Classical Physics Lecture 7

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Classical Physics Lecture 7
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good afternoon everybody its 12 30 so that could get started we have been making a little bit faster progress anticipated so today I could have started teaching stuff the next chapter whether that be confusing because learning about something and then take them a determined that get really questions as this summer term so will this whole off until after the midterm start of new topics in today I just I would do but problems so I'll budget problems here and what work from is there had no ideology take members crazy here are some Patel so the work the NATO questions are additional problems would ever feel that they are right so remember repealing with energy and work tried and so all the way that we start solving these problems using conservation of energy energy from 1 country to another kind and depending on how the problem is new you right this is like gravitational energy plus energy initial equals gravitational energy potential energy plus kinetic energies final price this is if you have a problem with only the gravity and motion right Rice's this is the most general equation is slightly specific this equation example assumes is no energy loss he right is no friction as is energy-storing this spring Eritrea so even tho we often start wrong with this equation as if it's a very general equation however is not being most general in some situations you may have add another term life energy absorbed heater friction order because it was like to remember what assumptions were made a really cool thing about 1 of the reasons why this is so useful is that potential energy due to gravity depends just on high not on so crime the y-axis here have . 88 . be there the gravitational the change in the potential energy
riches were really interested in is registered in the difference between these 2 quantities of Delta it just ng each priority
Chesney height between pricey notice only on the of Heights is anything that's right doesn't depend on whether they took a straight shot would to dilute where they would do it Ethernet early-bird special came back really doesn't matter which is amazed it's amazing that all the information that ended July energy contained just in initial and final position even know why that is part what why wall but the not only did the that was shot wide but so what if we had another nearby planetary objects that was also giving is gravity this would make dreamer where the next component to gravity because utility the difference my question is would been depend on the path he took for only an initial from a position a question is why the gravitational Junjie only depend on the initial opposition and not on a quest to get it because it's only wider made another proved that he could rotate reacted to the vaccines and still new ideas because energies things are a bit but virtually frictional forces in truth that that this is the gator frictional forthright say you're pushing something I say you either I you know you're playing the slippery slide a place USEPA's saliva with sandpaper and you're running along their current junk-bond sandpaper slide along at a lot of energy getting it turned heat right and shredded but it's a rare now in a few slices that led this way and slide back and they them again take
3 terms me a lot more energy want her right so there's a big difference between 1 trip in 3
trips even leave the same initial opposition so the case of friction it does depend on the path which is gravity only depends on initial Our opposition but to my question is why such River gravity and not for other sources of energy forgery you have start there is version the he's a rap can deliver what about potential remixes true all it is all is just another way of saying the same thing I'm asking Why is this half the only depend on initial composition things because of potential energy yeah when they get back OK let's investigate back along that direction lies the solution mind some so say instead of going straight here right go from here to here you lose potential energy what happens but make it simple ETD detour up comeback what happens is you go up you gain potential energy bill you come back when a Lucas and how much exactly the same amount as you have to be right so imagine this is the simplest have no imagine a small deviation from Uvira come back to the path of aviation you're going to I'd legends some deviation from this past right and cut that aviation half the amount Dingell energy difference in the 1st part of that is canceled by the 2nd part any deviation from the path potential energy use his sorry when you deviate from the path you change your potential energy when you return at path that change is negated exactly by a return because the potential energies linear there are so few details of any deviation from Catholic straight up and come back down to gain additional potential energy than you lose it we return that's why it's true for gravity enough friction is different right friction you lose energy of a whale a new losing without right gravity as linear dependence which means you gain and the potential energy OK so that is
that simple fact gravity makes a lot of physics problems a lot easier than they they really have a right to be for example so as to the first one sorrow there the questions whether concept well there is more about feel reader
