Basic Physics Lecture 7

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Basic Physics Lecture 7
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Today will organ be focusing not an again I borders of humans like but They were really focusing on his motion and more than 1 dimension so we have done a lot of kinematics of what is being Wendy motion with constant acceleration and this week were in a focus on what happens if you move into directions duty motion stick with constant acceleration and
To do this as I said we started at the very end of yesterday the online quit This kind of reviewed the key elements of actors but Targeted is briefly go all over those additional rules and mediation properties of actors Because that we can't even more important to me more than a dozen 1 8 black A lobby ideas we went over about catching things having a delay Having to objects move versus having won the objects have 2 different modes All of these basic physics are still important and still apply in 2 dimensions sewage is building on that so that all come back Any questions on that up as 1 you'll see for most of these problems there at least 2 ways I do it So when the solution get posted you'll see 1 that focuses on dry actors was holographical solution and 1 that focuses on using components so again flying the muddy you're most comfortable with and use that as you go on Jews from the house at the height of everything we're dealing with an equation like that and I mentioned earlier this to pieces to it What are vectors Are multiplied by numbers so you have to remember what that does so by have V not mn I multiplied by time that just makes it longer but it keeps the direction the saying What is the only number I can multiply by our type of number that might change the direction of electorate NATO What is the lighter side Just is the direction So I do have a situation where multiply by any negative number would reverse You have to keep that in mind The other major events But we highlighted is the process of adding to doctors So read you have to add 2 vectors we've done a lot and a lot of different ways But now organ actually summarize it or a nice formal picture Arrange a 4 2 dimensions as I said earlier in the class The real world is 3 D right you have to worry about ex-wife normally But everything we do because it's easier to draw on a piece of paper we do too Because a lot of emotion Just did so it works and also Reid is appended on hard work and it's basically the same so Doesn't really make much sense to do it Now among them add 2 vectors So there's vector egg there's vectors be there might be some angle theta between them and they equal vector C 1 thing you could do it and you were really good with your triangles and drag you would remember But the length of city because a square Cosby square Minors Through a Cosigned times that angle theta right there between us There was a lot like the white factory in Europe because they were remember what the coastline of 90 years 0 So When that angles 90 degrees this goes away and you have a quite in the arm This can be a useful short cut it may be problem you also is called Pollock oversight we also the the fact that these signs of Bader divided by city by adding that angle alpha
It is a sign of Alpha Divided by D Islam lot signs now I put this out here I want to be clear I'm putting aside their if you feel really really comfortable with geometry and trade it you down and his major nervous don't right now but I do want a point out people that this could be a very useful thing and it's something you're comfortable with you might say why my showing well some of you will want to use it now the more useful And common things that have happened As with some vector Eddie there were adding to some vertical Vector B because remember These are common to vectors to use their which direction is GE 2 points where straight down so the vertical so there is a very often and are Rob a right angle That's related something important the problem may be the destitute travel And often you know this other distance so you can figure out beside saves B minus 8 And I went through on Friday as a marketer reputed hair value can you sign cosine and tangent In this situation and Sylvester There's actually A very powerful and I would argue very useful thing For you to review and if you get comfortable with that it will really help you a lot of the problems and so that help you with that like set up the information led As a PDF called cinematic review and I go through it Detail how to use this I also do it and example problems again to do this week soda really help Any any questions on that we can quickly on Friday for chat There more common thing That most people have learned about are components so you make it acts and a Y axis often called I have NJ Hakim was sealed its use in a minute and you have some vector eh And we break it into the components A Y And a AX notice are components were really are strictly speaking vectors the vector SA is the sum of 2 vectors the vector in the direction and the Vectra y direction and we write these As a times are ahead of us A times J. hat or we write them as a pair of AXA a Trend These numbers hair Give us the size or magnitude of the component and also by convention there the plus or minus sign for The direction along the axis so let's be clear on all the different pieces Right Notice from the way I do the picture This is just our standard That's ax doesn't look like it vector addition we went Head detailed and then tailed ahead we got the the factory and we write it In this notation worthy I had and the J. that are vectors in the direction of the coordinates so strictly speaking user still live actors right here And the other way we can write it as a pair of numbers that are court so the lot and ever notation you'll see and the but or a different situations the test you have and what I'm ready now as a couple of demonstrations here the letter Snow White A bit These components can be used as white hair even useful so we open with a quicker question
