Assalamu’alaikum/ apa kabar semua?/ ketemu lagi dengan ka Dzikri masih di acara Shabat mau tahu?/ yu cari tahu!/
Hari ini ka Dzikri sedang berada di SD ..../ wah .... lihat ada yang naek jungkat-jungkit. Ikut yu!
Hai semua .... mau ikutan dong/ anak-anak: ya boleh ka/ lalu ka Dzikri naik jungkat jungkit, tetapi tidak dapat menyeimbangkan berat anak/ anak-anak: ahh kakak ga bisa/ayo yang lain, tambahin beratnya/ akhirnya jungkat-jungkit bisa berjalan.
2.Pengarahan ke tema melalui:
> penayangan video
Wah rame ya/ sekarang ka Dzikri punya video/ sahabat mau tahu?/ yuk cari tahu/
Video
Narasi
Sepeda yang berjalan diatas tali
Sirkus (orang yang berjalan diatas tali)
Jungkat jungkit
Pertanyaan-pertanyaan untuk mengarahkan pada konsep.
3.Pengarahan ke segmen 2 dengan memberikan pernyataan:
“Setelah ini kakak akan menunjukan demonstrasi dan memberikan tantangan yang dapat menjelaskan fenomena yang telah disebutkan diatas”
Segmen 2
1.Host menunjukan demonstrasi kesetimbangan dengan menggunakan garpu dan sendok.
Lihat ini/ kakak punya sendok, garpu, dan korek api/ kaka ingin membuat keduanya bisa seimbang di atas mulut botol/ ada yang bisa?/
Host menunjukkan demonstrasi
Anak-anak: ko bisa sih ka?/ wah magic!/ ini bukan magic, tapi ini tuh fisika/
2.Host memberikan tantangan untuk membuat keseimbangan dengan menggunakan paku.
Sekarang kakak punya tantangan/ kakak mempunyai .... paku/ nah kaka ingin semua paku salaing bertumpu, dan dapat seimbang di atas sebuah paku/
3.Siswa mencoba untuk membuat keseimbangan dengan menggunakan paku.
4.Host menjelaskan bagaimana membuat paku seimbang.
Nah/ untuk membuat semua paku dapat seimbang/ maka setiap sisi harus sama dan terdistribusi/
5.Host memberikan pertanyaan arahan,
Apa fungsi dari batang korek api?/ Mengapa batang korek api harus diletakan ditengah-tengah dari susunan garpu dan sendok?/ Mengapa susunan tersebut tidak jatuh kesalah satu sisi?/ Apa yang terjadi ketika jumlah paku di kedua sisi tidak sama?/ Mengapa jumlah paku harus sama di kedua sisi?/
Tahu mengapa sendok dan garpu dapat seimbang?/ dan paku juga dapat seimbang?/ hal ini dikarenakan terdapat titik pusat massa/ ketika benda berada pada titik pusat, maka benda itu akan seimbang/ Jadi batang korek api itu dibuat agar menjadi titik pusat massanya.
Animasi untuk penjelasan.
6.Pengarahan untuk segmen 3 dengan memberikan pernyataan :
Berikutnya kita akan membuat sebuah mainan yang menarik dengan konsep yang sama/ sahabat mau tahu?/ yuk cari tahu.
Segmen 3
1.Menunjukan alat dan bahan untuk membuat mainan keseimbangan.
Nah tadi kakak bilang akan mengjarkan kalian untuk membuat mainan keseimbangan/ bahan-bahannya ini dia/ kakak kasih kalian satu-satu ya/
2.Membuat boneka seimbang.
3.Anak-anak mencoba boneka yang telah dibuatnya.
Yu kita coba bonekanya/
4.Memberi quiz keseimbangan
Ayo, siapa yang tahu mengapa bonekanya bolak-balik?/ tidak berputar?/ untuk apa batu yang ada di dalam?/
Segmen 4
1.Host menyimpulkan konsep keseimbangan (disertai animasi).
