Transcript of a2-tutorial
==========


_0:02_: Astronomy to Relativity and Gravitation Electricals.

_0:12_: Electric tutorial so-called

_0:14_: and it's fairly three format. I never I've never convinced I

_0:19_: have a a really good plan for what to do in this hour, but

_0:26_: unimaginative. But I think going through a couple of the

_0:29_: exercises in the exercise collection is probably a decent

_0:33_: idea, if not necessarily terribly exciting one.

_0:37_: Does anyone have any meeting suggestions for a better for

_0:41_: better plans?

_0:44_: Other particular areas you are particularly hoping I'll cover?

_0:53_: Yeah, yeah, I'll certainly mention those. Yeah.

_0:56_: In fact, let's just keep going on that.

_1:01_: So as I

_1:04_: mentioned in the

_1:07_: I mentioned a couple of times

_1:09_: and also on the on the padlet, the

_1:14_: aims objectives are several pedagogical fashions out of

_1:18_: date. But I find that the distinction useful.

_1:22_: The distinction being that the aims are the point and the

_1:25_: objectives are the accessible things.

_1:29_: So you, you, you, you, you've seen this document, it's no you

_1:33_: haven't seen this compendium version. But you have the the

_1:37_: aims, objectives at the beginning of each chapter and

_1:41_: and and I will if necessary tweak those next semester once I

_1:45_: I start thinking about this a little bit more. But they have

_1:50_: settled down over the last couple of years to to to what

_1:54_: they are.

_1:56_: The aims, as I mentioned, are the high level

_1:59_: point of the course, but they tend to be expressed in terms of

_2:03_: understand, appreciate, blah blah blah rather than things

_2:07_: that you can actually put in an exam and so the objectives

_2:12_: which roughly match. But I'm not the same thing, as the aims are

_2:16_: the things that I think are fair game for the examiner.

_2:21_: There's rather a long list of these. If you if you put them

_2:24_: all together in one document that you do end up with quite a

_2:26_: few of them. I'm not going to go through them step by step,

_2:29_: but the reason that they're

_2:32_: there's lots of them. It's simply because

_2:35_: I I find it useful to,

_2:39_: you know, concretize. What do I think is the accessible thing in

_2:44_: this in this chapter?

_2:46_: So, so that's why there's several of them.

_2:49_: There's also quite a few of them to give me a little bit of scope

_2:52_: when I'm making the exam. So these are all individually,

_2:55_: there's too small to see, but you've got them in in in the, in

_2:58_: the, in the notes. These are all individually quite small things.

_3:03_: Very few of them are. Remember such and such.

_3:06_: Basically I don't have a good memory for for, for, for, XYZI.

_3:10_: Don't feel it's it's fair game to get you to memorise things,

_3:14_: which I, I I wouldn't. And similarly derivations people

_3:18_: sometimes people would like to put. It's an easy exam question,

_3:22_: you recite the derivation of of such and such. It's not a very

_3:26_: exciting exam question. It's not actually very useful thing to be

_3:30_: able to do,

_3:32_: so there aren't. There are a couple of things where I see you

_3:35_: should be able to

_3:37_: remember this blah blah. I think one of them is for example,

_3:42_: to quote the expression for the scalar product between 24

_3:45_: vectors.

_3:46_: I think you should have to do that because of heaven's sake.

_3:50_: If you can't do that, you know that's pretty bad, but that but

_3:53_: that should that should just come naturally in a sense,

_3:57_: because you have used it several times in doing the exercises. So

_4:00_: take those seriously. Things that are clearly not covered by

_4:04_: the objectives are.

_4:07_: I will regard it out of scope for the exam.

_4:10_: Things which are clearly, you know covered by that I very much

_4:13_: regarded in school for the exam

_4:15_: Italy and it's borderline. Do feel free to ask for

_4:18_: clarification, OK, but that that's the I I look at that when

_4:22_: I'm when I'm making the exam.

_4:26_: Any questions,

_4:29_: less of them, I will. Yes. Yeah

_4:34_: it's just duplicating what's in each chapter but I

_4:39_: in previous years I have sometimes used slightly edited

_4:41_: the list when making turn it into a a full document just

_4:44_: because I I've, I've I've gone through them and thought that's

_4:47_: not very clearly expressed or something. So I think yes, I

_4:50_: will. I, I will put up the I can bend your version of of that and

_4:54_: probably next around the time when you're starting to worry

_4:57_: about you

_4:59_: anything else on that particular topic.

_5:03_: OK. So does that, does that answer you the question you had

_5:08_: to some extent,

_5:10_: Yep.

_5:14_: OK

_5:17_: and you were also in the lecture. That folder there is

_5:21_: the list of all the exercises.

_5:24_: And again this is we will, I will be going through to

_5:28_: touching on this

_5:32_: you the rest of the hour

_5:36_: just to repeat myself again, the A2 tutorial handbook that's

_5:40_: mentioned in in the Moodle includes a section on includes

_5:44_: exercises for the vote, the four sub courses within a 2, the

_5:48_: section of relativity. They're good exercises. They're not

_5:52_: particularly keys to the way I've ended up doing these

_5:55_: lectures. So when I talk about the exercises, it's these ones.

