinetic energy is the energy of motion, and in the case of the centrifugal pump kinetic energy is developed by rotating parts within the pump and transferred to the liquid contained within the pump.  In other words, the liquid is moved through the pump by means of centrifugal force.

     To illustrate this concept, we can tie a rope to the handle of a bucket that has a small hole punched in the bottom.  Now, you know what will happen if you fill the bucket with water…  There’s a hole in the bucket, Dear Liza, Dear Liza…  That’s right, the water will just dribble out of the hole, thanks to gravity.  But before we fix the hole as Liza suggests, let’s do an experiment.  Pick up the rope and spin the bucket around as fast as you can in a circle.  You’ll notice that this rapid spinning creates centrifugal force, resulting in a rather powerful stream of water shooting from the hole.  The faster you spin the bucket, the stronger the stream.

     When it comes to centrifugal pumps, the idea is basically the same.  The objective is to forcefully spin water around in a circle, thus ejecting it from the pump.  This is accomplished with a rotating part called an impeller.  See Figure 2.

Figure 2 – Cutaway View of a Centrifugal Pump    

 

     In our illustration the impeller is attached to a shaft that’s powered by some source of mechanical energy, such as an electric motor.  The water enters the pump at the center of the rotating impeller, referred to as the “eye.”  The water then slides over the face of the impeller, moving from the center to its edge due to the action of centrifugal force.  That force pushes it off the impeller and into the pump housing.  You’ll note that the housing has a special shape, called a “volute.”  This volute looks a lot like a spiraled snail shell.  The shape of the volute helps direct the water coming off the impeller into an opening in the side of the pump where it is discharged.  The faster the pump impeller rotates, the more kinetic energy the water picks up from the impeller.

     This ends our discussion on pumps.  Next time, we’ll move on to a new topic of discussion, braking systems.

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