Now we have a demonstration I was gonna happen is when I pull this
Drain bears little thing will fire and And it will shoot out the ball that is sitting here So there is 1 Better be sitting here and that will launch the ball in that direction so be it Horizontally Some initial horizontal velocity that is the war Answer answering The ball is just sitting here
So As it fires this pin disappears and the was false And you'll be able to tell when they hit by the sale That want series that was a preview and the glass guests The rule exactly the same time or close exactly as we come with our clever device right
And so the question is which hit the ground for the horizontal 1 going drop that depends on Fast awards always thrown up or they had at the same time not bad that you're going for days because of course every nite at the same time right realizes that you learned a lesson the class some of us think depends on the speed of the ball drop
Forces going ahead So actually do this demo
So yeah the kid is to listen carefully books So does your only once Survey
At the same time So back keep in mind but that accord they both at the same time now embittered this is Atlanta reset it Where I will launch a ball up at an angle Alomar challenge in this version doesn't always work but now ask yourselves which had at the same time or as 1 minute 1st Well I can't bend over the summer Like getting it 1st Other otherwise but again at the same time so let's get this set up while you think about it and about about a everybody's got the ball being dropped 1st pretty much brigade as said
Nevertheless carefully where you're trying to separate rejects key
But I it's easier for me I'm standing right here But this 1 does A little before that 1 Added that he believed the LA
The success visits at work on it I'll try 1 more more time right civic until the even more What about that but it's not It's not that site until this it's it's whether or not these things will fall off bike tilted too much And they're not not as development partners and that really quite the same height but their close enough to the Niger really the different and that their Burns really was not from a slight difference in height
What is going on in these 2 examples What we want as the following features are dead
It we can easily draw a map of first one We have a situation where we have 2 balls starting up the same height and their land at the same position So this is some So they're starting at the same height bait And I'd never exist 1 of them has vii not equal to 0 and the otherwise has been not at all horizontal direction so by wanted draw the displacement vector diagram at a drug these 2 vectors Added to double To do that well this 1 as simple does have 1 one-half GE to 1 square However long it takes the fall This 1 over here Has been not to be noticed He can't do anything to the interaction of being not adjustments at lumber and insisted to edit has won have G T 2 square and this is Delta acts for that ball ball number 2 Notice without Actually have to do any algebra Percy considered That invests vector Has equal this back there because they both equal the height And so there is no choice but for 1 have GATT 1 square to equal 1 have G T 2 square but I can cancel all that and I see immediately but 1 has People to 2 so they have to hit at the same time make sense Where would you didn't There's take a minute Draw the same picture for the case Where the It is lunch at an angle And decide whether they should at the same time or different time and related talk of a person that to go ahead and do that 2 True President When a letter like to volunteer a picture or your Coburn faced work now They rely on Monday Richard wore white what should be not look like For this ball over here But dropped a four-year arms were being to go Excellent And Of course That is also the same as did not take that way all my 1 duties were go They go down met here is the key This is what makes drive picture so useful when GTE square has started on which in this case a 0 0 draw at work at the end rely because That's would the exits right X final minus X initial and not plus one-half 18 squared house and not be the same as that vector so the head of a to square has them up At the end point of dealt acts of I'd come over here The not to We might have to draw 1 have teachers square the year-to-year visited too I have to go from the end of the not teachers that's what I'm added to and I have to end were dealt ends and I know it ends on the ground so or writing from drying the picture correctly without any numbers right I know that 1 have Gigi 1 square is less than one-half teacher Square just look at the length of the vectors that once H and this 1 has to be bigger than age by some amount Therefore when I gentle everything out to is Bigger than want And so 1 shot at Longer default Again I'm going do any Algebra II need any numbers And I found out that the Any questions on that that is No understanding that he's powder draw 1 to square Relative to be not Act will save your tongue of time in these kinematic problem at a really be helpful that Exactly how this year or theirs Absolutely no impact and did not Can't because vests by definition and possibly 8 Not is containing no part of H whatsoever But But while will hit the ground at the same time as you drop a ball that As long as you fire horizontally land very very far away A actually knew I'd like to If you like you find videos of you to bet that showed that You have to do something that and me this may not be right I think even Mythbusters that work I believe right yet so Viva Mythbusters episode it takes better equipment that we haven't been 11 shoot guns