# Hi,I'm in high school and have been given an assignment regarding

by sahil_n
Tags: assignment, school
 P: 6 Hi, I'm in high school and have been given an assignment regarding heat, which is a term I don't fully understand mainly because any definition I have come accross makes use of the term Energy. This leads me to my question: What is energy? I know of the existence of the thread 'What is energy?' (http://www.physicsforums.com/showthread.php?t=507345) and I've had a look at it but that thread soon became quite technical (I'm 14), went off track from the original question (i.e what is energy?) and moreover, raised more questions than what it answered. Now, I must let you know that I have researched this extensively and cannot get a reasonable explanation. Most sites/textbooks claim it to be the capactiy to do work. Capacity? So is it like a gas tank? in my body? that when full makes me run really fast? This is the kind of useless visual imagiry I get when I see definitions like this. Here is my (own made up) understanding of energy so far: It exists everywhere there is matter. It seems to be closesly related to matter. It has different forms. It is transferable. BUT........what is it? what does it look like? does it even have a 'look'? Utterly confused as you can tell. Please help. Sahil
 HW Helper Sci Advisor P: 6,352 Energy can be thought of as a measure of the ability of something to apply a force through a distance. Energy is defined this way because we find it to be useful. It is useful because it is a quantity that is conserved in physical interactions. Because it is conserved, we tend to think of energy as something tangible. But it is really just a mathematical quantity that is associated with a system of matter. Energy and momentum are similar. They are both mathematical quantities that are useful in physical interactions because they are conserved. But whereas momentum is always conserved in the same form (ie. mass x velocity) energy is not. Energy exists in many forms: eg. kinetic energy, gravitational potential energy, electrical potential energy electromagnetic energy (e.g.light). The total energy is always conserved in some form, but not necessarily the same form. AM
P: 351
 Quote by sahil_n Hi, I'm in high school and have been given an assignment regarding heat, which is a term I don't fully understand mainly because any definition I have come accross makes use of the term Energy. This leads me to my question: What is energy? I know of the existence of the thread 'What is energy?' (http://www.physicsforums.com/showthread.php?t=507345) and I've had a look at it but that thread soon became quite technical (I'm 14), went off track from the original question (i.e what is energy?) and moreover, raised more questions than what it answered. Now, I must let you know that I have researched this extensively and cannot get a reasonable explanation. Most sites/textbooks claim it to be the capactiy to do work. Capacity? So is it like a gas tank? in my body? that when full makes me run really fast? This is the kind of useless visual imagiry I get when I see definitions like this. Here is my (own made up) understanding of energy so far: It exists everywhere there is matter. It seems to be closesly related to matter. It has different forms. It is transferable. BUT........what is it? what does it look like? does it even have a 'look'? Utterly confused as you can tell. Please help. Sahil
Actually, Richard Feynman, the renowned physicist blew his stack when he saw several definitions of energy in text-books he was reviewing for California State education. His wife heard him thundering from downstairs. Too often they were completely wrong. So you don't have to worry about being confused.

I would cut to the chase, and examine directly the UNITS that energy is measured with, and how they are put together. This will give you something of an inductive exercise, and you can use some sleuthing skills. Look up each unit and see how it is defined and used. If you don't understand the units alone involved in energy and their relationship in energy, then how will you understand energy itself?

That may sound hard at your level, but it will pay off later, and give real formal meaning to the concepts. Right now you are just trying to get touchy-feely understanding just using ordinary words and ideas. That's good too, but it's not working for you, apparently.

And besides, scientists themselves often have to deal with things they cannot visualize. They have to work mathematically. You may as well get used to it.