_5:59_: I mean,

_6:01_: OK and in

_6:04_: it's a long story, but in previous years these exercises

_6:06_: were included in the

_6:09_: the lecture notes document chapters that you you downloaded

_6:13_: and they were taken out because folks thought there were too

_6:17_: many pages in those files and and and OK, but I think I

_6:20_: probably should put them back in because it's a bit confusing

_6:24_: having them separate. But you will find that document in the

_6:28_: Election Notes folder.

_6:30_: There are quite a few of them, as you will see if you examine

_6:33_: it

_6:34_: and

_6:36_: for example.

_6:42_: But you didn't have example. OK, it's slightly too small to see,

_6:46_: but at the end of each of them you'll see which objectives they

_6:51_: actually I I feel they

_6:53_: touch on

_6:55_: and some of them marked as slightly more difficult or

_6:58_: slightly less difficult than than the main and some are

_7:01_: marked as particularly useful.

_7:03_: So this

_7:06_: the minus is I I think that all all the quick questions they ask

_7:10_: in the in in the lecture are D minus are particularly easy

_7:14_: ones. The one at the top there is a hard one and so on. So

_7:18_: that's what that notation means in case you're thinking of what

_7:22_: wants to select

_7:27_: and

_7:30_: neither the the the the the total exercise vary quite a lot

_7:35_: they from from very simple very simple things just like the

_7:38_: quick questions in the lectures to things which are quite

_7:41_: thoughtful and we'll we'll we'll have you puzzling over them for

_7:44_: an afternoon. So there's quite a lot of variation in those. So

_7:47_: those really aren't. I mean, that's a good question. Those

_7:50_: are are are a poor guide to what's in the in a test or an

_7:53_: exam

_7:54_: because some of them are

_7:58_: yeah. The the the fairly variable and and and and and.

_8:01_: Next next semester I will post a a documentary includes notes on

_8:06_: the on on solutions of them.

_8:08_: I don't do that in the first semester because reasons, but I

_8:11_: I will post an answer. This and some of some of those notes are

_8:15_: like a couple of lines. Some of them are are extensive

_8:18_: discussion of of of the of the point.

_8:21_: So as usual the best guide to what's in the class test or

_8:24_: exams or the like is previously previous papers as usual and

_8:28_: those tend to have when I'm marking them. I tend to write

_8:32_: notes about what people did and what people the the various

_8:36_: things that odd things people and put when answering questions

_8:40_: and to those those notes and fairly chatty for past papers

_8:44_: for the relative reputation stuff. And those are much longer

_8:48_: than would be model model answers.

_8:51_: They tend to be as they chatty or anything else. So. So that's

_8:56_: I'm talking too much.

_9:01_: I thought of a couple of these exercises which it would be

_9:05_: useful to go through

_9:09_: slowly now. Can I get rid of this

_9:12_: thing on the right? Probably not,

_9:15_: you know, a bit bigger,

_9:17_: I think. I thought of

_9:20_: Access 4.7.

_9:27_: OK,

_9:29_: this is quite a nice exercise. Let's see if we can make that a

_9:32_: bit bigger still.

_9:40_: Is excess 4.7

_9:43_: caught Mcrae's?

_9:45_: And this is the real thing? This isn't just a I mean, I mean that

_9:48_: thing is a real bit of of observational particle physics.

_9:51_: If you like

_9:52_: quick raise from the top of the atmosphere, collide with it and

_9:56_: it just shows of elementary particles, there's this happens.

_9:60_: So, companies

_10:01_: coming from the cosmos.

_10:04_: Mysterious source.

_10:06_: We showed them elementary particles including

_10:10_: a variety of exotic particles and all ones that reached the

_10:14_: ground are muons, which are sort of heavy electron,

_10:17_: which are unstable and decay with a half life of of 2.2

_10:21_: microseconds.

_10:27_: And they're the troubling relativistic speeds because the

_10:30_: Cosby rates at the atmosphere at very high speeds at at ultra

_10:34_: relativistic speeds. So the muons are moving at similarly at

_10:38_: relativistic speeds.

_10:40_: And the majority of the of the muons that are produced behind

_10:43_: the atmosphere reach the ground

_10:46_: to produce interesting. And you and you can you can test that

_10:50_: you can observe that by observing the the Muon flux at

_10:53_: altitude on top of the mountain and the ground level and it it

_10:56_: all matches up. So, so, so this is happening.

_10:60_: So supposing that these muons are created at a nominal height

_11:03_: of 15 kilometres currently, how long it takes them to reach the

_11:08_: ground in the earth frame giving the answer in seconds and then

_11:12_: half lives.

_11:13_: So this is setting up our our

_11:17_: leading you through as as solving this.

_11:21_: So what I will do therefore is. I think it's

_11:25_: and this one which is the one which is on the E360 rather

_11:29_: unfortunately would be better than the other one. Could you

_11:33_: could talk on the on my left knee that adequately here.

