My name is Vinak Hegde, I am VP of Engineering at HelpShift and prior to this I actually have worked at InMobi where I actually built the first few generations of the data stack which I think Amrishwari just talked about. I contributed to the data warehouse as well as the first Hadoop installation and I think in India it was one of the first and probably one of the biggest probably exhibition of maybe Flipkart in India and before that also have been doing analytics I was working at a company called Akma which is a content delivery network and we also built analytics stack a complete product line out of that. So, I was the architect there and even in InMobi I was the first guy in the data team and here at HelpShift we have an in-app mobile help desk. So, we are building a data stack from scratch again. So, while I have taken we have built you know data stacks at three different places what I have come up with is a framework for making decisions regarding you know what components to choose what are the trade-offs that you need to make a lot of it is like hard fought hard fought hard work advice where we didn't take the right decisions and then we had to wake up in the middle of the night and fix it. So, I am going to share some of my experiences regarding that. So, what I am going to do is divide this into like three parts the first part I am going to talk about the nature of data because some a lot of people are not aware of the second part is I am going to talk about the framework and use that framework in the third part to talk about very specific examples of software which fit into each of the layers of the framework and comparing contrast you know why something is better than the other. It is a lot of material to cover. So, let me see how well I do but I see not this not as a see this not as a talk but start of a conversation. So, feel free to you know connect with me I will be hanging around at the conference for a couple of days as today and tomorrow and also I will be around at Nexus VP partners booth as well. So, let us get started. So, this is an oil rig data is like the new oil and it is not just in terms of people want to the metaphor is quite rich because even if you look at the terminology we talk about data mining or you know refining data. So, just like oil everybody wants to look at look at raw data and then gleam insights out of it refine it and you know maybe sell it at a higher price or you know use that to kind of fuel their engines of growth and that is something that everybody wants to do. So, also on the on the farrier side we are I think at peak big data as well just like we are at peak oil and you can already see the next bird's word coming up which is like internet of things which is also kind of fueling big data as well. So, how do we understand data? If you look at data there are certain aspects of it that we should know when we collect data a single data point it does not tell us much it may be it is a sensor reading or you know the bid rate for an ad network things like that. But then if you understand the relationship or take two different seams and combine them for example, in ad network you have a you have an impression and you have a click. So, if you have a click it tells you yeah there is an intent there and that then it becomes like information you know something more from a single data point. So, on the left hand side you will see that there is connectedness on the on the bottom axis you can see there is understanding then you can take some of this information and then you probably aggregate it and you start seeing patterns where that is where kind of machine learning statistical analysis fits in and once you have done that when you you can take the same kind of understanding and knowledge and apply to different domains that is when it becomes wisdom that if you know that these are the patterns that I continuously keep on seeing and I can use those pattern in a different industry right that is when it becomes wisdom. So, this is like the hierarchy of you know of data and always that we should try to move up the hierarchy and down the hierarchy to move from data itself and see how we can combine and go towards wisdom because that is where the real action is. So, this is what the data stack looks like at the bottom you have data generation where which could be like sensor networks it could be a mobile phone it could be a click stream it could be a web browser then there is data collection and transport if it is a web browser it could be like JavaScript sending you know or a pixel that is firing or it could be something like you know like low powered sensor networks where they collect data or it could be data that is typically transferred at web scale between data centers or between maybe an ad server and maybe the Hadoop ecosystem or in the case of mobile it could be something that collects stuff from the mobile and then sends it back then once you have collected all of that data you need to store it somewhere physically right. So, what are the decisions that you need to do when you are designing storage right. So, I am going to talk a little bit about that finally, once you have got all the data in right you have to take all of this data and you know transform it do various kind of transformations with it and do the processing and make it ready and kind of ingested put it in the format which is ready for analysis because the raw data may not be good enough to perform any analysis. So, maybe you need to do cross feed validations and stuff like that and finally, you take all of this and at the highest level your visualization which is like a data narrative. So, you have gone from a single data point and you have taken all of that together you have taken the connectedness of the data and then you are telling a narrative about from that data using the visualization. So, mainly I am going to talk about the bottom four layers I am not going to concentrate so much on the top two layers because of one lack of time and I also feel that that is going to get covered in tomorrow's talk towards the end by Shailesh Kumar. So, I am going to cover the top bottom four and he is probably going to cover the top two a little more in detail, but I will talk a little bit about those two as well. So, there are two different approaches to getting insights you start off with a hypothesis and then you find data that can support or refute that hypothesis. For example, you feel that if you introduce if you are in a retail market and you feel that you can change maybe the arrangement of SKUs or arrangement of items on the shelf and that can probably increase your sales because maybe the items that have a higher margin or maybe at a high level and those which have lower margin are at a lower levels. So, typically most people will say hey what is available in this category buy that and just go off right not everybody will look at all of the alternatives evaluate them and do that. So, you are pushing the user to do that. So, maybe that start off with a hypothesis and see if it works you see with if a certain shelf arrangement works or not right that is one way of doing it the other way of doing it is a bottom up approach you look at the one data showed in the slide before you start off with a data point then you try and see if you can combine with anything else then you try to find out if there are any patterns and then try to see you know if if there are certain principles which you can apply to kind of enhance the data. So, it is like so, this is another approach that you can use. So, what do you mean by nature of data? Nature of data could be mean could mean like if it is a social network like your connectivity of friends friends right that could be one level it could be inter relationships also for example, if you are using Twitter not only the message is also the location is important right where are you coming from. So, what so, Twitter does that right from what location are people we can even set the trends on a localized basis and that is because they have used the nature of data exploited that you also look at the interrelationships between different entities right is it like a one many relationship is there like a is it a peer to peer relationship so on and so forth often what is useful is to look at the ratios distributions variances and the medians to look at look at the shape of the distribution and it can have a huge impact rather than talking about this in a very dry way a great example is the retail industry which everybody of you can relate with right. Suppose you have a chain of stores and you want to optimize maybe revenue how do you do that there are so many approaches to doing that right you could you could