2.Pemberian jawaban quiz keseimbangan.
Nah, jadi boneka itu dapat bolak-balik karena ada titik pusat massa/ batu yang di dalan digunakan untuk penempatan pusat massanya.
3.Trivia (info mengenai keseimbangan).
4.Penutupan.
Lampiran
1.Cara membuat garpu dan sendok seimbang
> kepala sendok diselipkan disela-sela gigi garpu
> selipkan batang korek api pada sela-sela yang tersisa antara gapu dan sendok
> letakan ujung batang korek api yang telah dipasangkan dengan sendok dan garpu pada mulut botol
> sendok dan garpu berada pada keadaan yang seimbang.
2.Cara untuk membuat paku seimbang
> letakan sebuah paku secara mendatar
> letakan paku yang lain diatas paku yang mendatar secara berselang seling posisi kepala pakunya di kedua bagian paku yang mendatar
>letakan sebuah paku yang lain secara mendatar sejajar dengan paku yang pertama diletakan secara mendatar
>angkatlah susunan paku tersebut dan letakan diatas sebuah paku yang vertikal ( dengan ujung runcing paku vertikal tepat ditengah tengah susunan paku agar sistem seimbang).
3.Pertanyaan arahan.
> “Apa fungsi dari batang korek api?”
>” Mengapa batang korek api harus diletakan ditengah-tengah dari susunan garpu dan sendok?”
>“Mengapa susunan tersebut tidak jatuh kesalah satu sisi?
>”Apa yang terjadi ketika jumlah paku di kedua sisi tidak sama?”
2.Salam Pembuka (assalammu’alaikum wr.wb… ketemu lagi bersama Ka ..... dalam acara Sahabat Mau Tahu…. Yuk Cari tahu!…. Sekarang kaka sedang berada di ..............................//) eh... disana ada adik-adik yang sedang kumpul-kumpul, kita sapa mereka yuk...!!!
-Assalamu’alaikum,, halloo adik-adik sedang ngapain nih?
-(anak-anak) sedang diskusi tentang magnet nih ka,...
-Wah .. kebetulan,.. coba lihat, kaka bawa apa nih???
-(anak-anak) Apa itu ka??
-Ini lah yang dinamakan magnet...
-(anak-anak) Ko bentuk magnetnya berbeda-beda sih ka??
-Iya, magnet ada bermacam-macam bentuknya, ada yang berbentuk batang, silinder, jarum, cincin, cakram, jarum, juga berbentuk ladam.
-Eh, sebelumnya kalian tahu tidak bagaimana sejarahnya magnet bisa ditemukan???
-(Anak-anak)Tidak!!!
-Sahabat mau tahu??? Yuk cari tahu!!!!
Pemutaran video/animasi sejarah penemuan magnet!!! (video dan narasi)
Segmen 2
-Halo adik-adik,, masih bersama kakak dalam acara sahabat mau tau? Yuk cari tahu!!//
-Ok,... tadi kan kalian sudah tahu sejarah penemuan magnet seperti apa? dan bentuk magnet apa saja??
-Sekarang kita cari tahu apa aja sih sifat-sifat yang terdapat pada magnet...
-Sebelumnya, coba kalian jawab, apa yang terjadi jika magnet ini kakak dekatkan pada penjepit kertas? (anak-anak) nempel kak!!! Ya, penjepit kertas akan tertarik dan menempel pada magnet.
·Kutub-kutub magnet.
-Mempelajari bagian magnet yang memiliki tarikan paling kuat yang disebut dengan Kutub magnet. Caranya yaitu menempelkan sejumlah penjepit kertas pada salah dua kutub magnet yang dirangkai saling menempel pada penjepit kertas serta bagian tengah magnet. Manakah rangkaian penjepit kertas yang paling banyak??