Back that's sadly changing I was an undergrad there's a devil with actual drawing been shot under a piece of wood And there is a nice piece of glass between us and them yet What do you ever do so that's an interesting question if you shoot Fast enough Horizontally so that it goes Into orbit By Bates adding a bad back but Then you write the assumption that they had at the same time relied on the ground not Kirby right as soon as it goes Far enough that the ground then I have to draw different picture Right then drawing 1 have Gigi squared like that Drive did not There was a large regions were aboard But and yes this now takes a longer day because it witnesses But But that is the fact that I have brought different grammar and so yes the answer your question as fine driver ground flat I assume it's not going so fast that theorist curves any amount The question and again that's where these pictures of But The pictures Actually let you know what you're assuming what you doing what you not doing any other questions Excellent Wigan got a quicker questioned 3 now
But What I have here is My my rocket launcher at 1 Article missiles so the bottle lines vertically the where wire when it gets here Releases a sweat and the borders large trade up foot questionnaires World War land the court And Ms. lighting a logical answer velocity Past that point and the question is does the Bobby large vertically Where In the car behind the car in front of the fire and it depends on how I and the speed of the car on a starter could request no I did not so that we started With a pretty solid voting bloc today 50 per cent went within the park so let's see what happens Bad there now is is rest here too there is a little bit of air resistance I'll try bit faster how landed in the cart adjustment danced our soil like my party But the main thing not the matter Fans they went They landed back in the car now face again we can get from drawing the pictures But but harder so let's think about these pictures for a moment the 1 that's easy drop as the car is just moving some velocity city and the horizontal directive so it's displacement times t because the acceleration of the cart is 0 Man how we think about the ball Wrap food 1st of all we do have to recall that helpful to recall on this case Frame of reference I show you where the ball is doing well The car remember constant velocity we said we can't tell every has be the same no matter what frame of reference for use in the frame of reference of the cart remember the cards velocity is now 0 the ball move straight out so they are living in do is fall back down so the frame of reference of the car ball lands in the car and death Is a central piece of AT & You are dealing with Constant velocity frames of reference the physics answer can change and so I have a collision in 1 frame of reference that the ball lands in the car but we all have to agree with the ball the car so you know you see the car moving so that happens in the car frame of reference that the ball lands in it You have to decide the ball lands in the car so What is that me let's look at it from our frame of reference and I'm frame of reference the velocity of sets an angle so it has blasted the ball Times tying it has won half GTE squared m is dealt the acts of ball has Delta acts of the car and against launched at some angle theta notice the various physics we used be in this situation right here we use a collision means saying position Now when I write down over here dealt the acts of the car equals via the car times equals and I look at my picture VEB of the ball times tee times Show coastline of data which is Delta acts of the ball with fact that I use a single time comes from the fact that I have a collision which also means same time noticed there was no delay here there was no way being there was no anything else right The broad outlines of the same time the car going and they land The collision the same time same place so I like my 1st demo Notice here I had a T 1 and to at the beginning because I didn't know they were going ahead at the same time not right They're hitting the ground at completely different places There's no real agenda so I don't necessarily need Same time for them to hit the the ground here I determined by using the frame of reference that the ball landed in the car therefore I have a collision and therefore for I can write this equation that is a central piece there that'll come up over over again in these problems so you really wanna be aware of that and that's how I like the idea of what we mean by a component of the velocity notice we do write these equations as via the cart times time and we could write is VEB shows Haider times time and we call this the X component or resign or component when I made my cordon system If you're going to use components you better have Roddick warning system is components and you don't drop system you will lose points Because This only makes sense because I drew their yes This is just like I have a right triangle because energy is always perpendicular I once a right triangle this side is my James the So Oh That's act you know what But me quickly review that in a bigger piece of paper I did Israeli quickly On Friday right But we will often have the adjacent opposite My partners And You learned it as Site is adjacent alright news signed data is Opposite overnight news The most common way we're going be use on an hour physics problems is we will know that and we will know that everyone knows that her that and so it's useful to rewrite each of these errors The adjacent side is the hypotenuse times cosigned later the opposite side is partners time signed it and to remember this form of verses that for now it you don't remember this but you remember this is that you learn so long ago They just do the 2 steps Now some people make the following mistake they assume that this is an equation for the ax component and this is an equation for the white phone it and then you'll be doing a problem and you'll have an X Angola wide-angle and this will be The And it'll be next to the Y axis this Always works this doesn't always work this won't work in this case So that was kind of a warning That now Any other questions on this 1 so that they aim final message of all 3 demos where you realize it or not is that components 5 Perpendicular coordinates The bark Independent so I have