those the mayor says says a light rigid Rod is pivoted on a low friction horizontal Paxil the lot of length L hang straight down the rest of the small massive ball attached to bottom and there's still a lot of length L here With a mass attached to it think of it like this says they're over the direction you strike the ball suddenly giving it the horizontal velocity so this swings around a full circle there so it goes here and come back what is the minimum speed at the bottom required to make the ball go over the top the question is what velocity you have to give the ball here so that it makes it all I beseech you just barely touch it it's going go back and forth a little bit to TO harder logo hot the question is with the minimum velocity necessary for it to make it all the way Adam is always 1 with energy judge also so if you could already see the solution they you could drop a lot terms in advance but if you're not sure exactly don't quite have been set yet the sailors problem is solved starchy great and if so what terms are there energy is no friction there is no spring just motion in gravity but said alright gravitational initial potential energy kinetic energy initial gravitational final energy plus kinetic energy final OK now would simplify let's say called 0 2 l from by taxis be anything like said 0 down negative million miles could made by calculations while it uses to 0 because then initial potential energy jobs out fewer terms of would better similarly What is the final kinetic energy 0 why 0 America did this thing really hard it's been around for so long right wiser fine Connecticut Energy 0 for the prom asks us what is the minimum speed required to make the ball go over the top of the circle that implies what is seeking to give it the bottom so it just makes it a top I so his hero velocity but that would be the minimum whatever speaking each year so that all the gets turned a potential energy and at the top is no velocity that is so file kinetic energy 0 so as our friends said From the kinetic energy into potential energy essential energy very simple right it's an G 2 comedic energy 1 of MB square now the mass drops out of right very easy problem right knee and if you just users introduced kinematics you have to think about its motion circle and these were all our attention from wrong all the don't think about any of that doesn't matter that its stature of abroad as a matter that because of a circle all that matters is you've given a kinetic energy here that's turned the Accenture Ltd the essential energy very easily calculate comedic energies very easy calculate with respect velocity she could very easily relate velocity height that's a key hero turned Connecticut potential energy back into each other translating velocity another really nasty seen problem solved very easily with a thank you grab having these property grows review has no gravity is no user the fastest because that the only fundamental force for which we have no quantum description at every other fundamental forces electricity magnetism the weak nuclear force stormed their force with idea how works quantum scaled and microscopic scale exchanging of the tiny little particles between each other for gravity we don't know no quantum theory of gravity enormous outstanding period of his problem you're than the 1st all that is a giant on the field lines so don't imagine that physics is all done a really big obvious stuff to do OK it is and it and if gravity had a quantum nature quantum gravity particles which called Tong U.S. noting that these searches for graft on an autograph Thomas yeah it's a communicator for the gravitational force with me means sucker little wave packaging gravity so a wave in space time and space time is experiment in Louisiana also in Washington really recalled looking for this bestowed by 2 minutes itself and set up a leg 1 mile aside so this is the building 1 the L-shaped one-mile aside and have a laser here that she's against mirroring comes back and measure how long it takes a little over there Back in doing so they measure distance very precise simultaneously measured the distance with another list too late any use interferometry make it really said they would have really precision distance measurements hoping that some Gravatai will be created by like a neutron star will bring a black hole the high-speed to black holes sliding into each other somewhere out there the universe some crazy gravitational creating a ground on which washes through universe toward us if gravity on comes the away space time which means it's contracting and would happen is wanted to let you get short the Arab and so what they did is looking for a wiggle like that will only 1 leg gets shorter careless high precision and the reason there 90 each other so they could see the matter what direction and they have 1 of these in Louisiana 1 in Washington state and Italy so that if real revelation