actually say for example, your pantaloons or your west side you could either try to increase the number of footballs in which case you have to do outreach and marketing a little more and then you see how many you measure how many footballs are there how many people are coming into your store or you could say once the customer is in I am going to try to maximize how much money I would make out of that customer which is the classic argument which is average revenue per user average revenue per customer right. So, each of these the metric you try to optimize is very very important because that metric can actually make your business grow like crazy or it can actually destroy a business because you optimize for the wrong thing it can have a huge impact on your business right. So, let me let start going the going up the stack starting with the most basic thing the first thing that you need to kind of know is like what data needs to be generated for if you are for example, if you are in a retail store you could check maybe number of items average price of the item do they buy it in groups like for example, shaving blades would typically be bought in groups or diapers would be bought in groups right or so what is what is it that is kind of important. So, you have to see like understand the domain and see what what needs to be generated you also have to look at the frequency of generation for example, if you are looking at a meteorological data how good is the data generation for example, do you need to take samples every minute do you need to take samples every every hour or is it ok if I take it maybe like just once a day and take the max and min and that is good enough right. So, this is one of the most fundamental things that people miss and this is extremely important I cannot emphasize this enough because the quality of your data that goes into any of the upper layers matters because you can take good data and take make garbage out of it, but you cannot take garbage and make you know gold out of it and I often find people get obsessed about frameworks you know should I use Hadoop should I use Spark they do not look at what is the nature of data and that is like a real huge fallacy is kind of unfortunate in our industry right. So, this is so in this talk I am going to kind of counter that mentality it is also possible to pre aggregate stuff right or you can sample stuff, but when you sample you have to be sure that the sample is representative of the population. So, population is all the possible values of the outcomes and the sample is a small representation of that for example right if you do an exit poll you could typically you know ask people whom they voted for the on the internet is it a good sample probably not because it represents a section of people who have access to the internet which means that they are a certain economic strata right and maybe all of them voted for maybe the BJP and all the poor people actually who are larger in number voted for the congress. So, in that case you will have issues with getting we getting insights out of the data because your data sampling is itself also other thing to kind of watch out for especially which has a huge impact in the analysis analysis stages look at the metadata that you can attach right for a tweet has a huge amount of metadata for example it has a location it has if you have replied to somebody it also has probably things about like what what client are using from that also actually look at what what you can gather around a single data point that metadata is really useful there some examples are sensor reading itemized store purchase data and impression data right. So, these are some data formats I will quickly go through them and tell you why choosing a good data format is kind of important right. If you look at csv which is like the bare minimum that you have or tap separated which which which is which actually emphasizes a row based row based approach and it is very hard to kind of represent network data for example in a csv right the other is the next slightly more evolved format is json right. So, json has has a notion of hierarchy you can embed elements inside it and that is slightly better the third format is thrift thrift has rich data types and it does not care about the language or anything because it serializes to this and it has different it has different language adapters where you can read from that data which serializes to this and finally, rc file I think most of you might not be aware of it, but especially those who are looking at Hadoop and especially for analytics should look at rc file. So, what rc file does is your huge amount of data which has tons of columns and tons of rows tons of dimensions and measures it actually splits the data in a columnar fashion and that is especially important for analytics and I will dig a little deeper into that in this into this file format or this sort of thinking a little bit later in the talk, but I put this here so that you can Google it and you know probably look at these alternatives because you should not only look at csv. Then we will look at data collection and transport data collection and transport you can do some aggregation at the source or send every data point you can also do some pre aggregation locally or store forward. There are two different methodologies that people typically use either one is that you either push the data or you accumulate it and then you know there will be some kind of network API or some kind of callback that will keep on you know pulling this data. So, both of them have their pros and cons in a push scenario so typically it can be synchronous, but it though it is not necessary pull is better because it is easier to scale. For example, if I need to sample data right if I use a push methodology I can and my server which is collecting it is down I can do some updates, but if I if I have some kind of local aggregation and I use the pull methodology if I put the server down for maintenance and I pulled the data from it then that can work really better. So, push versus pull methodology is something fundamental that you need to think when you are collecting data. There are also factors in choice of underlying transport protocol there are some of them I think you are already aware of so I won't go into TCP and UDP TCP is connection oriented and reliable UDP is connection less and hence unreliable HTTP API is most aware of, but something interesting that most people don't know about is MQTT. MQTT is a transport protocol which is useful for sensor data and resource consent environment. I have seen also people successfully use this as a pub sub mechanism for collecting data from mobile. So, it is not just when I say resource constraint it need not be just sensor networks and you know stuff that is out in the desert for example, it can actually be mobiles or equipment that is moving around for example, GPS or if you are maybe correcting some of telemetry data that is what it was built for that you can use MQTT. So, there are alternatives to TCP and UDP which are the most popular ones and MQTT is one of them. Just going back there are a couple of factors in the choice of software here. There are some data where you might be ok if you miss a measurement. Maybe for example, you are taking meteorological data and you are taking a sample of the temperature reading every 5 minutes, but what you actually need is maybe for the R you know how the temperature varies on R. So, maybe if you miss a 1 5 minute thing then it is fine. So, that so the reliability constraint is actually it is actually relaxed there. The delivery policy is also something that needs to be thought of. You can do it you can have at most once right you deliver it at most once or you can have at least once or exactly once and that has huge implications on your design. This is something that lot of people do not think through when they build it and we will go into an example where this matters. And final one is like durability can the message be stored? Can it is it fault tolerant? Can I recover from failures if a node goes down? So, how many people use Kafka here? And how many people use Rabbit MQ? Fairly split. I hope you have made the choices thinking carefully because I am going to tell you where each of them excel. So, it helps you to use both and I will tell you why we use both. Typically you do not want software proliferation you want from operational standpoint you want to use one software and use it everywhere. So, because how it behaves under load and for deployment it becomes much easier to maintain one software rather than a bunch of softwares. So, Kafka is very producer centric what it does what that means is I just