_11:38_: OK. Then

_11:40_: what can do is we can talk about

_11:43_: no.

_11:46_: Can we see that

_11:49_: you only just

_11:57_: So where are we? We have, we have our

_12:01_: an altitude of 15,

_12:07_: there's metres

_12:08_: we have.

_12:13_: Uh,

_12:16_: well, we want to know how long it takes to reach the ground. So

_12:20_: what speed are these? Are these moving at

_12:25_: anyone

_12:27_: speed of light? Yes.

_12:29_: So you could work out exactly how fast the moving given the

_12:32_: gamma factor of or 40. But it's going to be so close to the

_12:34_: speed of light it makes no difference.

_12:37_: So you would just use the speed of light

_12:39_: I at their speed. So.

_12:44_: So there's no need for excess precision and a complicated

_12:48_: calculation to try and turn gamma equals 40 into A into a

_12:51_: very precise value.

_13:02_: Because your teams tend to the

_13:06_: 8 metres per second and I'm using physical units here rather

_13:10_: than natural natural units. Because the the question is

_13:14_: being framed in terms of of physical units. And the answer

_13:18_: I'm looking for is in terms of seconds and half lives and so

_13:22_: on. So there's no need to put any other complications there.

_13:26_: They're travelling a distance of 15,015 thousand metres in at at

_13:30_: a speed of of that. So the the time is equal to.

_13:35_: This has been a time

_13:38_: H over

_13:40_: V is going to be 15,

_13:46_: metres

_13:47_: over the times 10 to the eight

_13:52_: which is second and I'm being careful to put in the units and

_13:54_: I'm looking at that and going yes, I have that, that those

_13:57_: units cancel and give seconds. So I I do have that the right

_14:00_: way up.

_14:01_: And it's all the one of the reasons why you always put in

_14:04_: units for a numerical calculation is because that

_14:07_: means you can check that the units end up the right way up.

_14:10_: Because that's an easy, cheap check that you haven't made

_14:13_: some, you know, silly mistake and got things upside down.

_14:18_: I would then 15 / 3 is 510 to 3 -. 10 to the eight is 5 * 10 to

_14:25_: the minus

_14:28_: 31885. It's 5 * 10 to the minus

_14:35_: seconds.

_14:37_: Unless anyone is going to disagree with that,

_14:41_: which is

_14:44_: microseconds.

_14:46_: And the half life is 2.2 microseconds, so that you know I

_14:52_: divide that one by the other, giving 22 point, 22.7

_14:59_: T half

_15:01_: and

_15:03_: so I've done. There's no relativity here,

_15:07_: I've just done this is the Speed Times thing.

_15:11_: I'm being reasonably careful about this. I I think if this

_15:15_: were an assignment I'd I would make a stomach for a copy of

_15:18_: this before submitting it, but I'm being fairly systematic

_15:21_: about going about going through this. Good, so A is done and we

_15:25_: haven't had to think very hard, which is always very nice.

_15:30_: Calculate how long it takes the muons to reach earth in the

_15:34_: muons frame, giving the answer again in.

_15:39_: Seconds and half likes.

_15:41_: Now why does it see in the muons stream?

_15:46_: Yeah,

_15:49_: Temperance transformation

_15:51_: mostly right.

_15:53_: You don't have to use the range transformation because it's just

_15:56_: a matter of time dilation. So you can just use the time

_15:59_: dilation formula.

_16:01_: So, and I think that that's a a good point to emphasise, you

_16:04_: don't always have to use the right transformation

_16:09_: equation, and when you're doing these sort of calculations

_16:12_: you'll end up using a mixture of the transformation, time

_16:15_: dilation, length, contraction distance and speed times time

_16:20_: in using the right the right thing at the right time. So in

_16:24_: this case the question is asking that's time of 50 microseconds.

_16:29_: What? So between the Muon hitting the top of the

_16:33_: atmosphere and the Muon hitting the ground takes 50 microseconds

_16:38_: in the Earth frame.

_16:40_: What is the separation between those two events in the new on

_16:43_: stream? And you could set it up with the answer that the answer

_16:45_: is not wrong,

_16:47_: but you'd be making it hard for yourself because then you'd have

_16:49_: to think OK, what are the events, but you know and write

_16:51_: things down and then go turn the handle and get the answer. You

_16:54_: can just leap straight to the answer by going time relate.

_16:58_: How do you work out the the time in the beyond stream?

_17:07_: Why? Why over gamma?

_17:16_: That that's right. And and in a sense the the slightly cheating

_17:19_: answer is say because we expect it to be smaller

_17:22_: because you can remember L naughty L = L naughty over gamma

_17:27_: or lol or gamma times laughter, whichever. Whichever one it is.

_17:32_: I I can't remember which way up it is, but I know the lengths

_17:36_: contract

_17:38_: that moving, moving, moving, moving length, moving rod gets

_17:42_: shorter, eventually shorter, and that time dilates.