comes maybe able see propagating across the face of the earth which cool but really difficult experiment is that he super quiet like a lasers ask hanging from cables at Chinese isolated like a truck comes by shakes the whole thing and so they have a bad really complicated mechanical systems isolating of all sorts of acoustic noise and then they've looking has been running this thing like 8 years images will be seen absolutely nothing because you don't expect Varrato so it's a difficult Kermit colleagues just noise just shake you just do what this is is anything other How to compress it's so the definition grabbed sort things could give you a false compressed measurement cannot last things you really do all the final forces come in In back yet so let magnetism as the photon a photo of his little wiggle In electromagnetic fields but on the weak nuclear force as the W and Z goes on see both a lot like photo number has massed for every 4 Snowmass and the strong nuclear force is the when the the nucleus together are you ever wonder why the together a nucleus is a bunch of neutrons and protons prose the positively charged neutrons at no charge 1 of these part of the strong nuclear force this thing has for called the blue on loser nucleus together I'm not a charge articles it was chartered a very different all the a mail forces understood chemical level quantum theory of them and but we discovered particles produced and studied each of these but nobody's never made a profit on just an idea as part of a series of rebel assassins yes a name that's my kids of course that was a guy as a particle called the GATT psi is discovered simultaneously by 2 different groups want to my feet Stanford and they announced on the same day the discovers actually the longer story because these guys running a really long experiment it's a longtime circulated he's as it really powerful accelerator they had to know exactly where a lot of colleagues Burma where he knew will look you discovered a 20 minutes but not knowing where look makes a pretty hard these guys and the experiment in some people think that the information about whether they receive a leak the there people who came 1 day world replicate the results and announce results on the same day it would because they were too announcements this guy from MIT the same team named the GATT which apparently looks like the Chinese character his name and disdain for guys called the site particle because it's so looks in there and nobody could agree because he discovered at the same time we call it the GAO's West Side article stupid so whoever names against do Irvine tickets name of Back to mechanics come on problem but to grill kilogram block is attached to a spring force Constance 500 the block attached to a spring force constant is 500 new premier of the His 2 kilograms kg the block is pulled 5 centimeters to the right of equilibrium and released from rest foreign this year the bloc as it passes through equilibrium if there is no friction those sitting at 6 0 0 and its moved over 5 centimeters ratifying the speed of light so this problem is just like the other problems we have gravity emotion this cases of gravity gravity social and is replaced by potential energy spring so start from EU initial Eagles be final over the initial state is having compressed files is back with a gun the initial say we have the potential energy this initial plus initial kinetic energy potential energy the sprained her final final kinetic energy still initially to look at again urging that pushed the block back here holding it stationery the springs crust so there is some energy in the spring Russian right how much potential energy is in the Springs compression 1 has to be axed squared when I get that far I remember the a formula for but didn't remember and I did remember that the boss of a spring is negative case KTX I could calculate by doing in a role that she text is negative 1 that's right in a rural exodus exporter to so long as you remember this equation for the spring you could be derived we need 1 have squared down 0 was the final potential energy fraying 0 because were interested in the point when it spring is back at equilibrium were x equals 0 so this 1 0 and this is 1 half square question is asking us what the velocity well they told us with place Was it told us with Katie was also a mass was so it is also the velocity right I was pretty simple look at this as just the same as the driver problem said announced gravitational potential energy we have potential images of David then they make a little trickier they say I find this year the blockers vastly equilibrium if the coefficient of friction between the bloc and the surface is 0 . 3 5 and now we have friction and the game so result from now
will have to do them by friction to which
side initial Koizumi worked at an initial stage it's the work is done by purchases amid gets depends on the size I'm right leg but if the head so this is the term friction word I get this term well the work done by friction is returning what form just half force times the distance Pride of the force here In his 1st of force magnitude of the normal force coach fiction distance the normal force is as good balancing whatever the weight is block of that and GE New Year's deed that the term that is make sense out of there is I think about it your energy stored the spring that energy then gets turned into velocity and also into heat from friction right of the larger the coefficient of friction over the last energy you have left over from both for the philosophy that make sense to me as this goes to infinity disclosed a 0 in virtue would mean thing sticks even as the spring is proud of it so this doesn't add any competition really except for mathematically we know this number we know this number notice number we of this number is just a slight complexity so you all this looks very similar minors pricey notice to the velocity depends on this terms and in a negative way more velocity comes from a larger coefficient of friction it was at Otto the With the so we have a different model years started the same problem almost the same set up for the me change the universe working of restrictions so we have to write a different initial and final energy which had another term because the University of slumber of questions but on look it's only Syria have some system of this table top of the block on a tabletop connected by a road goes over Poli and the ball here before is 3 kilograms this when it is 5 kilograms and his physical picture of virtue between the 3 kilogram book on the surface is 0 . 