P: 351

## Hi,I'm in high school and have been given an assignment regarding

I suggest you start with the Wiki 'Joule' page, and examine the units kilogram, metres, seconds, and the examples of what a Joule can do for you down the page.

http://en.wikipedia.org/wiki/Joule

Never mind the N•m etc. parts there for now.

energy is a huge topic and takes many forms. You can only bite off a bit of it at a time.
 P: 28 Hi Sahil, I wonder if you would be able to aswer: "BUT........what is it? what does it look like? does it even have a 'look'?" For the concept of force? In what way are we aware of it?
 P: 5 Energy has a very intuitive meaning. In fact, you can FEEL energy. The next time you go up a flight of stairs, notice how tired you get at the top (depending on your level of fitness, of course). Or do a long bike ride, run, or walk, and notice if you have to eat more afterwards to relieve your hunger. Energy is defined as the integral of Force over Distance (or for a constant force, Force * Distance, aka E = F*d). So when you do some exercise that makes you apply a force for a long distance, you are using a lot of energy (in the form of chemical energy stored inside your body). Going up a long flight of stairs requires a lot of energy, since you have to oppose the force of gravity in order to move upwards.
P: 5,462
Hello Sahil,

 It exists everywhere there is matter. It seems to be closesly related to matter. It has different forms. It is transferable.
It also exists, as electromagnetic energy (already mentioned), in some places where there is no matter.

In Physics (and maths) there are several basic ideas we use that we only know from interactions.

This is called 'black box' theory because we don't know what is in the box but we know what happens (repeatably) when we interact with the box in a particular way.
Because we can observe interactions we conclude that there is something in the box so we call this 'energy'.

Here are some other useful interactions

Energy is always positive.

Energy is a scalar

For energy related to matter, energy is an extensive property. This means that the total is additive. So for instance to get the total energy in a body we add the energy contained in each of its parts.

(Compare extensive property with an intensive property such as temperature. For an intensive property we do not add but have one value to represent the whole)

I mention this because you said you are studying heat (extensive) and presumably temperature (intensive)

A caution about approaching energy through units. There is another very different quantity in Physics with the same units as energy (N-m) called a moment. I expect you have met this in mechanics?

One way to look at energy is to think of value and money in economics. In economics, value is very hard to define and explain. How do we compare the relative worth of say, a haircut and a motorbike? Money is used as a medium of exchange.
In a similar way energy provides a medium of exchange for different branches of Physics. Much scientific work in the late eighteenth and nineteenth centuries went into the the 'value' of this exchange between mechanical and heat energies. We have named the units of energy after one of the pioneers- the Joule.

go well
P: 6
Wow, thanks guys!

 Quote by Kiril Hi Sahil, I wonder if you would be able to aswer: "BUT........what is it? what does it look like? does it even have a 'look'?" For the concept of force? In what way are we aware of it?
I guess Force is another term that I've used loosely just like the term 'Time' (and I know there is a thread in this category entitled 'What is time?'). Unlike energy however, I can atleast comprehend force and it's not as un-settling. Well, here's my attempt at explaining what force is anyway:
Since I always look at all interactions in the physical world as atomic (or sub-atomic) , I look at force as a bunch of atoms pushing against each other and the more they are made to push against each other, the more force that is being generated. I may be completely wrong. How is this force being generated? I don't know.

I can't accept definitions like capacity to do work simply because I can't get a visual image of what's happening at the atomic level.

Okay, so I'm trying to convince myself that energy is simply a way to measure other....things. Studiot, your extensive use of the word value helped with this.

danR, I had a look at the wikipedia entry for Joule. It seems consistent with what jonspalding said about it being the integral of Force over distance. More precisely, I've accepted that it's proportional to a force being applied to a certain mass over a certain distance. However, I'm confused now about the over bit. I thought integral meant area under a curve. I've drawn a graph of (some made up) force (y-axis) against distance (x-axis) and when this force is constant, the area under the curve is simply the area of a rectangle (i.e force * distance). Am I doing something wrong here? Am i wrongly interpreting force over distance as force against distance?

Thanks again,
Sahil
HW Helper
P: 6,352
 Quote by Studiot Here are some other useful interactions Energy is always positive.
!! Energy can certainly be negative!

AM
P: 834
 Quote by Andrew Mason !! Energy can certainly be negative! AM
Are you sure?

I know energy transfer can be negative, but what is negative energy? Is this a parallel to anti-matter?

Take kinetic energy for example: KE = mv^2/2

This value will always be positive, even if velocity is negative.