_17:46_: So that in this case I expect to um

_17:50_: that the answer in the burn frame to be to be less so I know

_17:53_: I'm gonna I'm gonna have to divide by gamma. So that's

_17:56_: that's a bit like cheating but it's it's quite legitimate

_17:60_: because you are thinking through that that that you know what

_18:03_: physical answer you should get which is a lot smaller and so

_18:06_: you know where to multiply or divide. So I think for for this,

_18:11_: for Part B

_18:13_: and

_18:24_: this time,

_18:36_: and

_18:40_: let's rate, I'm going to jump back a bit and say that's that

_18:44_: That's time

_18:48_: T prime equals to T over gamma equal to.

_18:55_: Did prime equal to over gamma

_18:58_: equals.

_19:00_: With 50

_19:02_: microseconds

_19:04_: over, we were told the camera was 40,

_19:08_: which is equal to

_19:10_: 1.25

_19:13_: microseconds.

_19:14_: A question there

_19:19_: and frame travelling at the speed of light. No the frame.

_19:22_: The frame isn't travelling at the speed of light but we're

_19:27_: this this is as I'm making a central approximation so so the

_19:31_: muestrame isn't at the spiral light. When we were working

_19:34_: doing the calculation, the numerical calculation that

_19:37_: worked out what the the time elapsed time was we thought we

_19:40_: might as well take it to be special late because the

_19:43_: difference from that is going to be ignorable. If we're talking

_19:46_: about two significant figures in the in in the nominal height

_19:50_: then it doesn't matter. So I think that that that's being

_19:53_: applying a bit of physical common sense in important

_19:56_: number. Should we pick if we did it

_19:58_: this exact way and went from gamma equals 40 to V equals?

_20:04_: 2.9978 whatever. Then we would be injecting spurious accuracy.

_20:08_: So, so, so, so, so, so yes, the mainstream isn't moving at the

_20:12_: speed of light, but we can take it to be for medical purposes.

_20:19_: OK. Sorry, do you? Yes,

_20:23_: due to time dilation, whenever I'm writing carefully, there's

_20:26_: never enough time to write carefully. But due to time

_20:30_: relation, less time would pass in the nuance frame. Thus time T

_20:33_: prime equals T over gamma.

_20:37_: So although I said

_20:41_: that we know the number of good has got to get smaller,

_20:44_: therefore we divide, I don't write that down.

_20:47_: What I write down is an explanation which which

_20:50_: indicates that I have a clue

_20:52_: that I understand what what what's happening here and you

_20:57_: know, write it the right way around. OK, so I could give a

_21:01_: more elaborate explanation in terms of I could, I could, I

_21:05_: could write pages on that I'm sure, but I've written down

_21:09_: enough to make it clear to the person marking this what

_21:14_: that I understand what's happened.

_21:17_: OK, because the the, the, the secret with all exams and it

_21:20_: took me, I I never worked this out. When I was an

_21:23_: undergraduate, I never really realised that the people marking

_21:27_: my exams were the people teaching

_21:30_: and the humans teaching them. And there was a human sitting

_21:33_: there in the dark of the night, slogging through my, my, my exam

_21:36_: papers. Because if I had, I realised that the point the way

_21:40_: you do an exam is you're talking to someone,

_21:43_: you're talking to him and saying look, I'm clever,

_21:47_: bear that in mind. And so this due to time dilation less time

_21:51_: would be would pass in the millions frame. That's saying I

_21:55_: have a clue.

_21:56_: OK, so bear that in mind.

_21:59_: You don't have right? You don't have to write an epic, but you

_22:02_: have to write something. So. So just writing down t = 2 over

_22:05_: gamma T frame equal to over gamma would not get marked as

_22:08_: far as I'm concerned.

_22:09_: Just quoting the answer and jumping straight there wouldn't

_22:12_: get marked. You have to have something in there which says I

_22:15_: have a clue.

_22:17_: OK.

_22:19_: That by the way is my nature handwriting

_22:24_: part C and we've done it in ah yeah I need a lost a mark

_22:30_: I I failed to read the question and I failed to to to to write

_22:35_: down that that was what the number I have is 0.57

_22:47_: 0.57 half lives.

_22:50_: That was a free market nearly missed. Read the question.

_22:58_: OK, so we've done I I just checked and we have done Part B.

_23:01_: Now

_23:02_: which part C

_23:04_: can this be regarded as a test of special relativity?

_23:08_: What's the answer to that?

_23:16_: I mean, yes, yeah, yeah, but why? Why is it special?

_23:25_: That's it. Yeah. So so the the mere fact that the, the the

_23:32_: that the the naive calculation in part a is saying it takes the

_23:37_: muons 22 half lives to get to earth

_23:41_: means that the number of muons that you get to get to Earth

_23:44_: would be 1 / 2 to the 22

_23:47_: of the number that were at the end of the atmosphere. So almost

_23:50_: none.

_23:52_: So the the mere fact that, as the question said, most of the

_23:55_: muons arrive at Earth is telling you that the explanation that

_23:59_: you would that you would naively jump to from the calculation

_24:03_: part A can't be right.

