Cosmospostman’s Introduction to Energy 3

Energy Usage: Power

Almost as an afterthought, I’ve decided to add a short section here to discuss energy usage.  According to the definitive article on Wikipedia, a person climbing up a flight of stairs uses energy (or ‘does work’) at a rate of 200 joules per second.  Like ‘Work’, the word ‘Power’ has a technical meaning: the rate at which energy is transferred (lost or gained).  The unit of Power is the Watt, and to say that something uses one watt of power means that it uses one joule of energy per second.  The person climbing the stars draws 200 watts of power from their biological (chemical) energy reserves.

How much energy would our staircase adventurer burn if they climbed a very large staircase for one hour?  There are 3600 seconds in an hour, so she would burn a total of 3600*200 = 720 000 joules.  That’s 720 kilojoules, or according to Google, 172kcal.  This amount of energy could also be expressed as ’200 watt-hours’, which means ‘energy used by drawing 200 watts for one hour (or one watt for 200 hours, or anything in between)’.

Now comes the bit about your electricity bill: what does it mean to say that you used 1200 kilowatt hours over the last month?  It means that if you were to use your entire month’s worth of energy in just one hour, you would use energy at a rate of 1200 kilowatts, ie. 1200 kilojoules per second.  I think it’s slightly confusing to talk about energy in terms of ‘hours’.  It’s a bit like reading a credit card statement saying that you spent 5810 ‘dollar-hours’ (ie, $5810 dollars over an hour, or $1 per hour for 5810 hours).  Fortunately, kilowatt hours and joules measure the same thing (energy), so direct conversion is possible: 1 kilowatt hour is 3 600 kilojoules.  Nothing to do with time at all.

Examples

One

The Slippery Slope

Back to the unfortunate saga of our moose.  Suppose he has been dragged to one side of a steep valley by the hunter.  The hill is covered with very slippery ice, and the opposite side of the hill is only half as high.  The hunter has had enough of pulling the moose around all day, and decides to dispose of the carcass.  [1] At the top of the hill, the moose has nothing but gravitational potential energy.  Let’s ignore the chemical energy stored inside the moose (it won’t change), and regard any other types of energy as negligible.  The hunter gives the moose a very slight push, sending it sliding down the hill.  [2] Half way down the hill, moosie’s gravitational potential has been halved.  Most of it has been converted to kinetic energy, but some of it has been lost to the Work done to friction and drag.  [3] At the bottom of the hill, all of the gravitational potential has now been converted to kinetic energy.  A little more has been lost to friction and drag. [4] Having slid up to the opposite side of the valley (at half the height of the starting position), the moose has regained half of its initial gravitational potential energy.  It still has some kinetic energy left over, but even more energy has been used resisting friction and drag.

Two

The Romantic Cruise

Harriet and Kenichi decided to go on a romantic weekend sailing cruise.  [1] Initially, their yacht is at rest (no energy).  [2] A gust of wind blows against their ship’s sails, doing work on the ship (giving it kinetic energy).  [3] The wind stops, and by now the yacht is experiencing a significant drag force as it glides through the water.  It is losing energy.  [4]  The Work due to drag brings the yacht to a stop, and returns it to a state of ‘no energy’.  Of course, saying that the yacht has no energy is a bit of a lie in that there will be energy stored in Kenichi’s digital camera batteries, Harriet’s battery powered hair straightener and the couple’s romantic dinner for two.  However, those energy sources are ignored as they have no influence on the broad-scale sailing experience.

Recapitulation

Opening this one-way discussion was an explanation that boiled down to energy giving things the ability to push other things.  In this discussion, the words ‘push’ and ‘pull’ were synonymous.  Push is what initiates movement, and also what brings things to a halt.  Whenever energy is mentioned – however abstractly – it should be possible to identify how this concept of push is involved.  As a simple example, oil reserves store energy which will eventually allow the push required to move cars, buses, trains, ships and aeroplanes.  An ‘energy crisis’ is a big deal because if you can’t push and move things around your country (like food), things pretty much come to a standstill.