-Kemudian menjelaskan Setiap magnet memiliki daerah yang paling kuat menarik penjepit kertas itulah yang di sebut dengan kutub-kutub magnet.Ada dua kutub magnet yaitu kutub utara U dan kutub selatan S. Namun seringkalimenemukan kutub-kutub magnet yang bertuliskan N dan S. Jelaskan!
-Jika dua buah magnet didekatkan, kira-kira apa yang akan terjadi?
-Mempraktekan jika dua buah magnet dedekatkan maka akan terjadi tolak menolak atau tarik menarik, jelaskan syaratnya...
-Melakukan percobaan magnet yang melayang!!!
·Membuat magnet
-(anak-anak) kak mau tanya?? Magnet bisa dibuat oleh kita tidak kak?
-Bisa, jika kita memilki logam yang dapat ditarik magnet maka kita bisa membuat logam tersebut menjadi magnet/bersifat magnet. ada tiga cara dalam membuat magnet:
1.Digosok (searah) / sambil mempraktikan
2.Induksi (didekatkan dengan magnet)
3.Mengalirkan arus listrik pada kawat. Sambil di praktekan menggunakan baterai.
·Menghilangkan sifat magnet
(anak-anak) kak mau nanya lagi!, Iya silakan, sifat magnet pada logam bisa hilang ga?
Bisa,... magnet permanen (magnet tetap) dapat hilang jika magnet sering jatuh atau dipukul-pukul dan juga dibakar. Jika kita melakukan hal demikian maka magnet akan berkurang sifat kemagnetannya bahkan hilang.
Nah, adik-adik itulah kira-kira beberapa sifat dari magnet. Setelah ini kalian akan diajak oleh kakak membuat mainan dari magnet. Tentunya pasti akan seru!!!!
Kalian mau tahu ??? (anak-anak) Mau!!!
Baik teman-teman dirumah jangan kemana-mana ya,... tetap di acara Sahabat Mau Tahu??? Yuk Cari Tahu!!!!
Segmen 3
-Halo adik-adik,, masih bersama kakak dalam acara sahabat mau tahu? Yuk cari tahu!!//
Yap, kaka tadi sudah janji kalo sekarang kaka akan mengajak kalian membuat mainan dari magnet. Kalia tahu namanya apa? Namanya : Pensil terbang
·Membuat Pensil terbang
Alat dan bahan yang dibutuhkan
1.Sendal jepit bekas (1 buah)
2.Pensil 1 buah (1buah)
3.Kertas lipat berwarna (1 lembar)
4.Cutter (1 buah)
5.Koin (Rp 500 1 buah)
6.Magnet cincin ukuran kecil (6 buah)
7.Lem
8.Gunting
Prosedur pembuatan yaitu:
1.Buat tigairisan pada sandal jepit bekas untuk tempat koin dan magnet.
2.Tancapkan koin pada irisan yang telah dibuat pada sandal.
3.Pasang dua buah magnet cincin pada pensil
4.Tancapkanmagnet cincin pada irisan yang dibuat pada sandal. Masing-masing irisan dipasang dua buah magnet cincin.
.
Perhatikan kutub-kutub magnet, atur agar magnet yang dipasang pada pensil tolak menolak dengan magnet ada sandal.
5.Letakkan pensil (yang sudah dipasang magnet) diatas magnet yang dipasang pada sandal. Atur agar pensil dapat melayang. Kemudian pelintirkan pensil. Akhirnya pensil selain dapat melayang juga dapat memutar.
6.Agar putaran pensil dapat terlihat , maka potonglah kertas lipat membentuk jarum kemudanberi lem dan tempelkan kertas lipat pada pangkal pensil.
Tempelkan membentuk spiral
7.Selesai, akhirnya kita memliki mainan pensil yang dapat terbang sambil berputar.
Nah, adik-adik ini dia mainan nya,... coba kita perhatikan!!! Kenapa ya pensilnya bisa melayang??? Coba siapa yang bisa menjelaskan???