_24:05_: And the explanation that if there's less than one half life

_24:09_: in the Muon frame, it takes less than one half life in the muons

_24:14_: frame to get down to earth makes it perfectly reasonable that

_24:18_: most of the muons make it to Earth.

_24:21_: So the question then is how do I write that down in one sentence?

_24:25_: I don't have to write a book here, I can just write down

_24:28_: something like.

_24:31_: How do I freeze it

_24:36_: if

_24:38_: the muons

_24:40_: actually

_24:44_: it took 22

_24:48_: half

_24:49_: lives to reach

_24:53_: F

_24:57_: capital E

_25:00_: and

_25:02_: almost

_25:05_: none

_25:07_: would arrive

_25:10_: observationally,

_25:16_: most

_25:19_: so

_25:23_: much less

_25:26_: time than

_25:30_: half life

_25:33_: would

_25:34_: pass.

_25:35_: I am just getting really messy. Sorry about that,

_25:39_: Beyoncé.

_25:42_: And you're not here to watch me, right? Slowly. As you. Slowly.

_25:45_: Neatly. But

_25:49_: right now that's not quite enough,

_25:52_: because I haven't said I haven't mentioned the word special

_25:54_: relativity in that sentence yet.

_26:02_: How do I inject that?

_26:07_: Only special relativity

_26:11_: provides

_26:13_: this explanation,

_26:19_: right? What I've written down there is,

_26:23_: but that's gone off the bottom.

_26:32_: If the muons actually took 20 to half life to reach the Earth,

_26:35_: almost none would arrive. Observationally, I am linking it

_26:38_: to the question.

_26:40_: Most do so much less time than 1/2 life must would pass in the

_26:44_: muons frame. Only Sr provides this explanation and I should

_26:48_: probably therefore this confirms this corroborates Sr.

_26:52_: SO

_26:54_: I I think if I were about to submit that as as assessment I

_26:57_: would go back over that and thinking of I can reword that

_27:01_: bit a bit a little bit better. But the key points are I have

_27:04_: mentioned I I haven't just. I haven't stopped at the first

_27:07_: sentence there. I linked it to the question I I looked at what

_27:11_: I was actually asked to see

_27:13_: and I I I I made some sort of link to that. I said

_27:17_: observationally, most do that. That's the thing that is that is

_27:21_: the key thing.

_27:23_: And is this a taste of special relativity

_27:26_: such sentence? Yes it is basically. I could freeze that

_27:28_: better, but but, but but the, the, the, the. The point is to

_27:31_: read the question and make sure you actually do answer it.

_27:36_: If you haven't written a lot, I would

_27:39_: tater that little bit in in wording terms to to, to to to to

_27:43_: work an assessment. There's less time, of course, and exams, but

_27:49_: the the, the, the goal of the scene,

_27:52_: OK,

_27:54_: you have it.

_27:56_: No?

_27:58_: In the frame of the muons, the Earth is moving towards them at

_28:01_: approximately the speed of light.

_28:04_: Calculate the distance between the altitude of which the under

_28:07_: created and the surface of the earth in the Muon frame and thus

_28:10_: how long it takes for the mules to traverse it. Give you answers

_28:13_: again in seconds and half lives. So what's happening here? What

_28:16_: am I asking you to do

_28:19_: that students?

_28:21_: That's right.

_28:22_: Length contraction. Yeah, length contraction is the key thing.

_28:27_: So the in the burns frame the distance from the top of the

_28:31_: atmosphere to the bottom is much less than 15,000 metres. By how

_28:35_: much less? By that divided by a factor of of gamma.

_28:41_: So I have to indicate that I understand this. So

_28:48_: in the bum stream,

_28:58_: the atmosphere

_29:03_: is length.

_29:05_: Yeah,

_29:09_: by our factor of gamma.

_29:15_: Thus

_29:18_: each prime equals H over

_29:20_: gamma equals 15

_29:25_: those metres

_29:27_: over

_29:28_: 40, which is a less pretty number. What number do they cope

_29:32_: with? That should be the 105 metres

_29:38_: and

_29:43_: in the UMM stream.

_29:46_: OK

_29:48_: Do I stop there? No, I do not. The question didn't ask me how

_29:52_: he took asked me to do that, but it also said and thus how long

_29:55_: it takes the means to traverse it.

_29:59_: What speed is the Earth moving at in the beyond stream?

_30:03_: Should be like, yes. So the time it takes for the Earth to travel

_30:08_: 305 metres in the Muon stream.

_30:11_: Yeah,

_30:17_: travels with each prime

_30:21_: at

_30:23_: speech C in time

_30:27_: T Prime equals distance is speed.

_30:32_: It's each frame over C which is 3 and 75

_30:36_: metres

_30:39_: times 10 to the eight metres per second

_30:42_: because because that turned the number of seconds. That's good.