In the second round, different types of energy were identified.  Each type of energy gives an object the ability to push, and each type arises from different circumstances regarding phenomena like gravity, motion, magnetism and electricity.  One special case was that of chemical energy, in that it arises not from an object’s situation, but rather from the configuration of electrons.  The idea is that to make use of chemical energy, a chemical reaction takes place that liberates energy as push. With this as the exception, a point was made that objects ‘with’ energy are in a physical sense the same thing as they are ‘without’ energy – where as a person with a potato is physically different to a person without a potato.

The types of energy can be generalised into two categories: kinetic (moving) and potential (not moving).  Potential energy is real, but it can be hard to identify.  Energy is almost always an exercise in perspective and relativity, because energy ‘yardsticks’ are hard to come by.

Work, here a technical term, is energy as it is transferred between systems.  To transfer energy (“do work”), you need to push an object, and it has to move through a distance.  Just pushing won’t transfer energy: a helicopter parked on top of a skyscraper loses no energy, even as it continues to push down on the building.  Only if it were to move, then its energy would change.  Work is mathematically defined as the product of force and distance, and then we considered cases where the force applied was not in the same direction as movement.  This introduced some mathematical tools like vectors, the dot product and the line integral.

Friction and Drag are two forces that can be experienced when something moves.  Friction comes from the continual formation and breakage of molecular bonds, and Drag is due to you running into tiny particles of fluid as you move.  I didn’t explicitly point out that these forces, when experienced as an object moves through a distance, constitute Work.  Thus energy can be lost as a moving object does Work against friction and/or drag.

Power, another technical term, is how fast energy is transferred.  It is measured in Watts (joules per second).  Kilowatt-hours, the units of energy as seen on electricity bills everywhere, are directly convertible to Joules.  The kilowatt-hour, however, is a large amount of energy of magnitude suited to measuring electricity consumption.

The End

Well, I think that’s enough for now.  Please let me know if I’ve left you in a state of confusion, dear reader.  What’s been discussed represents a Classical view of energy – in other words, energy as experienced on scales greater than that of the atom but less than that of the galaxy.  Modern physics shows that things behave differently on very small and very large scales, and as such has developed concepts such as quantisation of energy and mass-energy equivalence.  Un-be-liev-able!  So when you think about it, the only thing that ends here is Cosmospostman’s Introduction to Energy.

Cosmospostman’s Introduction To Energy 2

Energy of a system

A system, for the purpose of energy analysis, is defined by an arbitrary, imaginary boundary that isolates one or more components from the rest of the world.  Having established a border, it is possible to keep track of how much energy comes in and out of the system.

Here the system is defined as "the ball", to which the footballer is an external influence.

You may recall that there are many different types of energy, which are categorised as either Kinetic or Potential.  By the way, the list given in part one was by no means exhaustive!  It’s possible for a system to have every single type of energy, although at the end of the day its total Energy (E) is equal to the sum of the Kinetic and Potential components, ie.

E = K + U

"Garden bed": Total Energy = Kinetic energy + Potential energy

There are a few more rules with regard to energy in a system:

1. It is possible to convert energy between forms inside the system, for example, from Gravitational Potential to Kinetic.  The system’s energy can be rearranged into any combination of forms, including forms that weren’t present to begin with.  If I were to hold a marble above my head, the system of “the marble” would contain nothing but gravitational potential.  When I let it go, the marble’s potential energy is converted to kinetic energy.
2. The conversion process itself does not add or remove energy from the system, however
3. In the process of conversion, some of the total energy may be lost to mechanical inefficiencies such as friction and drag (more on them soon).

I imagined such partitioning of a system’s energy to be similar in concept to partitioning of space in a computer’s hard drive.  Or perhaps altering the selection of plants grown in a vegetable patch.  Point is, the total amount of energy/storage/dirt remains available and you can arrange things however you like.

Remember how energy was described as ‘the ability to push’, where ‘push’ is defined as ‘exerting force through a distance’?  Energy is measured in units of joules.  One joule of energy enables a system to exert one newton of force over a distance of one metre.  The joule is a measure of push capability, or energy.