-Salah seoran anak menjawab: pensil dapat melayang karena magnet pada pensil mendapatkan gaya tolak dari magnet pada sendal!!!
-Bagus sekali,... ya jawabannya benar,... pensil dapat melayang karena magnet pada pensil mendapatkan gaya tolak dari magnet pada sendal!!!
-Jadi bagaimana kutub magnet pada senda dengan magnet pada pensil??? Jawab: senama..
Baik adik-adik, tetap jangan kemana-mana yah, setelah ini masih ada informasi buat adik-adik, yang pastinya penting buat adik-adik simak... tetap di acara Sahabat Mau Tahu??? Yuk Cari Tahu!!!
Segmen 4
-Sahabat, tadi kita sudah membuat mainan namanya pensil yang dapat terbang dan melayang. Mainan tersebut merupakan penerapan dari konsep kemagnetan.
-Sahabat tahu tidak? ternyata konsep kemagnetan itu banyak aplikasinya loh dalam kehidupan sehari-hari. Dari mulai penerapan dalam alat elektronik, kompas, sampai transportasi.
-(Anak-anak kaget!) haaaaah... transportasi??? Kok bisa kak??
-Iya bisa,... contohnya yaitu kereta api. Kalian tahu namanya kereta api apa?
-(anak-anak) tidak tahu kak!!
-Kalian mau tahu??? (anak-anak) mau kak, mau...!!!
-Sahabat di rumah juga mau tahu????? Yuk cari tahu!!!!!
Tayangan video seputar informasi Kereta Api Shinkansen Jepang! (video dan Narasi)
-Ok, adik-adik jadi sekarang kalian sudah paham tentang magnet? Jawab; sudah!!
-Ok kaka tanya kembali, disebut apakah daerah pada magnet yang memiliki tarikan atau tolakan paling kuat? Jawab: kutub magnet!
-Ada berapa kutub pada magnet? Jawab : 2. Sebutkan apa saja?jawab:Kutub Utara dan Selatan
-Apa yang akan terjadi jika kutub utara magnet satu didekatkan dengan kutub selatan magnet lain? Jawab: akan tarik menarik
-Apa yang akan terjadi jika kutub utara magnet satu didekatkan dengan kutub utara magnet lain? Jawab: akan tolak-menolak
-Ada berapa cara membuat magnet? Jawab: 3,. Coba sebutkan? Di gosok (satu arah), di Induksi, dan mengaliri arus listrik pada kawat.
-Bagaimana caranya agar magnet permanen dapt hilang sifat kemagnetannya?? Jawab: di pukul-pukul/dijatuhkan dan di bakar/dipanasi.
-Ok, seratus buat kalian....
-Karena adik-adik sudah paham maka saatnya kakak undur diri meninggalkan adik-adik di sini juga adik-adik dirumah... tetap saksikan acara Sahabat Mau tahu??? Yuk Cari tahu!! Dilain kesempatan,...
I'm going to talk today about energy in electromagnetic waves.
There must be energy in there, because we know that electric fields contain energy, and magnetic fields contain energy.
And you may remember that the electric field energy density is one-half epsilon 0 E squared, this is now in joules per cubic meter, and the magnetic energy field density, which also has come up earlier in the course, is 1/(2 mu 0) times B squared.
Again, joules per cubic meter.
Now, we -- when we deal with traveling waves, in vacuum, at any moment in time, the magnitude of B is E divided by C.
So this is also one divided by 2 mu 0, I can replace this by E squared / C squared.
But C squared is one over epsilon 0 mu 0.
So this is also one-half epsilon 0 E squared.
And when you see this, this is an absolutely amazing result, because what this tells you is that the energy density in the magnetic field of a traveling wave is exactly the same as the energy density in the electric field of an electromagnetic wave.
That's really an amazing thing, the symmetry is absolutely beautiful.
So the total energy density is the sum of the two, so I double this one, so that it's epsilon 0 E squared, joules per cubic meter, and of course, I can also write for that, epsilon 0, just one E, and then the other, I write B times C.