_30:46_: I've got something done stupid to put that upside down which is

_30:50_: equal to

_30:53_: and that is equal to 0 point 1.25 microseconds

_31:01_: which is equal to 0 point

_31:04_: 57T half. And I have remembered that I'm being asked for it to

_31:08_: put this in seconds and in microseconds and and in in

_31:12_: seconds and in numbers of half lives,

_31:18_: have I done everything? How long it takes for years, right? Yes,

_31:21_: in second-half. Yes, I've done that. So I have. I've done

_31:23_: answered the quest

_31:25_: good. No last bit

_31:31_: E

_31:32_: comment on the equality or inequality of your answers to

_31:37_: Part B and and D

_31:40_: No comment is a keyword that there There are numerous

_31:44_: keywords in exams.

_31:46_: One of the very important ones is write down. If you're asked

_31:50_: to write down something, it means you know this. You don't

_31:53_: need any explanation. It means that it's trivial to to just put

_31:57_: on paper, but you'll be asked to write down. So write down is a

_32:01_: keyword. It's just I'm not expecting you to to explain

_32:04_: this. You don't have to explain this

_32:08_: comment is another keyword for exams. It means say something

_32:11_: intelligent about.

_32:14_: So what is being?

_32:17_: What is it you're supposed to notice about the answers to part

_32:20_: B&D?

_32:24_: The equal Yeah.

_32:26_: So

_32:27_: the the time it takes for the Muon to get from the top of the

_32:31_: atmosphere to the bottom in the Muon frame. So the amount of

_32:35_: time it's got to decay

_32:37_: and the amount of time it takes for the Earth to get from

_32:41_: 1500 metres away to to

_32:46_: to the the the thickness of the atmosphere and the muons frame

_32:49_: is such that it takes only only that that time to get all the

_32:53_: way through it are the same.

_32:56_: If you just write down the other seam, I'll write down the seam

_33:01_: and

_33:09_: answer this. No, that's good. Correct tick.

_33:12_: Not, not all the marks, because I haven't said what's

_33:15_: interesting about that

_33:18_: and and and there's a couple of things I could write down there.

_33:22_: A sensible thing would be,

_33:24_: um to note that

_33:29_: and calculations in different frames must agree

_33:34_: the they have different explanations. In one case the

_33:37_: the time it the the the the the muellers clocks are being slowed

_33:41_: down because of time relation. In the other case, the

_33:45_: atmosphere is being compressed because of length contraction.

_33:49_: Different explanations which which come to the same

_33:54_: the same result.

_33:57_: Uh,

_33:59_: Calculations

_34:02_: India.

_34:04_: Different frames

_34:07_: of degree.

_34:11_: And I think if if I were writing an assignment, I would, you

_34:15_: know, obsessed a little bit about how to frame how to freeze

_34:18_: that. In writing that in an exam, I'd make sure I say

_34:21_: something like that, but not. I wouldn't obsess about it.

_34:25_: OK.

_34:28_: You know, you can see that in the.

_34:33_: In the question I said comment on the equality or inequality of

_34:35_: your answers to part B&D.

_34:37_: So I say hey, I I have been deliberately vague about whether

_34:41_: I whether those answers should be the same. Of course they

_34:45_: should be the same. But see, one way or another you

_34:49_: go different answers for those two for what would be and D

_34:53_: Perhaps just your arithmetics poor. OK,

_34:57_: so you so you think of that. Are you think? Should I have got the

_34:60_: same? Should they be the same?

_35:02_: Are they interestingly different? Or have I just made a

_35:05_: mistake

_35:06_: and you think about that, and you might be that you conclude

_35:09_: these should be the same.

_35:11_: I made a mistake.

_35:13_: That's fine. You write down these are different but they

_35:17_: should be the same because blah blah gives us an excellent

_35:20_: explanation

_35:22_: because that shows me you have a clue

_35:24_: and that's a general thing. In exams if things have gone all

_35:27_: out of port and you you, you, you realise you've written down

_35:30_: rubbish. You, you, you're the answer, you've written. Your

_35:33_: writing down is is wrong. Can't be right,

_35:36_: then see through. Don't just have a panic attack and score at

_35:39_: the last five pages of of your exam exam question. See, this

_35:43_: can't be right because

_35:45_: because if you if you're if the person making it sees that

_35:48_: you're thinking about this and that you you know what the

_35:51_: answer should be, roughly, and that you give a a reasonable

_35:54_: explanation for why it can't be right,

_35:57_: then OK, you lose some marks for whatever, whatever mistake it

_36:00_: was. But you'll get some marks. They'll find some marks for you.

_36:04_: For you being switched on enough to know this is this is clearly

_36:08_: wrong

_36:09_: for this intelligent reason.

_36:11_: So remember that

_36:14_: again talk to your mother

_36:19_: so that that's why I, you know the the order inequality is

_36:23_: there just in case

_36:25_: you said you retain the fact of the question but the the comment

_36:31_: that you had to it can be various.