It is worth pointing out the relativity of energy.  Suppose that I’m holding a tennis ball.  It’s still; the way I see it there’s no kinetic energy.  Now I tell you that I’m riding the Shinkansen, and you’re standing on the platform as I fly past at 300km/h.  You’re telling me that clearly the ball has twice the kinetic energy of a grand-slam tennis serve, even though I fail to see the ball moving at all.  Another example: you’re lying down in a hammock, barely above the ground.  Let’s say you have no gravitational potential.  Then I come along with my excavator and dig a trench underneath you, and before you know it, you’ve got potential.  Gravitational potential.  But you haven’t moved a muscle.  The reason you’ve gained energy is that your situation has changed.

Energy can be confusing because most of the time the ‘point of zero-reference’ is arbitrarily defined.  To one person, a tennis ball may have kinetic energy, but to somebody else in a different frame of reference it’s still.  More often than not, it’s best to think about change in energy, a concept that does not need a point of ‘zero energy’ to be defined.

Friction and Drag

Molecular bonds between the molecules (blue and yellow circles) of two objects being broken as the blue object is lifted off the yellow surface

Whenever two surfaces are in contact, molecular bonds between the two materials are formed.  The two materials are attached, in a way.  To separate them requires the breaking of these bonds, which in turn demands a small amount of energy.  Thus, when something rubs or moves over a surface (like a book being pushed across a table, a car driving on the road, or balls inside a bearing), molecular bonds are continuously made and broken.  The amount of force required to break such bonds is called frictional force.  ‘Energy loss to friction’ usually means that an object is spending some of its energy breaking molecular bonds with the surface it moves on, in order to continue moving.

Ball farm (CC licensed)

Imagine you’re surrounded with brightly coloured plastic balls.  Plastic balls make it hard to move, right?  I mean, you try to walk to the other side of the enclosure and you’ve got to keep pushing them out of your way.  This situation is similar to the one we face every day.  The air that surrounds us is composed of many little molecules, or ‘small plastic balls of air’ if you will.  While air molecules are smaller and lighter than plastic balls, they still need to be pushed out of the way if you want to move.  The effort required to do this is minimal at low speed, but is well known to the road cyclist at the front  of the pack, and to anybody who has ever stuck their hand out the window of a moving car.  The force felt on your hand as you hold it out in the wind is called the drag force, and will slow you down unless you use some additional energy to negate the effect of drag.

Energy Transfer: Work

In the last Energy post, I explained that there were two types of energy: kinetic and potential.  Then there’s Work, which here appears as a technical term with a slightly different meaning to the everyday word of the same name.  Work is the expenditure of energy.  Work is energy as it is transferred between systems.  Work is what happens when things are pushed.  “The footballer transferred some energy to the ball” could be rephrased into a the more technical, “The footballer did work on the ball”.

You see, Work has the same unit as energy – Joules.  In the case of energy, one joule is the ability to push one newton through one metre.  For Work, one joule is the push of one newton through one metre.  It’s as if there were two words for money, one word when it’s in the bank (energy) and one for when you spend it (work).

Got that? When you transfer energy between systems, the process is called Work.  We can also express the situation as

W=ΔE

That is, Work is the change in the amount of energy.  In order to do work, which is to say in order to give something energy, there needs to be a push or pull.  Work may be done either through direct contact (kicking a ball), or ‘action at a distance’ – where force is exerted without contact.  If you’ve ever been amused by a magnet and a paper clip, you would be acutely aware of how the two can interact with each other and exert force without coming into contact.  Energy can be transferred by exploiting such mechanisms, not just by physical contact.

Vectors, the Dot Product and Work

We’re going to describe Work using maths, but first let me briefly introduce a mathematical tool we’ll need: the vector.  Vectors allow you to keep track of amount and direction.  A commonly used vector quantity is velocity, which encapsulates an object’s speed along with the direction it’s travelling.  For example, ’20km/h, at 23 degrees east of north’ has exactly the information a vector needs to have: amount (20) and direction (N 23 E).  Simple.  Vectors can be represented graphically as arrows, but we’ll see more of that soon.