assumes that the producer will keep on producing and I will keep on queuing it. The consumer can come anytime pull the data and consume it right that is what it kind of assumes and its whole design philosophy is kind of designed around that. If you look at Rabbit MQ, Rabbit MQ says hey I am going to get a lot of data and I am going to be just like the central broker and just keep on routing it all the time right. So, that is where Rabbit MQ is good. So, Kafka is does not have very sophisticated routing capabilities. Whereas, if you look at Rabbit MQ it has fairly complex rules that you can set up to route data around combined data and you know replicate data as well. Kafka is also better for a durable messages what that means is like for example you can send everything from a anything from a CPU reading like how much CPU is getting used to an email in Kafka right and same thing in Rabbit MQ, but what would you use for both right. If you need durability right you cannot lose email maybe you can lose a reading I would I would highly recommend Kafka right because it is designed with disk as a story in mind. Rabbit MQ also does that by the way I know a lot of people will say hey Rabbit MQ also does durability. The fact is it is not the design decisions that they have taken were not designed for reliability for durability. So, it does it and the performance really sucks when you put you know use disk as a backup for that. Also Kafka is better for large messages. So, if you are giving like for example email or if you want to send a bunch of PDFs to people or you know just in this lot of data that is coming through PDF for whatever reasons or anything that has large message size then Kafka really works really well. Kafka is also extremely performant when it comes for large volume of messages. Whereas with Rabbit MQ what we have seen is when you increase the number of messages because it assumes that they are going to be transient it does not work very well for large volume of messages. So, the difference is like if you can do almost 100 plus K messages per second for Kafka, but you probably start hitting the barrier and you know starting getting CPU maxed out for Rabbit MQ for the same workload for something around maybe one-fifth or one-tenth of that. So, that is that is one of the things around Kafka. Okay, one last thing I wanted to say is that we use both for all operational data where we do not mind maybe losing you know some of the readings we use Rabbit MQ for stuff where we are where we actually don't want to lose stuff and we want at least once kind of processing for example email we use Kafka. So, you can see the complete split. So, one is optimized for one thing and other is optimized for a slightly different thing. They both do queuing they both have the same kind of design design goes, but the design decisions and the trade-offs they have taken are quite different. So, the next thing I am going to talk about is data storage. So, let's dive a little bit deep in that. There are different kinds of storage media SSD memory hard disk network and often because of AWS often combinations of these. There are also different storage formats. For example, there is B plus 3 which is the most common one. The most newest one that has that is kind of there in databases is called fractural trees. How many of you use MongoDB? How many of you are facing problems with MongoDB due to transactions? For example, okay. So, if you want to have the best of the world that you want to have transactions and you want to have a document store as well then there is a software called Toku MX that implements fractal trees and that uses MVCC kind of model for storing data. So, actually it can support transactions even with a document store and MongoDB doesn't. So, this is I don't know how many of you can read that. Can you read this at the back or quickly read through them? So, this is the data access latency from all the way from the CPU which has L1 cache to a branch misprediction which takes all these times are by the way in nanoseconds and there is a comma separator at thousands. So, this is something like 150 milliseconds and this is about 3 microseconds. Compressing 1k data, you can see where SSD fits in. 4k random read from SSD versus a network. Now, a lot of you might know this but a lot of people do not think this through when they design systems and they pay very dearly for it. A great example that I have seen is when people use AWS which is quite common with startups or even like enterprises when they don't want to scale out architecture. They use EBS. What is EBS? EBS uses the network and I don't like to say this but there is new kind of snake oil to some extent that Amazon has come up with. They allow you to have drives which are not rotational that are not magnetic but SSDs but the cache is it's over EBS. So, incur the network cost in spite of the fact that you are in SSD. So, you basically take this and add it to this. So, maybe it is better. Yeah, I am not saying it is not it is bad. It is obviously better compared to a magnetic disk but amount of stuff that you are doing over the network just kind of kills the performance. Honestly, there is no point. So, there I would probably recommend if you are using AWS to look at an option and design your architecture around ephemeral disk. There are problems with using the ephemeral disk because if your instance goes down for example, you lose all the data but you can make up for it by having multiple replicas. So, if you design your architecture for performance, use ephemeral disk. Don't use EBS. EBS is very low hanging fruit to use and the reason for that is snapshotting becomes easy. If your instance goes down, you still don't lose the data. So, it is actually very attractive to use but keep in mind the performance characteristics when you do this. The same thing for those of the back who cannot read all of these. It is represented in a visual format. So, every as you go from every partition to partition, there is an increase by 100 by factor of 100. So, you can see that L1 instruction takes about 2 nanoseconds and you can all the way here which you go through 3 orders of 3 multiple orders of a magnitude to a packet from California to Netherlands which is about 150 milliseconds. So, this is something that people don't think about. There was this interesting discussion yesterday at the Aerospike. Can I use the 45 minutes and maybe take the questions later? It is a lot of stuff to cover. You can take the questions maybe offline. I will try to make it. So, let me quickly go through to the next layer but this is something that you have to keep in mind while going through stuff. So, these are the different paradigms when you look at the data processing layer. So, the data processing layer actually is where you take all of the data fill in the missing value, do cross validation, you can combine different data. For example, if an ad server or you have request data, impression data, click data and then finally, you go to the landing page. You can take all of the streams and combine them together and this is where you do it. You take in data, you process it in some format, you aggregate it, you find out, you maybe do some windowing on it and find a median mode. Do any kind of statistical analysis and this is the layer that you kind of do it. There are various ways of doing it. You can use a message passing interface if you have a cluster. You can use micro batches, which is quite becoming popular due to Spark, which I will cover a little later. And you can also use Storm for real time streaming and obviously with Hadoop and even other systems, you can use batch processing. So, similar kind of example to before. Storm versus Spark, we have a, Storm uses a task parallel kind of architecture, where you can spawn different tasks. Whereas in Spark streaming, not Spark, but Spark streaming, it uses a data parallel architecture, where it splits the data across machines and the primitives in each case are slightly different as topology, which is like a hard to explain. Which is like a set of processes that keeps on running and processing data. Spouts is where you keep on ingesting data and bolts is where you actually process the data.  