Edit:
I found this http://www.wisegeek.com/what-is-negative-energy.htm
is that what you're referring to?
PF Patron
Thanks
P: 3,979
 Quote by DragonPetter Are you sure? I know energy transfer can be negative, but what is negative energy? Is this a parallel to anti-matter?
I believe he/she is talking about the negative - energy states that the dirac equation allows for electrons.
P: 5,462
 !! Energy can certainly be negative!
I am disappointed as this thread is not a philosophical debate it is an explanation for a high school pupil.

Energy is a positive definite quantity that can be transferred from A to B or B to A according to circumstances.

Apart from speculative physics no one has ever come across a bowlful of a negative quantity that has the same properties as energy.

Since I am replying I had prepared further information for sahil in the attachment.

You asked about the introduction of an integral of force over distance.

Yes indeed energy can be counted as an area.

We say that work is done when a force moves is point of application.

The movement is usually called displacement rather than distance so I have labelled one axis that way on my graphs.

Now the graphs are not the same as say, the graph showing the conversion of $to £. The area under such a graph has no meaning. All the meaning is in the line so we can read off say £8 = 10$.
I have shown this in fig 1 in the attachments. The only valid values lie on the line £ = contstant x \$

However we can allow our force to have any value and move any distance so any point in the xy plane is acceptable. this is shown in my fig2

Taking some particular values say F = 10 and d = 1 we can plot this as a point.
The movement must have started out at zero displacement and moved through all possible values of displacement < 1 until a displacement of 1 was reached.
If F is a constant force such as gravity, the action will have taken place along the dashed line in Fig3 parallel to the x axis at F=10.
The energy is equal to the work done = force times distance which is equal to the area of the rectangle under bounded by the two dashed lines.

If you like it is made up of all the little contributions from d = 0.1; d = 0.2 etc. That is what is meant by force over distance rather than just force times distance. The integral can also be used to calculate sums (if you have not yet covered this you will) and this is an example.

The energy figure or shape is not always a rectangle.
In fig 4 I have shown what happens if we extend a spring.
At the outset the restoring force is zero so no energy is used to extend it.
At some value of extension d there is a restoring force F which has built up from zero to F.
So we take the average or
$$\frac{{\left( {0 + F} \right)}}{2}$$
for the force and our area is a triangle as shown.

In fig 5 I have put some other numbers to the constant force graph for comparison

In figs 6, 7 and 8 I have shown different ways to obtain the same energy as

E = force x displacement

E = half the force x twice the displacement

E = twice the force x half the displacement

go well
Attached Thumbnails

P: 351
 Quote by sahil_n Wow, thanks guys! ...However, I'm confused now about the over bit. I thought integral meant area under a curve. I've drawn a graph of (some made up) force (y-axis) against distance (x-axis) and when this force is constant, the area under the curve is simply the area of a rectangle (i.e force * distance). Am I doing something wrong here? Am i wrongly interpreting force over distance as force against distance? Thanks again, Sahil
'over' means little more than 'divided by'. V=d/t, velocity equals 'distance over time'. It's just a math idiom. I can't help much any more. I have a course coming up shortly. Won't be on PF much.

'Energy' is what you might call an 'abstract object'. Abstract objects are best dealt with by fiddling with them, looking stuff up, scratching your head, and getting your hands dirty by manipulating the units, looking at the examples of what a 'Joule' can do, and moving on from there and exploring other manifestations of energy,understanding the component units, etc., reading what other people have said. It is understood by what it does better than what it 'is'.
PF Patron
P: 10,406
 I can't accept definitions like capacity to do work simply because I can't get a visual image of what's happening at the atomic level.
I can see that. The problem is that the phrase "capacity to do work" refers to what CAN happen. Effectively you can take a snapshot of something before and after and measure the changes and figure out the amount of "change" that happened. However, because we know how the different forces work and the amount of each needed to produce changes in objects, we can predict what will happen before the change occurs and condense it down to a simple number. Saying a photon has 100 keV of energy means that when that photon strikes something we can predict the probable reactions.
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P: 6,352
 Quote by DragonPetter Are you sure?
Of course. Orbital energies are always negative. The kinetic energy is always positive, but kinetic + potential energy < 0. (If it has positive total energy, it will escape orbit). If a negative charge at a position in an electric has positive potential energy, then a positive charge at the same position will have negative potential energy. They can't both have positive energy.

