Explaining E=M C^2 to 14 year olds ?

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In summary: The total 'Energy' (E) of some Matter (M) is equal to its speed (C), cubed (^3). So if you take a ball and drop it from a window it will make a depression in the ground where it lands. If you double to height (and so the ball’s speed) the hole will be eight times deeper. You have doubled the height (2 x the original) and speed of the ball and 2 x 2 = 4. So you get 8 times as much energy to make the depression in the ground.".In summary, Explaining E=M C^2 to 14 year olds is difficult because they must understand that energy and mass
  • #1
AlisonArulia
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Explaining E=M C^2 to 14 year olds ?

Hi,

I have been asked to give a "very" brief talk to to some 14 year old kids on the subject E=M C^2. I can write this all down using formula and it makes sense. But to "say" what this means at the right level, I am having BIG problems. I can only talk for a few minutes. So I need to keep it very simple. I really want the kids to come away with an understanding.

I realize that this may be way below the level that most people on this forum will be used to (talking to 14 year olds) but I would appreciate any help here. - specifically the end ... what on Earth do a say here with our writing anything down. OMG.

Many thanks

Here is what I have prepared at the moment.

__________________

E=M C^2
What does this mean?
It is (very basically) a formula which shows that energy and mass are the same thing in other words the amount of Energy that some Matter is equivalent to and vise versa.

E = Energy
From the Greek word Energeia meaning activity. This is a measure of the amount of work that can performed by a force. There are many different forms of energy such as Potential (stored), Thermal (heat), Kinetic (motion), Electromagnetic (e.g. Microwaves, Light, Gamma Rays, Microwaves, etc), Elastic (distortion), Etc, you should remember that the words in brackets are single words used to describe, sometimes, very complex forces.
Note - Any type of energy can be transformed into another type, but the total amount of energy stays the same.

M = Matter
This is anything that has Volume and Mass
There are many textbooks that still give a definition of mass as anything you can see or touch. This is not true – you can see light but it is not matter. Matter can be best described as anything that takes up space. This can be and size from a single atom (or even part of an atom) upwards.

C = The speed of light (important – see next section regarding C squared)
The letter C is used to denote the speed of light in mathematical calculations (from the Latin word celeritas meaning swift). Light travels, in a vacuum, at just under Three Hundred Thousand km per second (299,792,458m per second).

^2 = Squared
This means to multiply a number by itself. “But” in the formula E=M C^2, the C^2 does “not” mean a number multiplied by itself (regardless of how many books tell you it is). C and C^2 are two totally different things (C is a number and the other - C^2, isn’t). The C refers to the speed of light as a Unit (call it One Light Unit if you want or whatever you want) that’s just “one” unit, and One times One = One. So you do NOT take the speed of speed of light and multiply it by itself (as 1 x 1 = 1).

So, to put it all together –
The total “Energy” (E) of some Matter (M) is equal to its speed (C), squared (^2).
So if you take a ball and drop it from a window it will make a depression in the ground where it lands. If you double to height (and so the ball’s speed) the hole will be four times deeper. You have doubled the height (2 x the original) and speed of the ball and 2 x 2 = 4. So you get 4 times as much energy to make the depression in the ground.

Still doesn't sound very clear - any ideas please
 
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  • #2


AlisonArulia said:
Hi,

...
^2 = Squared
This means to multiply a number by itself. “But” in the formula E=M C^2, the C^2 does “not” mean a number multiplied by itself (regardless of how many books tell you it is). C and C^2 are two totally different things (C is a number and the other - C^2, isn’t). The C refers to the speed of light as a Unit (call it One Light Unit if you want or whatever you want) that’s just “one” unit, and One times One = One. So you do NOT take the speed of speed of light and multiply it by itself (as 1 x 1 = 1).

So, to put it all together –
The total “Energy” (E) of some Matter (M) is equal to its speed (C), squared (^2).
So if you take a ball and drop it from a window it will make a depression in the ground where it lands. If you double to height (and so the ball’s speed) the hole will be four times deeper. This is because …….

You were doing fine till you got to the squared bit. What you wrote sounds like serious nonsence to me. c2 is certinly the normal squaring. One of the most important things when talking to kids this age is not to feed them nonsense. Please drop that part.