If yes, then move it forward or drop it. Then you can use Storm or even if you want to keep on accumulating, like you want to keep on adding data that keeps on coming in, then maybe Storm is quite good. If you want to use micro batches, which is like you take a list of data and then take a list of data points and then you do some operations on them, then actually Spark is quite good. So, Spark actually shines really, really well in machine learning instances. You can do that stuff with Storm as well, but it is not kind of designed for that architecture. Again, there is a huge difference in the latency. Storm can guarantee subsequent latency at very, very high throughput. Spark, because it is batching stuff, there is a few seconds latency. Also, in terms of fault tolerance, Storm assures that it will get at least used once, whereas, Spark says exactly once it will be taken care of. So, that is like the difference there. I think part of this was covered in the previous talk. So, quickly for those who do not know OLTP versus OLAP, OLTP is typically if you go to a, for example, if you go to a bank branch and you do a transaction, it will be typically going to something like a MySQL database or a Postgres database or a Oracle database, which is like every individual item which has a lot of stuff associated with it. Whereas, if you want to know what is the average, where OLAP science is, where if you want to know what is the average amount of money that a certain depositor has in his bank account, you would not do those transformations or you would not do that query on the OLTP database simply because it is designed for high amount of rights and not for grouping. So, that is where you actually would use something like Infobrite. Actually, at Inmobi, the data warehouse initially was built on Infobrite, which was kind of covered in the talk before grill. So, MySQL is extremely good for example, transactional workload. Infobrite is actually quite good for analytical workload. When you ingest data using CSVs into MySQL, because there is a structure around it, you have to create indexes and whole lot of other kind of overheads, size actually increases typically when you ingest the CSV data. Whereas, Infobrite what it does is, if you look at the data, like let us say we have a database, analytical database of all the cricket matches that have happened. And I want to say find out what is the average of say Sehwag versus Tendulkar versus Ganguly. How many players could be there? May be like 5000, 6000. What happens is, this is all categorical data which does not have high cardinality. So, what Infobrite does is, takes all of this data, it compresses it. It creates a dictionary and then replace it by symbol and every time you can just dereference that and get extremely high compression. Inmobi we got about and I think Amrishwari if she is there, she can back up those numbers. We got about 40x compression. If you take 40 GB of data and which was already aggregated and put it into Infobrite, we got like it only used to compress down to 1 GB. But that also means like loading is slow and CPU intensive. It is also great for machine generated data because most of it is repetitive and in a certain range. For anything that is range bound and for analytical, something like Infobrite is quite good. Alternatives are also like Vertica and I think MonetDB. So, you did not use Infobrite. I have used Infobrite as an example here. The best part is that it is very easy to do sampling and do approximate queries. If I want, as I said, you can use a top-down approach and I want to know whether my distribution or my hypothesis is at least in the right direction. I can just do an approximate query without running the query on the whole data and I can say, if I am going in the right direction, then I can run the whole query and then slice and dice and analyze the data more. That is something that is unique about columnar database. There are also differences in which they are tuned for performance. One of them uses indexes and aggressive caching. MySQL, Postgres both do that. Infobrite actually uses something called a knowledge grid meta-etallia for better performance. Actually, that is a very good paper on the knowledge grid. I think those of you who have access to ACM digital library, it is worth reading about how they actually implement how do they actually implement the knowledge grid. Two minutes, that is it. Finally, there are no SQL data stores. One of them is Edgebase and the other is MongoDB. Some of them are kind of useful. Both of them do not have schema, but Edgebase can be thought of as a slightly different category, which is like a wide-column store. Whereas, document can have embedded stuff embedded and it can have some structure. Edgebase will have to kind of simulate that structure and it is really painful to do that. If you have one key and you know tons of columns that can be associated, especially if there are spars, then Edgebase is actually extremely good for that. But if you have documents in which there is not that much sparseness, then MongoDB actually is good. The other big difference also is that MongoDB does not have triggers. If you have an event or if you have a data point come in which matches a certain criteria, it is very hard to do that, process it in MongoDB, whereas Edgebase has observers where you can actually have a callback whenever an event happens. And also the scalability is good due to HDFS. MongoDB scalability is okay, but as you scale out the performance, what we have seen at Helpship is the performance suffers pretty badly. If you want to dig deep in MongoDB, actually there is a link to a blog at the end. We have talked about all the operational problems that we have faced with MongoDB and we are using it at huge amount of scale. We are doing almost like 50,000 documents per week and 2.7 billion events. Some of them do go into MongoDB, 7 billion events per month. So quickly, so I talked about most of this stuff. The other software that you need probably want to look at, but probably may not know about is something that does complex event processing. If you want to perform operations on a window of data and not individual data points, then something like S-Per which is open source software is quite good. You can actually use also Spark because Spark also has an idea of windows or micro batches. It is kind of similar, but not exactly the same thing. So that is something that you need to look at. I think most of the other stuff has been covered. Neo4j is actually good for like for graph databases. Finally, last couple of slides. The data analysis layer is when you take on all of this data and then you take with third party sources. For example, if you are doing marketing, collecting marketing data, then there is something called as designated market areas in the US where US is divided into DMAs where one city, for example, SF can have a lot of DMAs, but several states, for example, the Midwest can be kind of consolidated into one DMA and that is based on the demographics. It is also based on the income levels and then money spent on each of these DMAs. So that is something or even geopolitical boundaries. All of this data can be overlaid. For example, if you are on IP, you can find out the coordinates or you can find out at least the state in which it lies and then you can do overlay on that. So you can take one data point and then kind of amplify it by merging other kinds of metadata, taking third party data. You can use geo coding. Also incorporate human input, which is quite useful in supervised learning if you want to do that. So I am not going to talk much about this slide as I said before. Just let us move on to the visualization. Why is visualization important? Visualization is important because like I showed you the slide before, maybe you look at those numbers and you do not get a scale of those numbers, but if I show it to you visually, humans are visually, I mean, in the brain, the largest area of all the senses is actually covered by the one that processes the images or the visual input. And visualization can be huge factor in actually making a narrative. And you can see that happening more and more. I think there are some talks around that as well in this conference, where we use the visualization as a narrative to see how maybe a certain industry is doing this. Towards the end, there is a link to a stream graph. This, for example, if you search for the most popular box office receipts of most popular movies, I think for like seven years or eight years, it actually shows you, this is the axis of time and actually shows you how much each movie made. And within one shot, you can find out various information. For example, you can color code the genre. You can, the height can be the amount of revenue it has made. The other axis is time. So, you can find out which movies did well. You can also have, overlay some kind of input on top of it by the distributor of that. So, that is quite useful. Visualization is quite useful for bringing out the different aspects of data and finding out the interrelationships between different data. The other one, which is quite good is Sunburst. If you have a hierarchy, for