X and Y axes and I have some vector egg and that's right angle theta then AXT equals the magnitude of a precise data a wife was the magnitude of a sign that have another Vector B with the same sort of thing I wanna make into the act Direct like electrifying city is a was And in the wider actions I came to see why SAY Cosby wife and batter give me the vector CD which is acts I have a citywide J. So I can do it In this traditional component In addition to just looking at the track And that sometimes were this is actually a little bit faster purity now the components notice as in this case All I cared about 1 the most in the act directed Once I picked X and wife And using these components is an easy thing to do So As we got the examples rigorous start when now and when you get to discuss insects and 1 of the main things this week is to decide for yourself you know Wait which more comfortable with your use components where you'll see after the game trainer Jack minus sign do other stuff for Do I the picture and is use the train straight from the picture where you have to be really careful to draw a picture right in user trick so By Simitis is about And depending whether you're more graphical and actor or more algebraic you'll like 1 more than the other Any questions so our problems but Where robot 30 meter class with initial are still at an angle 30 degrees arrest where does it lands So 8 We draw picture We have a 30 meter high class throw the ball It's being launched with V not of 25 meters per 2nd and an angle of 30 degrees above the horizontal ever ask Where does the So what This 1 is as about as standard and straightforward and simple Has become a couple things to keep promoting It As we draw the various pictures about it here notice this vector is dealt the ax rise starts from X initialed our initial position because X final our final position notice There's some angle here for dealt the acts or cause award but also notice that we will land With this final velocity velocity of you recall we defined in his wife's importer definitions is tangent to our trajectory right it was a derivative of acts with respect time so it's was slope this curve were making notice the angle we land that our out Does not equal failure a while whose variant poor and the use of a sort of things that will you have used to from the English if I ask where it lands I'm talking about displacement if I ask what angle and hits the the ground away What am I talking about Displaced when a velocity Velocity velocity is the direct your moving so velocity is the angle you had things where so you wanna know what angle you're hitting some with through another going upper down any of those sort of things that Velocity you might need to use the displacement equations the solve the problem but alternately going after velocity that and that's really important to keep these 2 angles set in your mind But it cost more So let's said this problem organist start since we wanted no part Klara goes that's where the displacement vector so that's what we're going draw is this vector equation And to draw but we have a V not teach remember one-half Gigi squares always vertical we know this is 30 meters so we can make a right angle here and we know that this is 30 meters this is what we wanna find the distance D that it goes and we know this angle is 30 degrees but also tells right away that writing here we won have due to squared minus 30 meters Now we pretty much have everything we need to solve a problem if we look right here We see that this side It is jazz via not TV Cosigned later That's what we did earlier the cosine of the data is But Jason DE over hypotenuse peanut food so This I know This I know if I can find to be on guard A noticeable right here I know this I know this And I know that so I also know tangent of 30 is 1 have GTE squared minus 30 the opposite Over the hypotenuse V not Favor know that sorry tangent I'd like to you can't it Opposite Over adjacent so that over 30 wide-eyed opposite over Jason because I only have time in the numerator right if I did sign when I started the right was signed a 30 and that has achieved the numerator denominator makes Dodge role of water Thanks So tangents opposite over adjacent now I'm an equation this will give me T I once I've TI comply game here so I'm going to do is write that down you I'm sorry Oh my gosh I clearly had not had enough sleep as we can I gotta days confused myself with my picture not my notes I'm glad someone is awakens class and it's not me so let's Harper lowered assigned into the harder version of the problem I still not everything here ignore everything I said about that When you get so I was just testing you as we do all the time so ignore that I could have done it the other way and centers would be even harder so I have the 1 Hagerty square miners might be not signed there would not right here Mr. copies for my notes that shows up minus 30 meters Epa's era The desire a quarter of its formula duty Equals minus 1 . 5 seconds and 4 seconds so when new ideas For sad because I want when lands in the future I like that in here and I get out a distance of 86 . 6 meters are what I'm going to do is I will do this again correctly But with components Wednesday Iran's the other question what I want you to see if you can answer before Wednesday what angle do I land that did you get enter that for Wednesday