So I write for E, B times C.
So this is, again, in joules per cubic meter.
Yes, I'm happy with that, that's fine.
Now, I want to ask the question, if electromagnetic waves come by me, how much energy passes through one square meter?
It's like an energy flux.
And so I have here one square meter, and this one square meter is perpendicular to the direction that the electromagnetic wave is going, and I want to know how much energy flows through there.
1 square meter every second.
In 1 second, light travels a distance C, which is a horrendous distance, 300000 kilometers.
This side of this box is what light travels in 1 second.
And this is 1 square meter, and I'm going to calculate how energy now goes through this 1 square meter in 1 second.
Of course, I could have chosen this box a billion times smaller, would have gotten the same answer of course, but for convenience, I choose this to be C, and this to be 1 square meter.
So the volume of that box is C cubic meters.
And all the energy of that box is going to come out here in 1 second, because I know that electromagnetic waves move with the speed of light, which is C.
And so therefore, the energy that comes out here per square meter per second is that U total there that I have, which is the amount of energy for every cubic meter, but I have so many cubic meters.
And so I can use this result, now, here, and I can substitute that here, so I get epsilon 0 E B C squared.
I have to multiply it by this C here.
And this, of course, is also E B / by mu 0, because C squared, in vacuum, is one over epsilon 0 mu 0.
And this, now, is joules per square meter, per second.
Because in one second, all that energy comes out, and I have already chosen one square meter area.
Let me see whether I'm happy with that, yes, I'm happy with that.
We call this the Poynting vector.
And we write it, in general as a vector.
We write it, S with a vector, and it's called the Poynting vector with a y, and we write that as E cross B divided by mu 0.
E B divided by mu 0.
You don't need the cross, really, because E and B are always perpendicular to each other in a traveling wave.
The advantage of this notation is that S, which is the energy flux, goes in a certain direction, and the velocity of the wave is always in the direction of E cross B, so it also tells you, then, in which direction the radiation is flowing, whereas here, you -- you lack that information.
And so this, then, to remind you, is in these units, which is watts per square meter.
How many joules per second?
1 square meter through a plane perpendicular to the direction of propagation.
Now, E and B are changing with a frequency omega, cosines omega T or sines omega T.
And so S is changing with the cosine square of omega T.
If you are somewhere in space, and this electromagnetic wave comes by, there are moments that S is 0, namely, when E and B happen to be 0.
And there are moments that it is at maximum, when E and B happen to be at maximum.
And so when we deal with electromagnetic radiation, it's more meaningful to discuss the time-average value.
And the time-average value of the Poynting vector is, first of all, the time-average of the cosine square omega T, or the sine square omega T, whatever the case may be.
And the average value of cosine squared is one-half.
And then I can write now, for E, E0, and for B, I can write B0, which is now the maximum value possible, divided by mu 0.
And if you want to write it differently, if you want to write it only in terms of E 0, then you can write down one-half E0 squared divided by mu 0 times C.
So this is the more practical equation, that gives you a number which is time-averaged over the oscillations.
Let me make sure that there is nowhere, a slip of the pen -- no, there isn't -- I hate to have slips of the pen, because you can't edit them out later on your videotape.
Slips of the tongue, you can edit it.
The slips of the pen, you can't.
OK, this looks good.
So now, we have an average value for the Poynting vector, and so we can calculate, now, how much energy flows through 1 square meter per second.
And I can give you an example, suppose I have a plane electromagnetic wave, and E0 is 100 volts per meter.
That's just what it is, how we get it, that's a different story.
And this could be radio emission, this could infrared, this could be light, I d- I don't specify the frequency.
I don't have to.
Frequency doesn't come up there.
And so the value for -- average value for the Poynting vector, I can pick this equation.
E0 is 100.
I know mu 0, I know C, so I can calculate what it is.