4 the system start out from rests was the speed of the 5 kilograms ball when it is falling 1 . 5 days his above velocity so this is you clearly energy problem right you have potential energy here you have virtually energy here these 2 things also connected by that same acceleration so soon variety initial energy while energy so what terms we have initial image gravity and we can write initial only know already that 0 because everything starts rest so it's pretty simple the only thing we have in initial state is gravitational potential energy then packets turned into other gravitational potential emerging so were interested in his difference right plus kinetic energy final plus the work done by friction just like that the spring from adjusted potential as spring with turned and emotionally object plus he from friction here the potential energies returned to the motion of the pair of objects plus he from OK Salesforce think about this gravitational potential energy by this is MGH due the relative height here I'm in wanting to be explicit is to say that final height is 0 this 1 is 1 . 5 this goes away now whether master put here for the the potential energy to it to 8 kilograms 3 kilograms by the Wi-Fi that I was moving up-or-down the potential energy here depends only and is now this thing . 3 kilograms 3 thousand kilograms doesn't change the potential interviewer here it will change the acceleration of the system because of harder to accelerate this thing which really heavy but it won't change the potential energy guy the cops the massive these 2 guys will come into the kinetic energy here if this was justified guys services 5 times Jeter . 5 rewrite of the kinetic energy manic energy here we riders 1 half 5 plus 3 right this is the mass that kinetic energy the combined system they both have kinetic energy you know once hanging a once sitting on a table the same velocity was connected by ropes Richie was 1 system with mass 5 plus 3 doing think about that way what could released a separate terms write a Quranic energy for this and then energy for that and then all that here's group with parentheses is a real physical inside the critical thing is noting that they have the same velocity have you want me to your friend of with 1 equation to unknown not salt in the that same velocities is key to simplify the problem is that the kinetic energy charm and then we have the work done from friction right for them from friction it again and Jeannine D right now what matters to use for this 1 but 3 Red is the the only 1 that feels friction and there we have G knew which is given and then we have the distance half are resisting go well it travels horizontally the same distance at the other one's life so the results of a new 1 . 5 so
now we have we know everything in this problem except for the velocity why have you know that Molossidae because it connected by but for for where growth is without
merit it seems stupid group of our warm the Pegasus later your is selected to be few after a while you fond they all start seeing the same nite and that's because there aren't that many terms of me and formula that against a potential energy work lost leader friction that's all that there is isn't problem everything a promises from where the mix that information of the Church of the day's so here we have an 8 cm. rod pivot around it around its center a sues the axis and half of it is 40 centimeters by half a kilogram rat sits on 1 hand it was a rat more from other cat their rats about 1 end and a half a kilogram nobody knows a reasonable amount a one-pound rat as a predictable but in chatted about such cat arrest as a catcher pioneer status of the Parthenon arrived and the other side is 8 . 2 kilograms mouse is apparently out smaller Minihane the more can't look anywhere . 2 kilograms about the other side and now the question is because this guy's head you know this guy this will eventually be like this Arad hanging on for dear life here the mouse is here and the question is what are the animals speeds when they reach the vertical facies starter Mark here an imbalance in the year from the masses put this way what their most beats but so is that this 1 out so what are the energy terms on initial states there's potential energy right gravitational potential energy could write a kinetic energy just make sure thinking about it but they're 0 velocity initial skates at 0 right and then there's gravitational potential energy plus final potential urging practitioners rotational last Saturday Elsinore's this elite rat prior to that date so now we do potential energy off we choose 1 position be 0 To make it simple price initial state to be 0 after 0 30 years couple enjoys you could make right to choose based Iraq so the initial state has no potential emerging choose 0 down here and there that really matter because were interested in is the change in potential so it's just due 0 to be here and there we Disney to calculate change of potential energy related and rights so the change of potential energy is just relative to the heights and the masses right so for more for the EU mouse it's and mouse times Jean times call this they'll and then authorities because the