Two vector quantities that pertain to the study of energy are force and displacement (how far something moves).  Remember that you apply force when you push things, regardless of whether they move or not.  You can apply an amount of force in any direction you like, and you can travel a certain distance in any direction you like as well.  Recognise that they both contain a magnitude (amount of force, distance) and a direction.

Suppose I’m dragging a dead moose along the ground.  I’m applying force of, say, 15 newtons through the rope, which is at 30 degrees to the ground.  The moose moves horizontally to the right, for 10 metres.  Let’s put all of that information in a diagram:

The force vector is shown as a blue arrow, and the displacement vector is in brown. The length of the vector represents the amount, and the arrow points in the direction in which the vector acts.

Note that the diagram is not to scale, and that the two vectors have a different unit of measurement (which is why the brown one, although it has a smaller number, is longer).  What the diagram shows is that the moose is being pulled 10 metres to the right, as in brown.  The 15N of force (blue) acts at all times as the moose is dragged, and doesn’t change in either size nor direction.

Clearly, the force vector is not in the same direction as the displacement vector.  Not all of the force exerted is being used to move the moose .  How much force, then, is in the direction of displacement?’  Let’s investigate ‘how much’ of the blue vector is in the direction of the brown one, by changing the angle between them:

Dot product

Let’s call the force vector F, and the displacement vector d.  The lengths (‘size’, or magnitude) of these vectors are notated by |F| and |d|, which equal 15 and 10 respectively.  At any one time, the amount of force being applied to move the object – the numeric answer to the ‘how much’ question above – will be |F| cos θ, where θ (theta) is the angle between F and d.  In the case of the moose, only 13N of the original 15N is being used to pull the moose.  The other 2N goes towards trying to pull the moose up off the ground, but that’s not happening.

OK, so now we know that it’s 13N of force instead of 15 that’s moving the moose.  The moose is pulled 10 metres horizontally with a force of 13N.  Multiplying the force applied by the distance moved gives a value for the Work done on the moose, in other words – how much pulling was done.  We can summarise the relationship between Work done (ie, energy given to the moose), force applied and distance moved with a constant angle by

W = |F||d| cos θ

This equation can be expressed in shorthand using something called the Vector Dot Product, which here looks like

W = F‧d

The Line Integral and Work

The dot product definition of work is only valid when (i) the angle at which force is applied remains constant, (ii) the amount of force remains constant, and (iii) movement is in a straight line.  For cases where one or more of these conditions is not met, a more general definition of work is needed.  Enter the line intergral.

The blue arrows, while no longer technically vectors, still represent the amount of force applied (after angles have been considered) at intervals along the path of movement

Consider the familiar: where our moose hunter applies constant force in a straight line.  We’ll assume that any angles have already been taken into consideration, ie F is a constant 13N.  Let’s draw this as a graph of Force vs Displacement, on the left.  Note that the graph does not indicate the angle at which force is applied, only the amount.  The work done is represented as the area between the force arrows and the displacement arrow, which here is W=Fd.  The shaded area is a rectangle, simple.  Expressed as an integral, it’s W=∫ F ds.  All this means is, ‘Find the area between the force arrows F and the displacement s, and call it the Work done”.

Now imagine that the moose hunter varies the amount of force being applied to the moose (either by changing the amount or angle at which he pulls).  This would look more like the middle graph, although the concept remains the same: Work is the the area between the force arrows and the displacement arrow.

Imagine now that our moose hunter took a curvy path instead of a direct one, perhaps to avoid some trees.  This is pictured on the right.  Although the ‘displacement vector’ is now curved, that doesn’t stop us finding the area.  In terms of the mathematics required to work things out, it’s exactly the same as before – as long as we’ve got force able to be expressed as a function of displacement.  It doesn’t matter how curvy a path Ms Moose Hunter takes, it’s still essentially W=∫ F ds.  Instead, it’s awarded a Line Integral notation for its efforts, and is now written as W=∮ F ds.