Not sure where you are going with the comparaision to kinetic energy but tread caefully.
 
  • #3


Hi there! I'm going to comment on each part of this little talk you're preparing:

E: This section seems good and could definitely be elaborated on more. Energy is such an abstract concept it would help to give a few concrete examples to solidify what you mean by energy.

M: No need to really muddle the matter making the distinction between matter/mass, seems unnecessary to the target audience.

C: Also could be elaborated on more. Perhaps talk about the significance of the speed of light?

^2: This section seems totally irrelevant. I don't really know what you're trying to get at drawing a large distinction between c and c^2, is it units? Regardless, this paragraph didn't even make sense to me so I doubt a 14-yo will fare much better.

Put it all together: seems like you're just giving a really simple example of conversion of gravitational PE to KE to some sort of deformation in the surface. This actually has nothing to do with einstein's equation, though. Useful for the discussion of energy, yes. Also, your numbers you try to put to this example are just wrong. From basic kinematics you see that if you double the height, you increase the speed by a factor of sqrt(2), not 2. Energy doubles, but speed only increases by this amount.

Rather than belaboring a lot of the finer points, you should focus on what comes out of E=mc^2. Namely that anything with mass has an associated energy content regardless of what it is. Give some analogy like you could burn a sheet of paper and light up the room for a split second. But if you were to convert the entire mass of the paper into energy, via E=mc^2, you could light an entire city.

Also something I noticed, no need to set c=1. That usually doesn't happen until a sophomore college SR course anyways.
 
  • #4


1) What on Earth are you trying to say about the c^2? Of course this means c times c. What else?! c^2 has dimensions of velocity squared: m^2/s^2, as it should (compare E=mv^2/2).
2) You talk about work ("This is a measure of the amount of work that can performed by a force."), but without ever explaining what '(doing) work' means. This is very confusing.
3)
So if you take a ball and drop it from a window it will make a depression in the ground where it lands. If you double to height (and so the ball’s speed) the hole will be four times deeper. You have doubled the height (2 x the original) and speed of the ball and 2 x 2 = 4. So you get 4 times as much energy to make the depression in the ground.
This doesn't make any sense. Here, you are just talking about a CLASSICAL situation, where E=mv^2/2+mgh. This has nothing to do with the RELATIVISTIC equation E=mc^2. Instead, say something about nuclear energy, where a small difference in mass gives a huge amount of energy.
 
  • #5


:smile: I seem to have got it all wrong. I am pleased that you pointed this out. Better then getting it totally wrong in the talk.

Basic problem is that I think I am in way over my head.

Does anyone know of a "simple" site that I could read to get some more details.

Thanks again for your input. I"really" do appreciate it.



Integral said:
You were doing fine till you got to the squared bit. What you wrote sounds like serious nonsence to me..

Nabeshin said:
^2: This section seems totally irrelevant. I don't really know what you're trying to get at drawing a large distinction between c and c^2, is it units? Regardless, this paragraph didn't even make sense to me so I doubt a 14-yo will fare much better.

Landau said:
1) What on Earth are you trying to say about the c^2? Of course this means c times c.
 
  • #6


It seems you don't have a deep understanding of the material yourself, that makes it kinda hard to explain it well to others. So I'm wondering where/how did you learn it?

Of course, a good starting point would be wikipedia: http://en.wikipedia.org/wiki/Mass–energy_equivalence.
A "derivation" of E=mc^2 at high school level: http://instytutfotonowy.pl/index.php?main_page=page&id=6&zenid=f8e8906b4f5fae8889dcc3355c852a5d
 
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  • #7


Landau said:
It seems you don't have a deep understanding of the material yourself, that makes it kinda hard to explain it well to others. So I'm wondering where/how did you learn it?

Of course, a good starting point would be wikipedia: http://en.wikipedia.org/wiki/Mass–energy_equivalence.
A "derivation" of E=mc^2 at high school level: http://instytutfotonowy.pl/index.php?main_page=page&id=6&zenid=f8e8906b4f5fae8889dcc3355c852a5d


I learn from reading books and helping my son do his homework. I went to school in 70's and w didn't get this deep into phisics - but I really do want to learn.