mouse on top right and wrapped his indeed am rats times G times mind so it's GE tell them Laura plus 1 one-half and these where analysts Otsego go the other signs right this guy here this has to be positive as velocity were positive masses positive the same terraces which should be negative the writer is heavier the this is back give us number it looks like we chose our act consistently and because of the velocity Of the result of their philosophy that would be putting here but total right as again we don't have to worry about the fearful rotational this rotating make every much more complicated but we're afterward that just as were initial configuration and the final configuration thank you grab programs here's another 1 but uh Averyl force death is maintained canes into a frictionless similar circular surface Moslems and similar hemisphere that the radius ain't down here we have a spring which is wrapped around this hemisphere and and a block here variable force death is maintained he injured and to the surface however this effort it's pulling its long this crazy by slow variations in the forests the block is moved in the spring to which it is attached a stretch From position 1 to Position to calculate the work done
in terms of the radius day and this tangle what is this problem the 1st solitary reading because it has in words and twice slowly
variations in the course of blocking moved in the spring to which it is attached stretch why did they say by slow variations in the report that seems to me like there's only 1 could only talk to us sports like some special words that they're hoping to communicate from physics to a right state the system equilibrium or at rests with translate that 0 velocity turned for what variation where we sort of it is changing social the host but watch out ideas for foresight so they're basically history is telling us is no kinetic energy prices very slowly being moved the mood in the mood for initial the final positions and no kinetic energy either case by slow
variations in the forest a block is moved and this spring to which it is attached stretched from position 1 position so it's just
another way of saying final velocity 0 but may still has no kinetic energy initial say no kinetic energy in the final state what is their problem attention is efficiently spring and his rapid rise and the only reason this is different from any other gravity bring from visiting gets wrapped around the block what is and that has an affect us how solve problems with the like normal forces they know that's all scale down so what we have to worry about well remember with it asked us to calculate the answer from the a and data so we calculate the gravitational potential energy Real calculate the height in terms of and they we're interested in how far this spring stretched because the war could be stored the spring one-half case Banks weird or X is how much the springs would stretch from equilibrium so to calculate X room at the better terms a really really this problem is the same as is the problem worse brings pulled a one-dimensional but they invented the axis for us to make it a little more complicated and what we can do is say potential energy gravity gets turned into potential energy from the spraying Due to serve from the general equation of initial filed state energy but only is only spring energy in initial state gravitational states as mayor and so the gravitational energy is Ng times Delta why ride always dealt wine in this case so it is converted do they signed up front expressed the
energy terms in these in these quantities of fastest for prayer What
about this spring well this is 1 hatch Kate X where have right next squared you're times they wrote the distance around her it there so that all energy from Basel
problem so is often the case with ease as problems they seem cop
OK with that To when you read them set up correctly the matter is pretty straightforward if you get really Harry math often is a son done something wrong it was 1st on Iraq aged 4 have played they might think a less unfair like what directly from me so convoluted Wendy and Lucy appreciate over remember that the visit which are assault visits from real life your life sometimes gives you complex problem it's a real achievement of physics reliever Turner complex rely problem into a simple model handle easily tools was that according figure out how to use the models you have to apply the rules solutions to dance a lot of this class seems to be extracting simple but situation because that's a problem of so here's another
nasty looking woman and the Book
of the gravitational pull the Earth an object is inversely proportional to the square of the distance of the objects from the center and so we already know that probably further down says the gravitational pull it is proportional to the square of the distance of the object from the center of the earth at Earth's surface this force is equal to the objects normal weight and is not going to and a large distances forces so that tells us we got write this force as end Gene so this is this from said earlier this is the radius of earth so they told us that were 1 of our squared fine and they tell us at your service the values and MG such a step this up put right Constance so that if you in the Earth's surface for little are you get MG is so so far richer as it would told into math OK and a large justices of forces 0 some expenses are good affinity for what is now the question is if a 2000 kilogram asteroid 2 thousand kilograms area under a 20 thousand kilogram