To reconsider the angle between force applied and distance moved, all we need now is to reintroduce the dot product (1), which expands to (2)

1.  W =∮ F‧ ds

2.  W =∮ F cos θ ds

The expressions above signify a process of finding the the ‘area’ between the force arrows and displacement.  It says, ‘Start with the displacement curve s.  Let’s chop it up into infinitely small pieces, ds.  For each piece ds, multiply it by the force F and cos θ, as experienced at that point along the curve.  Add the individual results together and you’ve got the Work done.

Cosmospostman’s Introduction To Energy 1

People discuss energy every day – renewable energy, energy independence, energy stockpiles and ultra-cute, high-energy black puppy dogs are a few examples I can think of right now.  Everyone talks about it, but few people know what it really means.  My sister did a year 9 Science report on Energy – and while promising to furnish us with definitions, provided nothing more than a comparative review of coal vs solar vs biofuels vs whatever.

Given that ‘energy’ is such a key player in this modern life of ours, I think very few people have a grip on who this slippery fellow called Energy really is.  Let me personify: she’s a moderately attractive brunette in a tight black leather jacket employed by the Moscow Circus as a contortionist.  No – he’s an old granddad gliding swiftly along on a motorised scooter, flatuating in the hot summer breeze.  Actually, some have even reported Energy to be the fat lady behind the counter at the local school tuckshop [canteen] serving meat pies to the twelve year olds.  Point is, energy takes many forms, and is hard to pin down and identify.  So I’d like to get up on my soap box and expose the true identity of this 21st century fugitive.  Did I mention he’s invisible?

What exactly is energy?

Let’s start with a loose definition: “Energy is the ability of something to ‘push’ (or pull) other things, ie, to apply to an object some force over a distance“.

That little boy's got energy! (CC licenced)

It’s all about being able to push.  If you have energy, it means you can push things – simple as that.  If you have no energy, you can’t do anything at all.  More on that later, but for now imagine you’ve come home from a long hot day on the mango paddock and you’re completely buggered.  You slouch down on a chair and vegetate.  Mother Dearest yells from the kitchen, ‘for the seventh time, somebody bring those bloody clothes in off the line IMMEDIATELY or I’m going to hit the roof!!!!’ (not really).  You reply, ‘but mum, I’ve got no energy!  I can’t do that! Triangulate and chillよ!’  What you mean to say in a more technical sense is, ‘Oh, I’d love to lend a hand Mother Dearest, but I’m physically incapable of doing so because I’ve got absolutely no energy left in me whatsoever. What that means is, I completely lack the ability to remove the clothes from the line, and furthermore, am unable to apply force to the clothes trolley over the distance it takes to push it back to the house. I’m so sorry.  I’m sure my sister can lend you a hand, though’.  Energy means you can push things.  If you can’t push things, you can’t do anything.  Recapitulation of ‘force through distance’ and ‘push is everything’ later, but I’m hoping that’s enough for now.

Types of energy

Energy comes in two varieties: kinetic (moving) and potential (could be moving), assigned the symbols K and U respectively.  Kinetic energy means, ‘because an object is moving, it is able to push things’.  Just picture a pedestrian being pushed over by a moving car.  Potential energy means, ‘While not moving, an object is still able to push things due to the situation it is in’.  Imagine lifting weights above your head, and how in such a situation they have the ability to push down on you.  If that doesn’t work, imagine Stephen Conroy [link] pushing a pile of poo [link] up a hill.  He’s half way up and stops for a breather.  Even though the poo is not moving, it has gained some gravitational potential energy.  In other words, the poo now has the ability to push back down on Conroy, which is what will happen unless some restraining force is placed upon the poo in the meantime.

Every type of energy can be categorised into either kinetic or potential.  Here are a few examples:

• Kinetic:
  • Translational, if the object is moving in a line
  • Rotational, if the object is moving in a circular fashion
• Potential:
  • Gravitational, due to interactions between two or more bodies with mass
  • Electrostatic, due to interactions between two or more bodies with charge
  • Spring/Elastic, the energy stored in a stretched spring or rubber band
  • Nuclear (aka Chemical), where energy is stored in the electron configuration of an atom. Little to do with nuclear power.
• Special cases:
  • ‘Thermal Energy’, or Heat, is merely the vibrations of an object’s constituent atoms (energy here oscillates between potential and kinetic)
  • ‘Food Energy’, is the same as Nuclear Energy above.  Digestion of food is a chemical process which ultimately leaves the body’s electrons in a higher state of energy.