But you are correct when you say I don't have a deep understanding, but I am trying to lern very hard.

I will look at the sites you gave me - thank you
 
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  • #8


What are the characteristics of these 14 year-olds? Are they aspiring physicists/scientists, or just a general class of students with little knowledge of physics?

If it's the latter, I think going into a lot of detail (think in terms of a 14 year old here, not yourself) will lose them during the presentation. An alternative would be to simply express what the terms stand for--E stands for energy, and so on. I would focus on the historical aspects, like how Einstein derived the equation (not the actual derivation! :smile:) and it shows that there is an equivalence between mass and energy, and also, how the equation became associated with nuclear weapons during the Manhattan Project, although we really didn't need the equation to build the weapons (we needed to understand fission). You could then do some simple calculations for the rest energy of a particle (e.g. proton), mass of a human, mass of fissionable material in a nuke (assuming all of it is converted to energy), mass of sun, etc--the scale in numbers may astound them.

EDIT: Check the link for more background on subject: http://en.wikipedia.org/wiki/Mass–energy_equivalence

EDIT2: Actually, to be more precise, E stands for the the "rest" energy.
 
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  • #9


buffordboy23 said:
What are the characteristics of these 14 year-olds? Are they aspiring physicists/scientists, or just a general class of students with little knowledge of physics?

If it's the latter, I think going into a lot of detail (think in terms of a 14 year old here, not yourself) will lose them during the presentation.
EDIT: Check the link for more background on subject: http://en.wikipedia.org/wiki/Mass–energy_equivalence

Thank you for your time and your kind answer. I will look at the link you gave me and try to learn more.
 
  • #10


Nabeshin said:
Give some analogy like you could burn a sheet of paper and light up the room for a split second. But if you were to convert the entire mass of the paper into energy, via E=mc^2, you could light an entire city.

I missed this and this is what I trying to go for in my post...a shock factor. For this, E has a magnitude around 10^16 J.
 
  • #11
  • #12


AlisonArulia said:
Hi Again (sorry to keep bothering you)

I found this on WikipediaAnswers. This is the type of thing I was looking for. Not too technical but full of information and interest.
http://wiki.answers.com/Q/Why_is_there_snow_on_top_of_mountains_if_hot_air_rises

I assume it's been checked by wikipeda so it should be ok ??
Ths is the type of thing I would like to know about e=mc2

The site apparently is owned by Answers.com. A wiki is a generic term. The information is generated by the public so there is no guarantee that the information is accurate. Wikipedia for example, has many many articles ranging from simple mistakes to downright falsehoods.
 
  • #13


Pengwuino said:
The site apparently is owned by Answers.com. A wiki is a generic term. The information is generated by the public so there is no guarantee that the information is accurate. Wikipedia for example, has many many articles ranging from simple mistakes to downright falsehoods.

So how can we check that what we are reading is true.
Is that article OK for example?
 
  • #14


AlisonArulia,

Why are you trying to teach this to 14 year olds in the first place? You don't have a good grasp of it yourself. Why don't you teach them something appropriate for their level, like Newton's third law?

- Warren
 
  • #16


Also something I noticed, no need to set c=1. That usually doesn't happen until a sophomore college SR course anyways.

I know that this doesn't happen at high school, but it is a good way to teach the meaning of E = m c^2. If you get rid of the c, then the equation reads:

E = m

which to most lay persons would suggests that energy and mass are the same thing and that is in fact the correct meaning. There is no "conversion" of mass into energy. That can't happen because of conservation of total energy. So, if an object has a mass of m, then that means that its rest energy is E = m c^2, the factor c^2 is an irrelevant conversion factor that arises because we traditionally use incompatible units for mass and energy.
 
  • #17


Why not talk about the history of how we came to learn E=m? Talk about what conservation means, and how the realization that energy itself was conserved was learned relatively recently. Then the separate conservation laws of mass and of energy had to merge into a deeper form because of Einstein. A narrative is more interesting than a bunch of facts.