AM
P: 5,462
 Are you sure? I know energy transfer can be negative, but what is negative energy? Is this a parallel to anti-matter?
There is a difference.

The assignation of sign to a quantity such as energy is merely a bookkeeping exercise, determined by external matters. It is a sign convention. What it tells us is which way the energy will be transferred or will flow. The energy itself is always positive (or negative if you choose the opposite sign convention).

Being matter or antimatter is inherent in the object itself, their properties are such that external circumstances play no part in determining sign. An electron has a negative charge and a positron a positive charge regardless of external matters. The only influence external matters have is the choice of sign convention they still will have opposite charge.

Consider Andrew’s example.

Yes I can accept a universe which contains only a single charge. But in such a universe the only possible electric field is the one due to the single charge.
The only way to introduce an independent electric field is to introduce (at least) a second charge.
So now we have a universe with two charges.

Let us fix one charge (call it C1) and position the other (call it C2) at point P.

The potential energy of C2 at P is defined as the work done to bring C2 from infinity to P.

First consider the situation where C1 and C2 have the same charge sign.
As we move C2 from infinity there is a force of repulsion between the charges..
Clearly unless C1 is held in place by the rest of the universe it will move off, stage left.
So the rest of the universe, through the medium of C1, exerts a force on C2.
The point of application of this force is moved from infinity to P so the work done is the integral of F.dr over this distance.
Energy is transferred from the universe to C2

Now consider the situation where the charges have the opposite sign.
F is a vector and now points in the opposite direction.
So the scalar product (energy) now flows in the opposite direction.
Energy is transferred from C2 to the universe.

Actually in truth the energy belongs to both charges, it is only for ease of calculation that we assign it to only one.

You can call this ‘negative energy’ if you like but in both cases a positive quantity is transferred, it’s just the direction that is different.
P: 6
Thanks studiot for those examples. The graph that I drew was similar so atleast we are on the same page. However, my confusion regarding the over bit still remains. Yes, I know over means division and that's precisely what's confusing me. Please refer to an earlier post from jonspalding.

 Quote by jonspalding Energy is defined as the integral of Force over Distance (or for a constant force, Force * Distance, aka E = F*d).
So is it force / distance or force * distance?
P: 6
 Quote by Studiot There is a difference. The assignation of sign to a quantity such as energy is merely a bookkeeping exercise, determined by external matters. It is a sign convention. What it tells us is which way the energy will be transferred or will flow. The energy itself is always positive (or negative if you choose the opposite sign convention). Being matter or antimatter is inherent in the object itself, their properties are such that external circumstances play no part in determining sign. An electron has a negative charge and a positron a positive charge regardless of external matters. The only influence external matters have is the choice of sign convention they still will have opposite charge. Consider Andrew’s example. Yes I can accept a universe which contains only a single charge. But in such a universe the only possible electric field is the one due to the single charge. The only way to introduce an independent electric field is to introduce (at least) a second charge. So now we have a universe with two charges. Let us fix one charge (call it C1) and position the other (call it C2) at point P. The potential energy of C2 at P is defined as the work done to bring C2 from infinity to P. First consider the situation where C1 and C2 have the same charge sign. As we move C2 from infinity there is a force of repulsion between the charges.. Clearly unless C1 is held in place by the rest of the universe it will move off, stage left. So the rest of the universe, through the medium of C1, exerts a force on C2. The point of application of this force is moved from infinity to P so the work done is the integral of F.dr over this distance. Energy is transferred from the universe to C2 Now consider the situation where the charges have the opposite sign. F is a vector and now points in the opposite direction. So the scalar product (energy) now flows in the opposite direction. Energy is transferred from C2 to the universe. Actually in truth the energy belongs to both charges, it is only for ease of calculation that we assign it to only one. You can call this ‘negative energy’ if you like but in both cases a positive quantity is transferred, it’s just the direction that is different.
So....just like a vector where the magnitude can never actually be negative but can only be considered negative depending on the direction with respect to another vector in the opposite direction?

I've just started learning about vectors....

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