Dear reader, I challenge you to suggest a type of energy that does not fit into either the Kinetic or Potential category.

How Energy Exists

Evan has many golf balls.  Penny has gained a lot of respect recently.  Intrabella lost her booze cache.  Alfred has energy.  Here, as is the case most of the time when communicating in English, there is a sense of ‘active possession’.  If you have something, like golf balls or booze, you can hold it.  Make an effort to get it and it’s yours.  It belongs to you.  Even intangible things like respect need to be earned, and one could in a way consider themselves to be an ‘owner’ of some respect.  I just wanted to clarify that feature of language before asking, how does something attain the ability to push?

One answer to such a question would reference the transfer of energy, ie. something else pushing on you and you gaining energy.  While accurate, I find that such an explanation to be self-referencing, not to mention revealing little about the nature of energy.  Instead, I offer reasoning based on the notion of ‘passive possession’:

Is a watermelon the same at the bottom of an elevator shaft as it is at the top?  Yes, in fact I could take the watermelon up and down the elevator all day and it would not change one bit.  Barak Obama was reportedly caught saying during his recent election campaign, “You can take a watermelon to the top of an elevator shaft, but it’s still a watermelon”.  This infamous quote caused a considerable amount of outrage in the watermelon industry, and amongst Republicans – who misinterpreted this statement as a jab at Sarah Palin’s watermelon-like qualities (whatever they happen to be).   However, the energy (in particular, gravitational potential and kinetic) of the melon varies as I move up and down the building.  It seems that watermelons remain identical with themselves no matter how much energy they have.  How, then, can a watermelon have energy?

Low and high energy watermelon (CC Derivative)

I would argue that having energy is different to having golf balls and booze.  A person with lots of alcohol is physically not the same as a person without alcohol, where as a body physically remains the same no matter how much energy it has.  The way I see it, you have energy due to the situation you happen to be in, quite different to wearing a backpack full of goon.  Energy is really just circumstantial.  As such, it may be confusing to refer to a ‘quantity of energy’.  Furthermore, the idea of ‘energy possession’ is actually misleading – ‘state of energy’ or even ‘level of energy’ do a better job of taking stock of the situation, because objects don’t really have energy; rather they have the attribute of energy associated with them due to their predicament.  The exception to this way of thinking is Chemical energy, which comes about by moving electrons inside an object so that they are better poised to push.

Simply put, energy, rather than being intrinsic, arises from situation.  It doesn’t really exist in the sense that it’s more of a concept than a physical entity.

Applicability of the model

Let’s stop and think.  To do almost anything in this universe, you need energy, right?  By our definition, this means push is involved wherever energy is.  Let’s see… setting something in motion requires you to push it, either directly or by way of force-at-a-distance (like gravitational or electrostatic pull).  Remember that once in motion, bodies remain in motion unless an external force acts on them, which is why space probes such as the Voyager twins continue speeding off to galaxies far, far away, even after flying through space for over 30 years already.

‘Electricity grid’ is the name given to a regime that pushes electrons through wires all day long.  On a smaller scale, computers need energy – for they need to push electric charges around a circuit board in order to store and operate on information.  Similarly, biological thought requires that electric pulses be fired (pushed) from neuron to neuron inside the brain.  The production of sound requires air molecules to be pushed into a state of vibration, and the propagation of a sound wave is nothing more than air molecules pushing on each other.  Can you think of any action that does not require push?

Summary

1. Energy is the ability to push or pull things (apply force through distance)
2. The ability to push arises from an object’s position in regards to its surroundings
3. Push/pull is at the core of all action
4. Energy is classified as either Kinetic or Potential

I posted this with the intention of being clear-cut and simple, so please tell me if your reading experience suggests otherwise.

PS. Bumdom, I have matched your previous post; burden of reciprocation is now on you

PPS. Changed the theme to one which gives more text per row and a better font, on my browser anyway.