_36:35_: So that's quite a a I think that was that was A

_36:40_: and I think assignment one or something a few years ago. So

_36:44_: that's that's a sort of Simon type question rather than exam

_36:47_: type question. So. So they're not very good guide to exam

_36:50_: things but I think it's a nice question to pick here because it

_36:54_: covers quite a lot of things And interestingly this is from

_36:57_: Chapter 4 so it's before the Lorentz transformation. So we

_37:00_: haven't had to use the range transformation at all in this

_37:04_: one. We just had to think about what's happening here just to

_37:07_: speed times time length contraction time relation and

_37:10_: and so on.

_37:11_: So the more elaborate version of that we we we could ask but you

_37:15_: don't have to use as I I think I said at one point that all

_37:19_: relatively exam questions are the same, but just you know here

_37:23_: are some numbers use the rent transformation to them from one

_37:27_: frame to another. That's not actually true as you can see,

_37:30_: but it's just that the range transformation is a nice

_37:34_: straightforward way of

_37:36_: doing this sort of calculate

_37:40_: and that I meant that to take about 20 minutes, 25 minutes

_37:43_: rather than

_37:45_: I was chatting a lot at the begin.

_37:48_: Other questions about that

_37:53_: OK,

_37:54_: Is that reassuring or terrifying or or,

_38:00_: you know,

_38:01_: are you happy?

_38:06_: Actually rather 4 miles there.

_38:11_: OK

_38:13_: and

_38:16_: OK, let's try another one. Um,

_38:19_: is it the other quite nice one?

_38:24_: The traditional traffic lights for example,

_38:32_: so 615

_38:50_: OK,

_38:51_: you're driving towards some traffic lights

_38:54_: showing red

_38:56_: and and no one will wavelength there.

_38:58_: How fast do you have to be driving through a Doppler?

_39:01_: Shifted enough that they appear to be green

_39:04_: normal wavelength,

_39:06_: and the question gives hints on how to how to approach this.

_39:11_: OK, So what this is. This is a question about the Doppler

_39:16_: shift. Obviously

_39:18_: A

_39:21_: SO 614.

_39:31_: So here, what with with most of the of the

_39:37_: questions about the Doppler shift,

_39:40_: the question the the The challenge with them is always

_39:44_: basically the same.

_39:46_: Try not to get confused with which frame you're talking about

_39:48_: and don't lose track of maintains,

_39:51_: because you'll always end up having to think in which we're

_39:55_: under my pointing here and it. Therefore, this is one of the

_39:59_: cases where it's very important to be very clear about what is

_40:03_: what moving what direction in which frame.

_40:06_: So

_40:09_: frame,

_40:12_: yes.

_40:13_: Yeah,

_40:18_: Fear of Lights.

_40:20_: S Prime is the

_40:25_: with the car.

_40:26_: OK, I'll write it down

_40:29_: straightforwardly,

_40:31_: and let's say we have and in this case we. I think we want a

_40:35_: diagram.

_40:38_: So this is,

_40:40_: yes, Prime

_40:42_: and we're moving towards

_40:46_: some traffic lights,

_40:48_: yeah.

_40:51_: And here I'm

_40:54_: this is, I mean Koski diagram. It's just as an ex Y diagram

_40:59_: but I'm writing I'm I'm writing down that this is moving at

_41:03_: speed V

_41:05_: towards the right.

_41:06_: OK,

_41:08_: just because I'll mess up the minus signs otherwise.

_41:13_: And

_41:14_: in the frame of the traffic lights,

_41:19_: the

_41:23_: has

_41:26_: if you can see F equals, we said 600 metres.

_41:36_: No it doesn't. It doesn't.

_41:39_: It has frequency Lambda equals 600,

_41:44_: 90 metres. One year I actually

_41:49_: wrote and distributed and people sat the exam in which I wrote

_41:53_: and I talked about frequency of 600 nanometers and no one

_41:56_: noticed. I didn't notice. The internal checkers didn't notice.

_41:60_: None of the students noticed because they were. They somehow

_42:03_: magically fixed it in their heads. But it was slightly

_42:06_: embarrassing, but

_42:09_: easier than you think to do

_42:12_: anyway. So frequency, wavelength, Wavelength is

_42:14_: different frequency as you learned in first year and our

_42:17_: wavelength is 600 metres.

_42:20_: And

_42:23_: what do we have to the the, the

_42:27_: in?

_42:29_: It's primed

_42:31_: observed at

_42:34_: Lambda prime which we don't know.

_42:39_: Ohh no, we do not equal 600

_42:43_: 500 nanometers. Ohh, numbers

_42:50_: 500 nanometers. OK, So what do we have to play with here? What?

_42:54_: What do we know about the Doppler shift? What we can do is

_42:59_: we can jump back to.

_43:02_: We'll scan through our notes here and and and and recall

_43:06_: we have an expression

_43:09_: Lake

_43:11_: UH

_43:15_: from Notes F primed.

_43:19_: You know F

_43:21_: equals F primed

_43:23_: gamma

_43:25_: one plus

_43:27_: Cos Theta V Cos Theta.

_43:36_: OK, now did that help us?