example, if you want to look at disk space usage and you have a directory structure and want to find out where is there is some pesky movie, which I have never seen, but it is lying in some folder somewhere. But I am not, I am deleting all the small files. How do I find out? So, if somebody shows you a Sunburst, so the innermost ring is the top level components and then you have the hierarchy actually showing up. So, you can actually use that to kind of zero into maybe the files, which you would need to delete to make space on your disk. You can use it for relative populations of administrative blocks, market cap of sectors, which are listed on stock market index. So, in one, in just one visualization, you can actually have a tons of data that is encoded using different layers. There is extremely good library if, for those of you, you have not used or I think the killer application for just like Ruby on Redis for Ruby is a library called ggplot. We use it fairly heavily at Inmobi for finding out outliers in fraud detection. So, you take a list of bunch of data and then you kind of do a scatter plot and you can color each of the dots based on certain metadata and then you can see what bands they like. So, just by kind of running those scripts, you get a good idea of how your distribution looks like. Yeah. Mr. Hegde, if you don't mind my apologies, but we're going to have to cut you off there. Yeah, I'm done. Thank you so much. So, my timing was good. Actually, we have time for one question. We're going to push the time for one question. If you think you have a mind blowing question, your hand went up first. The gentleman please. Okay. So, you can check out the links on to the blog where we're talking about MongoDB, for example, and also some benchmarks that we have run. Follow me on Twitter and or you can send me an email if you want to follow up some questions. Hi Vinayak, I'm Sandeep. Where are you here? Okay. Hi. I wanted to ask you about that MongoDB versus HBase comparison. There you specifically have a point that is HBase has triggers and whereas MongoDB doesn't have do you give me any kind of example where you would like to use triggers like some some real example or you have used something. So trigger could be like if you have some outliers that are coming in right like for example, you are an operational database and maybe the CPU spikes about about say 80% for example, and you want to know that you want to do some alerting based on that or maybe bucket it on based on a certain criteria then triggers are quite useful for something like that. Okay. So it is based on the data events. The other place where I see it use very heavily is also like in Postgres not MongoDB but triggers in general is that it is also used for table based replication. Thank you.


Mystery House, that strange publishing firm owned by Dan and Barbara Glenn, where each new novel is acted out by the Mystery House staff before it is accepted for publication. Mystery House. The title for the story we're trying out tonight for a Mystery House novel, Barbie. Murder is an accident. I suppose it's about a murder that's made to look like an accident? It's a story about a murder that is an accident, Dan. Huh? Well, but murder is never an accident. If it's an accident, well, it just isn't murder. Well, this is. Wait and see. Oh, now don't tell me you're going to try to fool me with a little technicality. Well, say Mr. Glenn, don't sneer at little technicalities. They're very important. Not to me, Tom. Well, they're important to everybody, Mr. Glenn. That's why we have to be so scrupulously careful of what we say in my part of the show. Everything exactly right. Here's what I mean. Okay, places, everybody. Set the scene, will you, Tom? Death is an accident. Tonight's story opens in a car that's rolling along a country road at 5.30 in the morning. Hal Bennett, editor of a country weekly paper, is driving, and his wife is registering a mild protest. I could learn to hate you, Hal. Getting me out of bed at 5 o'clock just because some guy disappeared three years ago. Oh, now, Pam, I thought you were a mystery fiend. Besides, I need you as a cameraman. Well, photography's a wonderful science, but you can't take pictures of something that happened three years ago. So why bother me just when I was having a wonderful dream? Well, wake up and listen. You remember when Carl Jordan disappeared? Clarion, and moved here from Chicago. Yeah. You remember how upset his wife was? I might even be upset if you disappeared. Well, she said the last time she'd seen him was the night that a stranger came to the farm and asked for some help with his car. And Jordan went out to help the stranger and crystal. No more Jordan. Yeah. But what does that have to do with my beauty sleep? Well, just this, my pet. Who do you think walked in and signed a confession last night? You. Yeah, oh, now be serious. Henry Paulson. Not Henry Paulson, the president of the farmer's state bank. The sheriff's got him out on a farm now looking for Jordan's grave. Grave? You mean Henry Paulson murdered Jordan? Well, could be. Sheriff Olson's being very mysterious about the whole business, has some kind of a signed confession.  I thought you said murder mystery. There's only one suspect and he's already confessed. Listen, my love, big operators like Henry Paulson don't sign confessions unless they have an ace up the sleeve. Extenuating circumstances to you, my dear. And we're going to find the catch. Okay, I surrender. Only give me two more minutes to sleep. Oh, no, you don't. No, no. We're here. The Paulson farm. Hey, is that the sheriff over there digging? Yeah, looks like him. And that's Paulson with him. Come on. We'll go down and see if they found the grave. Walking through a cornfield is certainly great on Nile Island. I'll make Olson get you a new pair on his expense account. Hey, Oscar, how you doing? Bennett, I'm out to know you as far and out about this. Why don't you newspaper snoozes mind your own business? You will get no news till I want you to have it. Ah, now take it easy, Oscar.  We just want to help you out. Excuse me, Mrs. Bennett, I don't mean to be rude, but I got to watch when your husband is around. And besides, I got the very important suspect. Important? I don't know why you should treat Henry Paulson any different from any other criminal. You aren't afraid of him, are you? I ain't afraid of nobody, but I got to find Carl Jordan's body, and Paulson is the only one who knows where it is. I got to be nice to him just until... Oh, we understand, Sheriff. He's admitted the murder, has he? He says Carl Jordan died accidental, and he buried him secret to avoid scandal for the bank. Oh, brother, does that sound fishy? Accident, eh? Well, Henry Paulson's been... Excuse me, Mrs. Bennett, sort of sweet on Carl Jordan's wife for many years. Oh, you don't need to apologize for mentioning it, Sheriff. I remember a case like that in Chicago. Why, Mrs. Jordan has a grown son. That's right. He just got back from Chile. Yo, mining engineer. He's coming back. That is why Henry Paulson confessed. Some slack the Jordan boy made his mother tell him everything about all Carl's disappearance. Mrs. Jordan told her son Paulson killed Carl. She told him enough so Paulson were afraid of the Jordan boy start talking. That is why Paulson come to me to tell his story. He admits being responsible for Jordan's death? He says Carl Jordan took some kettle in Tomahawen. His wife think he don't come back for several days. I could tell it to your husband better. You mean Paulson was making a good thing out of the husband's absence? Yeah. He was visiting Mrs. Jordan and Jordan come home early and found him in the living room. Of course, Jordan was plenty mad. How unreasonable. He start to slug Paulson and Paulson slug right back and all at once Paulson say he sees Jordan fall and on the floor beside him is a big heavy brass vase. A brass vase? Paulson claimed the vase fall off the mantle and cracked Jordan's skull. Paulson swears he don't have his hands on it. And that's supposed to make Jordan's death an accident? Maybe. What about Mrs. Jordan though? Well, I got anything out there now. Well, isn't she involved too?  