There are also a bunch of fun questions that you can ask, and make the presentation quite interactive. Like for example, if E=m, then does an alarm clock weigh more when you wind it?
 
  • #18


A neat visual representation of the equation of interest: http://www.navsource.org/archives/02/026530.jpg" . All U.S. submarines and aircraft carriers are powered by nuclear energy (the Enterprise has eight nuclear reactors) and ultimately the equivalence of mass and energy.
 
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  • #19


Count Iblis said:
I know that this doesn't happen at high school, but it is a good way to teach the meaning of E = m c^2. If you get rid of the c, then the equation reads:

E = m

which to most lay persons would suggests that energy and mass are the same thing and that is in fact the correct meaning. There is no "conversion" of mass into energy. That can't happen because of conservation of total energy. So, if an object has a mass of m, then that means that its rest energy is E = m c^2, the factor c^2 is an irrelevant conversion factor that arises because we traditionally use incompatible units for mass and energy.
Actually I think that would confuse the heck out of most laypeople because they're so used to seeing [itex]E = mc^2[/itex]. I would imagine it takes a certain level of immersion in physics to be able to accept a concept like natural units, where [itex]c = 1[/itex]. I guess one could try explaining the idea to 14-year-olds but I have a feeling they're not going to get it, and they'll just get sidetracked from the main point, the equivalence of mass and energy.

Usually the explanation I see given to laypeople involves the following: since c is on the order of 3*108 (in SI units of course, since people are familiar with that scale), c2 is on the order of 1017, which is a really huge number. That in turn means that a small amount of mass corresponds to a humongous amount of energy. In this sense, c2 is just a number, a proportionality constant that ensures that the numbers agree with nature.
 
  • #20


I would just like to offer, again, my thanks to everyone who has taken the time to share their expertise with me. I am one of the people who try and learn "stuff" in later life that they weren't taught at school and folk like you are a real help to my understanding,

Thank you all.

(Don't though - I will come back with many more silly questions :smile:)
 
  • #21


If Id be the student, Id tell you:

I understand that E is the mass, but I don't understand how E is calculated. Why multiply M with the speed of light scuared? Why does this E=mc2 formula give me the amount of energy?

What would you reply?
 
  • #22


E=m*c*c=p*c etc. might be better than c2

An example of mass energy transformation might be helpful to explain this. See how much energy can be obtained from transforming a mass ( teacher's mass :P ) into energy. 75 kg would fuel the energy needs of the world for a long time.
 
  • #23


Just thinking about it now, as Cantab says it would make sense to start with conservation. As we know that stuff can't just disappear it has to go somewhere, this then relates nicely to nuclear power.

You can also make the comparison between a chemical reaction (blowing something up with dynamite or a coal fired plant) that even though mass appears to disappear it acutally doesn't it just changes or becomes too small to see. But in nuclear reactions mass actually does dissapear, so it has to go somewhere and that somewhere is energy.

From this you can compare the relative energy outputs, ie nuclear >>>> chemical.

It explains the relation without being techincal, which I think would suit the audience well.
 

What is E=mc^2?

E=mc^2 is a famous equation created by Albert Einstein, which shows the relationship between energy (E), mass (m), and the speed of light (c) in a vacuum. It states that the energy of an object is equal to its mass multiplied by the speed of light squared.

Why is E=mc^2 important?

E=mc^2 is important because it revolutionized our understanding of the universe and led to the development of nuclear energy and weapons. It also showed that energy and mass are interchangeable, and that even a small amount of mass can release a large amount of energy.

How can I understand E=mc^2 better?

You can understand E=mc^2 better by learning more about the concepts of energy, mass, and the speed of light. You can also try conducting simple experiments to see the equation in action, or watch videos and read explanations from reliable sources.

Can E=mc^2 be proven?

Yes, E=mc^2 has been proven through various experiments and observations. It is a fundamental principle of physics and has been confirmed by countless scientists and experiments.

Is E=mc^2 the most famous equation in the world?

E=mc^2 is often considered one of the most famous equations in the world, but some argue that other equations, such as F=ma or E=hf, may be just as well-known. However, E=mc^2 is certainly one of the most well-known and influential equations in history.

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