It's 100 squared divided by 2, divided by mu 0, divided by C.
And when I do that, I find that this is 13 watts per square meter.
So imagine that you would stand in this electromagnetic wave coming to you, we take all our clothes off and we let it hit us, and suppose it absorbed us.
Suppose it is radiation that absorbs us -- some radiation may go through you.
Gamma rays may go straight through you -- they are electromagnetic radiation.
But certainly, light will not go through you.
And radio waves, some of them will not go through you.
So you observe them with your body.
Would you notice that?
I doubt it.
You probably have a surface area that's close to 1 square meter.
13 watts, 13 joules per second, not very noticeable.
You radiate, yourself, 100 watts, 100 joules per second, so I don't think you will notice that.
But imagine, now, that we increase the value of E0, and we make it 1000 volts per meter.
Now, this goes up by a factor of a 100, because if E goes up by a factor of 10, automatically, B goes up by a factor of 10 -- remember, in electromagnetic waves, they're always coupled.
So the Poynting vector, which is the product of the two, goes up by a factor of 100, so now, you're talking about 1.3 kilowatts per square meter.
And if you absorb that on your body, believe me, uh, it may fry you.
Certainly if you do that out on the beach, you get a -- a deep suntan.
And if you do it long enough, then you can hurt yourself very badly.
So now comes the question, does a light bulb emit plane waves?
Well, not really.
Plane waves have no beginning and they have no end, they exist at all time and all space.
Look at my plane wave solutions from last lecture.
You can substitute in there any value for X, Y, and Z, and any moment in time, the year 5000 B.C., you get an answer.
Doesn't specify when, doesn't specify where.
And of course that's not very realistic.
In the real world, there is a beginning and there is an end to the electromagnetic radiation, and therefore, they have also a finite length.
Remember the quarter-nanosecond pulses that we sent to the moon that we discussed last time.
They were only 7 centimeters long.
That's not very much like a plane wave.
So I want to discuss with you a little further what these waves look like, and I want to take a closer look at how electromagnetic waves are produced by charges that we begin to shake, that we are accelerating.
Key in the whole process is that you accelerate a charge.
If a charge is just moving at a constant velocity, it will not produce electromagnetic radiation.
But I want to give you some feeling, at least some classical physical feeling on how these electromagnetic waves are produced.
It is a picture that has its own limitations, but it's still useful.
It's not a quantum mechanical treatment, but it is something that you and I can see and therefore, perhaps, appreciate.
Suppose I have here a charge which is not moving.
Just sitting there.
These are field lines, I just draw only a few field lines.
And if it's a positive charge, the arrows are outwards, if it's a negative charge, the arrows are inwards.
And I'm going to accelerate this for a time delta T.
Let's accelerate it in this direction.
And then we bring it, again, to a halt, say.
I redraw this.
This point is the same as this point here.
I accelerate it, and delta T seconds later, it happens to be here.
So this is T0, and this is T equals delta T.
And now I'm going to draw a circle -- it should actually be a sphere, three-dimensionally -- about this point.
And here is that sphere.
And this sphere has radius C delta T.
This field line, which was the field line that goes with this charge, is here, and this field line is here, and this one is here, I only draw three.
This one, this one, and this one.
And the message that I accelerated this charge could not possibly have reached this location in space, because that message can only travel with the speed of light.
So the electric field here is exactly the same as it was when it was still here.
So when the object is here, the electric field must still be like this here, and it must be like this here, and it must be like this there, because the message hasn't reached that point.
But now, look at this charge, which is now here at time d delta T.
Now, the electric field is like so, is like so, and is like so.
So this field line must somehow meet up with this one, it's one and the same field line.
And what does that mean?
That somewhere there, there must be a kink in the electric field.
And there must be a kink here.
Notice there is no kink here, which is interesting.
And so it is the collection of these kinks that propagate outwards, with the speed of light, and they produce an electromagnetic disturbance, a change.