_43:39_: It does because it has

_43:43_: F&F prime unit which can be proxy for V and for Lambda and

_43:47_: Lambda prime. We're going to think about that,

_43:51_: and it has

_43:52_: the speed V which is what we're trying to find out here,

_43:56_: so we don't. So this is a case where we're doing the Doppler

_43:59_: effect backwards, trying to find V given the change in frequency,

_44:02_: and it's got this angle Theta frame.

_44:05_: But what is Theta framed? A question.

_44:11_: Yes. If this were an exam question I would give that I

_44:14_: would give you that formula. Yeah. Because I I I wouldn't

_44:17_: expect you to That's one of the. I mean I think yeah I wouldn't

_44:20_: expect to memorise that partly because I don't think memorising

_44:24_: is terribly useful but also because it would it would be it

_44:27_: would be just so easy to get a frame with the wrong place and

_44:30_: and and scupper the whole question. So I think if if we're

_44:34_: an an exam question

_44:36_: I would either give it in the question or since last year the

_44:39_: question is the the question papers have been redesigned to.

_44:42_: There's a crib at the at the beginning, so there might be a

_44:45_: crib at the beginning of the of the of the paper which is just a

_44:49_: list of of equations with no context, no explanation of what

_44:52_: other symbols mean. Is just that that that that list there simply

_44:55_: so that you you can spot which one of the is the one with all

_44:58_: the primes in the right place.

_45:01_: So that would be quite memory. Well, running time almost.

_45:07_: But then what do you see? The frame here,

_45:09_: and this is the other bit that that that all of the Doppler

_45:13_: shift questions are all always getting you know our our

_45:16_: testing, what direction are we talking about here

_45:20_: and here the

_45:25_: the, the the the directions are in the

_45:28_: XY plane

_45:30_: of the of the street or of the car or whatever. And the

_45:33_: question is, in what direction in this plane is this light

_45:37_: moving?

_45:39_: OK,

_45:40_: So what direction is the light moving?

_45:43_: What? What?

_45:45_: That's right? So Theta prime is

_45:48_: new pie.

_45:51_: Yes. And that's and that's and that's the thing that what all

_45:54_: these doctors your questions are are are testing but can you tell

_45:57_: the difference 0 and π

_45:60_: and in this case the lights moving towards you so the light

_46:03_: coming from the traffic light

_46:06_: to the driver is moving

_46:08_: in the negative X direction

_46:11_: so Theta prime so so and and that's true in in both frames

_46:15_: but we'll be but this requires in the in the car drivers frame

_46:18_: what directions are moving in is moving in the direction opposite

_46:22_: to the X prime X prime axis. So the light is moving in direction

_46:25_: theatre frame.

_46:27_: Yeah,

_46:28_: Light moving

_46:31_: at Peter Prime

_46:34_: equals π,

_46:37_: so

_46:39_: F = F prime gamma 1 -, V

_46:47_: OK,

_46:48_: so the

_46:52_: and

_46:53_: this would be good progress here.

_46:56_: We can rewrite that as F / F prime equals gamma 1 minus

_47:03_: V

_47:06_: and uh

_47:08_: the the the the the question hints at. Right. Row equals F

_47:13_: primed over F, which is also Lambda over

_47:18_: Lambda prime either way up. So I'm I'm rushing slightly could

_47:22_: at the end here but this I think this would not be a a terrific

_47:26_: exam question because it requires you going back at you

_47:29_: you're thinking a little bit more carefully and going back I

_47:32_: think I've got that upside down and and so on so that there's

_47:36_: there's too many hostages to fortune for like this to be a

_47:39_: good exam question basically a very nice assessment question or

_47:43_: excess question. So I'm going to

_47:46_: skip a little bit

_47:48_: and and and and and. Note that at this point we've essentially

_47:51_: done all our work.

_47:53_: We've got

_47:55_: F / F prime,

_47:56_: which we know. We know that from from the the the data given in

_48:00_: the question we've got something on the right hand side which is

_48:10_: depends on on V So this is one over rho squared equals 1 -, v

_48:17_: ^2 / 1 -, v ^2.

_48:21_: And then it's just a bit of algebra

_48:24_: to turn.

_48:29_: I mean you know not trivial but not really hard to to to to

_48:32_: invert that and turn that from role as a function of V into V

_48:36_: as a function of row.

_48:38_: We rearrange it and then you could you you discover what V is

_48:42_: as a function of the role which you know is a six fifths blah

_48:47_: blah. Turn the handle and you get a speed which is I think

_48:51_: eleven 6080 / 81 disputed later, which is very fast.

_48:56_: So

_48:57_: I'll stop talking in just one moment. I'll point out that yes,

_49:00_: that's not a terrific exam question, but it's quite a good

_49:03_: exercise and quite assignment, and that it involves first

_49:07_: writing down what you know from the note and then thinking

_49:10_: carefully about what the what the symbols mean and not get and

_49:13_: and and watching your mind sings

_49:17_: so good they have only two more lectures to go and then at the

_49:21_: end of the