Paulson takes all the blame for that. He says he and the lady were good friends. But I can't arrest her for that. I've got to get back to my prisoner now. You better go away. Okay, Oscar. But don't forget now. Hey, help! Look! What's the matter? There's a man getting out of our car. Come on! Nylon! Hey, he's back in his own car now. We're too late. Quick, Pam, your camera. That telephoto lens will pick up the license plates. Okay. Hey, do you think he's told something from us? Just a hunch, sweetheart. But any guy roaming around here at this time of the morning must have something to do with the Paulson case. Now, let's go see your friend Mrs. Jordan. Looks like much happening here. Ah, let's go to the house and see if Mrs. Jordan will talk. We're not the only ones interested in the Jordan farm. Crossback rider. Who are you? What do you want? Well, you must be Donald Jordan. What about it? I'm Hal Bennett of the Clarion. This is my wife. We want to talk to you about your mother, about your father's disappearance. Disappearance? You mean murder? We've just talked to the sheriff, Mr. Jordan. He said Henry Paulson was helping him find the grave. What do you mean, helping? Paulson could find it quick enough if he wanted to. He dug it, didn't he? Was he handcuffed? You sound a little bitter. Why wouldn't I be? All right, just been.  We don't pamper them. Let them make fools out of officers. We don't... But you can't call Paulson a murderer yet. The sheriff seems to think it was an accident. He would. Because Paulson told him so, and Paulson's a big man. Big man? He's a mad man. He stops at nothing to get what he wants. Why, he's been threatening me since the day I got back from South America. That sounds like he figures you know something. Are you sure you didn't know anything about your father's death before you got back? Now look here, Bennett. I don't know anything about this, see? Nothing except that Paulson's guilty. Mr. Jordan, please. If he's guilty, the law will take care of him. The law? These American laws make me laugh. In South America, we know how to deal with murder. Paulson should be hanging now.  Now who's coming here? Just another of your great officers of the law. It's Hannigan. I thought Olson said he was already here questioning Mrs. Jordan. Hey. Hey, Hannigan. Hi, Bennett. Olson told me no visitors. I'll have to throw you out of here. Well, hello, Mr. Hannigan. We just want to talk to Mrs. Jordan a minute. Well, you can't for two reasons. She for which is she ain't here. What do you mean? I thought you were watching her. That's like the baby watching the nurse. If you know so much, wise guy, where's your mother? And where have you been? How should I know where my mother is? You were supposed to be watching her. As for me, it's my business where I've been. This is a free country, isn't it? Oh, come on. Let's find Mrs. Jordan. Olson will be plenty mad at you if she's disappeared, Hannigan. Then he'll just have to be mad. She's gone all right. I was talking to her and she has to be excused a minute. She never came back. But she couldn't just vanish. She must still be in the house. If she is, she's awful good at hide-and-seek. I looked every place. This is enough for me. So long. Hey, what do you think you're going? I'm going to hire some competent men to put on this case. Boy, you... No, no, no. Let him go, Hannigan. Come on. Let's search the house. Tent for you is having art through the place. Did you try all the doors? Sure thing. Bedroom? Mrs. Jordan. Here, Hannigan. Help me untire. This ain't right. I was right here. Hurry up on those roads, pal. Here, I'll get that rag out of her mouth. Mrs. Jordan, what happened to you? I don't know, Mrs. Bennett. Nobody could have tried her like this while I was here. Maybe not, Hannigan, but they did. Mrs. Jordan, what happened? I don't seem to remember.  Everything went black. And when I woke up, I was in that clothes closet with that rag in my mouth and my hands and ankles tied. Oh, it was awful. Did you look in this closet, Hannigan? I must have. I opened every door I come to. Well, you must have missed this one. I answered that. Will you, Bennett? Yeah. Hello? Yeah. He what? Wait a minute. How did he... Okay. Yeah, sure. We'll be on the lookout. Yeah. Thanks, Sheriff. Yeah, I'll tell Hannigan. Goodbye. What now? Paulson's escaped. Somebody drove his car out there and left it with the keys in. No. Oh, he'll blame me for everything. My son, he'll try to kill them. No, don't be so upset, Mrs. Jordan. He can't hurt anybody while Hannigan's here. But he has a gun in his car, a revolver. Donald made him go to the sheriff, and we've got to stop him some way. I'm afraid. You've got nothing to worry about, Mrs. Jordan. If he tries any funny stuff around here, I'll take care of him.  That night when he killed Carl...  I don't know. Can't you leave me alone? Can't you see I'm all upset? I don't know what I'm saying. Horton, stick him up, fella. No, no, wait a minute. He's hurt. Can't you see he's bleeding? Call a doctor, Pam. Henry, no, don't shoot Henry, for the love of...  Sheriff. Got me. Spark plug. You said... Save it, Pam. Save it. Change that call to the coroner. He's dead. Who engineered Henry Paulson's escape from the sheriff? Was it Donald Jordan? I hardly think so. Maybe there's someone mixed up in this thing we haven't met yet. And how did Henry Paulson get shot? Was it for murdering Carl Jordan three years ago? Or was that murder? Well, it looks like we have a lot of questions to be answered in the second act. And they'll be answered in short order. But first, act two of murder is an accident. Hal Bennett, the clarion editor, has just entered Sheriff Olson's office. Donald Jordan lounges incidentally against the desk. You get the photographs developed, Bennett. Right. And the numbers check. Eighty-eight. Why, seven-eighty-three. Just like on the car, Paulson drove away in. I hollered that the blame fooled to stop. He sort of know now, but chased him in my car. You fired the shot, did you? I drove up along the side of him and yelled like anything. He wouldn't stop, so I had to shoot. Then why did you let him make that scene at Mother's? Why didn't you take him right to jail? Are you trying to be funny? His car went off the road on into a ditch. By the time I climbed on there, Paulson was gone. You must be a very fast man. North-fist, maybe, but I'm doing a lot better than Paulson. Cut the clowning, Olson.  Just a minute, young man. Wait a minute, relax, Jordan. My wife's with her. And Pam can take care of any murderer in the world, bare-handed. Yeah, I'll bet. Photographed the car on the one Paulson drove away and both had the same license plates. And they're yours, Jordan. Mr. Jordan, where were you when Portson escaped? I... how should I know?  I was in town making a call to the city. Trying to hire some competent detectives. And before, where were you when Mr. Bennett came to the farm? Outriding. I've told you that a dozen times.  You half-baked clown, you can't frame me. You bungle this thing from the side of... Now, look, Donald, all the sheriff wants is a reasonable explanation of your actions. Reasonable? Yeah. The reason would be quite a novelty around here. I'll give him some reasoning. The kind we use in our mining game. Look out. Oh, no, you don't, sheriff. Give me that, don't spin it. Grab your slicks. Oh, I got to... Oh, no. You're gone, Olson. He's got your gun. Look out. And I know how to shoot it, too, Bennett. What's the matter with you, Jordan? Get down.  I've had enough of this. A man who killed my father is dead now, and that's all I'm interested in. That and getting my mother away from here. Come away from that window. You will get hurt. Thanks for worrying about me, sheriff. I'm going back to South America where they're more interested in justice than in theory. Jordan, come away from that window. Come on, Lord, give me that gun. You can't jump from that window. Jordan, you'll be killed. The IV on the wall will get me to the ground, Bennett. So long, you chups. Jordan, you're crazy. Come back.  He won't live long. Have you called his mother, Hale? Yeah, she'll be here in a minute. She better hurry if she wants to see him before he dies.  Come in, Mrs. Jordan. I'm sorry this happened. Hey, wait a minute. Where's Pam? Didn't she come with you? My son. Where is he? My poor son. At least in pretty bad shape, Mrs. Jordan. You're trying to tell me... Oh, that's another one to take care of. We better call a nurse and get her into bed, Hale. You're spented, I guess. Yeah, she dropped her purse. Well, pick it up while I find a nurse. Okay. It's open. Hey, wait a minute. Look at this. What? Money, border, papers? Not any woman's purse. Yes. A tractor wrench. I suppose women carry tractor wrenches in their purses these days, huh? Uh, fire.  