after his also Earth from a very great distance away what will be its fetuses strike the earth's surface so pulsar through greater very great distance away time so initial position are is basically affinity final position articles are priced at 2 thousand kilogram after from a very great distance away from what will be its few Louis strikes the Earth's surface and how much Connecticut Energy will import for playing ignore the effects of Earth's atmosphere so basically they're asking says what this speed and how much kinetic energy will import close to Obuasi connected right it speedily energy so is distracted Connecticut how exactly kinetic energy this thing gains from falling from infinity era service so wiser Singh gaining kinetic energy gravity is doing work on right is turning authorities turning gravitational potential energy into Connecticut so it starts out with a huge amount of gravitational potential energy because easily in the far away and it's a false and turns it into Connecticut now if we often right gravitational potential energy Ng each write to a right that here MGH beekeepers and into infinity North America and I would get let well NGH Eagles 1 of and these square Davies and virtually Astor's here that we know even if I wasn't due to relativity that would choose a Why does this work here but because this assumes that each is small compared to distance from the earlier figure on serves Earth which is very large a new doing problems but shooting baseball's or whatever it is that you could assume that she is constant and you can get the right answer because the changing G from here to here really if however your scale is this is the year of Yazoo you're talking about master kill trajectory that obviously obviously this they don't have that Russian after last week 1 that exploded over Russia last year fight a land its final resting what was in a lake huge told me eyes and itself was lovely and they had to wait for summer and bonded Doug thing up before anyway obviously the force of gravity me very different here here force gravity here we are told basically right so we can't use MGA batters we get Ng we got MGH by saying well the work is role of force that with distance Ryan every several forces is Ng doesn't change so becomes page but that's not true divorce now forced changes with age so we Weaver calculates what is Red obviously this is almost like cancer I just need to know what is the gravitational potential energy which we convert 2 kinetic energy the question is what it is this work done by gravity and so we do this calculation for F resistance said but various as a vector so let's think about the direction here we said this to be a positive are was the direction of the negative right OK so 1st but for negative they now have gone from a vector equations here one-dimensional equations here have said these vectors pointed opposite directions and so here I'm just writing Steelers put a negative sign reflect the fact that drops a direct result of a way to do this mathematically realize this is aware that we know it that is stingy you are squares right this is able to negative In a roulette but you guys like riding in will 1st former water integrating from they have integrated and G's they are EU squared off over Our square and the interval goes from where where you're from infinity too here right effect and if you have done this differently from cemented a role that Ng army comes out front for negative and jeans party and general are scared but not that hard mineral was able avoid over our spirit negative overall this becomes MGG are these times 1 overall evaluated from party to infinity and so the are Infinity is obviously 0 doesn't matter this is becomes where you're this this becomes and Jean and because the masses and the Lord of the Rings I got 1 . 2 5 times 10 to the 12th grade but then translate into velocity is a blistering 11 thousand meters per 2nd but a vivid how realistic is this summer things after a target to hit her their speed most affected by the gravity of the earth Nowhere is there speak most affected by the gravity of the sun right happen get in the way the CEC they're heading toward the sun orbiting the sun and its path is our gravity will affect it more like pull words as mostly effect grabbed signed which between these things going faster than if we adjust wrapped but in a Mozer problems were ever do have not happen on earth and you have to worry about doing in a role in calculating the work has enabled the
Jewish remember the assumptions inherent in the and they pushed amid yes the I was well I I am the focus
of his question was think about what do we know at infinite distance but no force right up these days and energy 0 does that mean no the actual value potential energy is not relic that had a million to any potential energies on your consistent wouldn't change so reached that is the difference in potential energy between 2 position prior to me never actually senators say here the 0 4 duties were likely the work involved in moving from 1 place with force to another place and moving through the gravitational field cut and the difference potential energy with a work Due to the forces equals 0 it will not end in the next chapter of of the midterm will grim analyzes in more detail essential functions have derived forces from potential energies we won't get into those details socket of Let's do a
problem like this there's a mail whole-wheat any other persons weapons duopoly and a real to
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