If you were out in space here, and if, for instance, I were to oscillate this charge back and forth, you would see these kinks go by all the time, these breaks in the electric field, and you would experience that as an electromagnetic wave, if there is a changing electric field, according to Maxwell's equations, there has to be also a changing magnetic field.
But the interesting thing is, even though this is an extremely simple picture, notice that in this direction, if you were here, you would not see any kinks.
So there's no electromagnetic radiation going in this direction, nor is there any going in this direction.
And the maximum is going in this direction, and something in between is going in that direction.
It's not much of a plane wave, for that matter.
I mean, if anything, it's more like a spherical wave.
But it's a very special spherical wave, not the same strength in all directions.
And so even though this is a rather classical picture, it helps me, at least, to see how these changing electric fields -- and therefore, associated B fields -- are formed by charges that we accelerate.
And I have a two-minute movie that shows that, also, in a slightly more detailed way than I was able to do.
And so let's look at that movie, Marcos, you ready for that?
OK, then you can start that.
Pengembangan Perkuliahan
1. Buatlah sebuah Esai mengenai materi perkuliahan ini
2. Buatlah sebuah kelompok berjumlah 5 orang untuk menganalisis materi perkuliahan ini
3. Lakukan Penelitian Sederhana dengan kelompok tersebut
4. Hasilkan sebuah produk yang dapat digunakan oleh masyarakat
5. Kembangkan produk tersebut dengan senantiasa meningkatkan kualitasnya
Instructors: Dr. Peter Dourmashkin Prof. Bruce Knuteson Prof. Gunther Roland Prof. Bolek Wyslouch Dr. Brian Wecht Prof. Eric Katsavounidis Prof. Robert Simcoe Prof. Joseph Formaggio
Course Co-Administrators: Dr. Peter Dourmashkin Prof. Robert Redwine
Technical Instructors: Andy Neely Matthew Strafuss
Course Material: Dr. Peter Dourmashkin Prof. Eric Hudson Dr. Sen-Ben Liao
All right, last time we talked exclusively about completely inelastic collisions.
Today I will talk about collisions in more general terms.
Let's take a one-dimensional case.
We have here m1 and we have here m2, and to make life a little easy, we'll make v2 zero and this particle has velocity v1.
After the collision, m2 has a velocity v2 prime, and m1, let it have a velocity v1 prime.
I don't even know whether it's in this direction or whether it is in that direction.
You will see that either one is possible.
To find v1 prime and to find v2 prime, it's clear that you now need two equations.
And if there is no net external force on the system as a whole during the collisions, then momentum is conserved.
And so you can write down that m1 v1 must be m1 v1 prime plus m2 v2 prime.
Now, you may want to put arrows over there to indicate that these are vectors, but since it's a one-dimensional case, you can leave the arrows off and the signs will then automatically take care of the direction.
If you call this plus, then if you get a minus sign, you know that the velocity is in the opposite direction.
So now we need a second equation.
Now, in physics we do believe very strongly in the conservation of energy, not necessarily in the conservation of kinetic energy.
As you have seen last time, you can destroy kinetic energy.
But somehow we believe that if you destroy energy, it must come out in some other form, and you cannot create energy out of nothing.
And in the case of the completely inelastic collisions that we have seen last time, we lost kinetic energy, which was converted to heat.
There was internal friction.
When the car wreck plowed into each other, there was internal friction--
no external friction--
and that took out kinetic energy.
And so, in its most general form, you can write down that the kinetic energy before the collision plus some number Q equals the kinetic energy after the collision.
And if you know Q, then you have a second equation, and then you can solve for v1 prime and for v2 prime.
If Q is larger than zero, then you have gained kinetic energy.
That is possible; we did that last time.
We had two cars which were connected by a spring, and we burned the wire and each went off in the opposite direction.
There was no kinetic energy before... if you want to call it the collision, but there was kinetic energy afterwards.
That was the potential energy of the spring that was converted into kinetic energy.
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