And the fire ain't here. Hello, operator? This is Sierra Fulton. Where's the fire? What? What? Oh, my goodness. Well, wherever it is, I'm not going with you, Sheriff. I've got to find Pam. I don't like this business of Mrs. Jordan coming here without her. Just a minute, Hale. The fire's at the Jordan farm. What? Well, here. Here. Grab her, Sheriff. But she's spented. She's got to be put to bed. Bed? Nothing. She's going to that fire. Hurry, Sheriff. With a lot of Mike's step on it. Hey, step any harder, and my foot goes through the floorboard. They're almost there. See the flimps? If anything's happened to Pam, I... Gee, I got her to stay with Mrs. Jordan. It'll be my fault now. Just don't get excited. She takes care of herself. Pretty good for a woman. Oh, well, hurry up. Will you? The place is practically burned down. If Pam's in there, I... Don't try to keep yourself down. Getting excited won't do any good. Hey, Sheriff. Over there with a blanket over it. Sheriff, it's a body. Pam me. No way. Come on and don't get all excited. Excited, but Pam, we take a look here. No, no. I don't want to look, Sheriff. I can't. What would you tell me? I guess I got to if that's the way you feel. You're your fate right here. Oh, I hope he's wrong. Well, I guess I got to do it. Hi, Sheriff. Isn't this the silliest thing you ever saw? The doctor said I was suffering from a shock, and he insisted on wrapping me in this blanket like an Egyptian mummy. Well, can't you say something? Say something. Sure. Mr. Bennett. Oh, Mr. Bennett. Oh, darling. Darling. Pam. Pam, just let me look at you, will you? Oh, but I got smudges all over my face. Well, you look pretty wonderful to me, baby. Smudges and all. But don't you ever scare me like that again. Scare you? Oh, I like that. If you think I staged this performance for your benefit, and speaking of being scared, how do you think I fell? I'll use all my fault, baby. I'll never leave you alone again. Alone? Yeah. Oh, hell, where is that awful woman? Did she get away? Mrs. Jordan? She's in the sheriff's car, out like a light. When she saw her son, you... What about her son? Well, he got excited and tried to climb down the ivy on the courthouse wall. Maybe dead by now. He tried to say he didn't know anything about Paulson, but... Well, of course he didn't know anything about Paulson. She did it. She's the murderer. What? What are you talking about? The sheriff shot Paulson, and Paulson killed Carl Jordan. No, Mrs. Jordan killed both of them. She told me. What? That shot I fired at Paulson. Hey, my car. Somebody... It's Mrs. Jordan. She's driving away. Come on. We'll take the fire she's caught. The fast one. Hurry. Don't worry. We'll catch her. I can't tell you how horrible. You're gaining on her, sheriff. Hey, catch her. Then we talk. Now, Pam, she's shooting at us. No, I'm getting mad. You hold on to the wheel. Sure, but what are you going to do? Hey, you better duck down, sheriff. I don't know what suits her so far, but they aim. And I'm aiming for the tires. No, Mrs. Jordan. I don't remember anything, sheriff. After my son, everything... I'm sorry.  I know. What happened, Pam? Well, after you left the farm, I tried to visit with her just to pass the time. She began to fidget around, and she was playing with a purse. You hated me. I could see it. Well, you didn't do much to build up any friendship, darling. I asked her to lie down, Hal, and when I tried to take her purse... I knew what you were after. You didn't fool me. When she wouldn't give it to me, I was disgusted and I started to walk away from her. Right then, something hit me on the head. That tractor rinse? Well, I wouldn't ever have known, except that she missed. The blow grazed me, and I went down stunned. Then she gave me a nice, neat crack before I could get up. When I came, too, I was tied up. And then she skipped out? No. She sat down and talked as sweet as... Well, you know how she always talked. And she asked me over and over again how I wanted to die. She said it had to be an accident. Death is an accident, she kept saying. All deaths are accidents. A woman is crazy. No, just tired. Very tired. It's been so long. So long since what? Since Carl disappeared, my husband... His death? Death was an accident? I never loved him, but he never knew it. The accident was it. He found out. Well, I'm afraid you're not making sense, Mrs. Jordan. It's so simple, though. I didn't love my husband. Henry Paulson and I were very happy because we arranged everything so carefully so that no one would ever guess we were in love. But your husband's dead, Mrs. York. Carl came home when he wasn't supposed to. He found Henry Paulson there, and he began to strike in it. It was then I knew I had to kill Henry Paulson.  Isn't it funny? She aimed the brass vase at Paulson, but it hit Jordan. I didn't dare let Mr. Paulson know I'd meant to kill him, of course. So he and I had to put together that story about Carl's disappearance. Yeah, but this morning Paulson's escaped.  I tricked you, Sheriff. I told Henry I'd have a car waiting on the road and that I'd have the spark plugs disconnected on your car so you couldn't follow it. I did, of course.  That's why I was talking about his gun. Oh, yeah, I remember. You said he tried to shoot you. Yes. I couldn't kill him. I had to fix it so the Sheriff would do it. Or Hannigan. It had to be an accident. And she tied herself up and put that gag in her mouth so nobody thinks she'd left the car for Paulson. What about the fire? That was no accident. But there was an accident. The neighbors reported the fire too soon. Otherwise, Mrs. Bennett, you'd have been accidentally burned to death. Well, there was one real accident, Mrs. Jordan. Your son. No, don't talk about it. I've had all the accidents I can stand. You've got one more coming, Mrs. Jordan. A trial by jury. A trial by jury.


So, let us move on to our first problem in the tutorial. What we have is we have a cylinder and the task that we want to do is this is the step and we want to pull the cylinder over the step that is what we want to do. And what is asked of us is this that the weight of cylinder 25 kg is given to us and we are told that at the point of contact A the coefficient of friction which in this case clearly is static friction is equal to 0.3. And what you are asked to find out that what is the maximum step size or what is the maximum height of the step edge which over which you can roll the cylinder over. So, we pull on this and we want to roll the cylinder over and we are asked to find out what is the maximum possible height given the coefficient of static friction between these two is 0.3 is possible for this problem. So, why do not we take around 10 minutes if you have any questions post on chat I will be available there and then after the end of 10 to 15 minutes we will go into the details of the problem what are the ideas what are the techniques that we are using. So, I could see from the chat that many colleges have done this problem properly. So, let me go over the problem so, what we have asked is that what is the maximum height at which this can be rolled over now the question is that if you try to exert force on this the cylinder will try to like roll about point A it may also try to slip both things can happen and it will lose this contact here. Now, the question is that that when it when it loses its contact here the cylinder is in somewhat hanging position that this will have the free body diagram of this cylinder will look like that this is the contact point this is the applied force and the cylinder has to be lifted off before you can tip it over now think about it the weight of the cylinder acts in the vertical direction as the horizontal force P which we have applied that and the weight by geometry they meet at point A. Now, this clearly is a 3 force body or is a 3 force member why because the force acts precisely at 3 points 1, 2 and 3 furthermore we also know the line of actions of W as well as P and when they meet at A for this entire body to be in equilibrium for this cylinder to be in equilibrium the reaction should clearly pass through A now what happens suppose this angle is 5 then this is an isosceles angle this angle should also be 5 and this is the outside angle which should be 2 5 then what do we have we have that for some given height h this is r-h okay this is r-h is equal to r cos 2 5 or we can rewrite this equation simple geometry okay this is r this is r-h this gap and r-h is nothing but this r times cos 2 5 or h is equal to r times 1-cos 2 5 now note one thing that to increase the height h what do we need to do the geometry dictates that to increase the height h this angle 5 has to keep increasing why because when angle 5 increases cos 2 5 decreases and this value keeps on increasing and h max when this 5 is as large as possible but now for this contacting surface the contact surface between the cylinder and this step what we know we know that the coefficient of friction is equal to 0.3 now since the coefficient of friction is equal to 0.3 the maximum angle and also note that the normal reaction between this as we had discussed earlier that this is the tangent okay at this point we draw a tangent and this line connecting the point of contact with the center of the cylinder is really the direction of the normal why because the tangent plane is this and the corresponding normal reaction or the normal direction will act in the direction connecting this point h and the center of the cylinder and now the friction will act tangential to this and this direction of r okay the angle this reaction r makes with this radius is nothing but the angle that the effective reaction r makes with the normal reaction because the normal reaction has to be along this is the effective reaction and that angle okay is the corresponding angle which cannot become more than the angle of friction which is tan inverse of mu s the maximum possible value of that angle okay we had discussed cone of friction okay the cone of friction in 2d is nothing but this effective angle this is essentially a 2 dimensional cone of friction and in this 2 dimensional cone of friction the reaction should can at most lie at the periphery of that cone of friction this phi becomes equal to phi s and that is the maximum angle that this reaction can make with the normal and so our h max will happen when phi is equal to phi max we substitute that value and we will see that height max or the maximum height of the step is equal to 0.248 now note there is one very interesting about this thing about this problem suppose okay that we have enough friction here we have some height we satisfy this criteria that the height is less than 0.248 when that happens okay the cylinder loses the contact and it is stable in this horizontal position exactly when height max becomes equal to 0.248 this angle phi becomes equal to phi s or this angle phi becomes equal to tan inverse of 0.3 then in that case there is an impending slippage that this is just about to slip any friction okay any value of friction or any value of lesser than 0.3 or any value of height more than this height will cause a slip here and the body will lose equilibrium now the question is that if we satisfy all these rules that h max is maximum equal to 0.248 then in that case can we say that we can roll this cylinder over afterwards if we can make it stable like this then can we just keep on going further and roll it over or will it slip at some intermediate position the answer is that that when we start pulling it just note that when you start raising the cylinder up you will see that the effective height of the step that the cylinder sees will keep decreasing because this point goes up and the effective height of the step is only this and as a result if you can keep the cylinder in equilibrium in this position you can just safely take it over and make it go and cross over the step okay. So we can take now a couple of questions 1 to 0 5 yes sir I want to ask this is friction depends on the velocity of body during motion. So I had discussed this earlier right briefly there was one question which was asked before that for dry friction or coulombic friction the frictional force between two moving surfaces does not depend on velocity but there are some other models which work for certain contacting surfaces in which the friction can depend on velocity but those kind of frictions are called as fluid friction but in the dry friction or the coulomb friction model. So this is one thing which I want to emphasize that this study about friction is an extremely complicated it is an extremely complicated problem and the model that we are using in this course and the model we are is typically used in engineering mechanics is one of the simpler models that does not mean it is a reality and it is true for any problem but for a large cases therefore a large number of solid contact problems this model where the contact force depend does not on the velocity but only on the normal reaction is a reasonable model and that is what model we are following of course there are some model models in which and there are certain problems in which the frictional force would clearly be proportional to velocity and maybe even be complicated dependent on velocity in some very complicated manners okay there are clearly instances of that but for this course we are worried only about the frictional force is proportional to the normal reaction 1071 I have a doubt about the friction okay consider two metallic surfaces okay while considering the surfaces the rough and smooth is based on coefficient of friction okay suppose the smooth surface having less friction compared to rough surface so friction that one thing I want to emphasize that friction is not property of an individual surface it is a property combined of the two surfaces okay so friction cannot be defined only for one material it has to define for a combined property it is like depends on two surfaces you cannot separate those two surfaces it is always glass on glass or metal on metal it is rubber on concrete it is like that it is never independently rubber or independently concrete or independently metal and other metal it is always a combined property so there is one okay nice question that is asked is that why do this is a question by center 1080 and I have asked that why do not we consider W in this problem it is not that we not consider okay let us go to the slide we clearly consider that the value of the P that you require okay how much P you need to apply depends on the weight but the beauty of this problem is that what it is telling you is that the criteria for slippage is completely independent of W it is purely dependent on the radius of the wheel and the height okay clearly if you solve this problem fully if you do equilibrium in the y direction in the x direction or for example if you take for this free body diagram moment balance about point H you will see that clearly that the value of P that is required will be equal to W so I am not taking W why because it is not relevant for the question asked that it the height does not depend on the weight it is independent but the amount of force I require if I want to lift a simple small cylinder which is of wood it is fine but if I want to lift a cylinder okay which is as big as the wheel of a road roller of course I have to apply a lot of load but the step size depending on the friction coefficient is the same it does not depend on the load it just depends on R and the coefficient of friction okay that is the answer to that question. The second question related to the problem is why reaction force passes through A okay think about it the force on this body acts at three points one is through the center which is the weight okay the body is already lifted up so the normal reaction we are completely disregarding then second is the horizontal force that we have applied and third is the reaction that passes from this point okay now the question is that why does this reaction passes through A now the question is the answer to that question is that this wheel has to be in equilibrium now this weight and this P they intersect at point A these two directions are given to us now if this reaction does not pass through A then what we can do is it has a line of action not passing through A so the moment that this force creates about A cannot be balanced so if the system has to be in equilibrium then the necessary and sufficient condition is that this reaction should pass through A okay so with this okay let us stop the discussion for this problem I can answer some questions on chat let us move on a problem number 3 okay this is a very very interesting problem so what we have is that we have almost massless Lender rod which is connected which is supported at peg C okay this peg C and it is supported on the other side of the wall at point B the coefficient of friction between both this and this is point 2 and this angle theta okay I have not mentioned here note that angle theta is 35 degrees okay angle theta here is 35 degrees please note that okay now when this angle theta is 35 degree what we are asked is if we apply a vertical load P to this rod then what is the what are the ranges of value of this ratio L by A that what is the upper limit and what is the lower limit on this ratio L which is the length of the rod and A which is the horizontal separation of this peg from the wall okay given that this angle theta is equal to 35 degrees which sorry I forgot to mention here and the coefficient of friction between C and the rod and between the B and the wall okay between between the rod and the wall is point 2 find out what is the upper limit on L by A what is the lower limit on L by A such that this rod remains in equilibrium when you apply a load P now the question is okay so let us take 10 minutes on this problem okay it may take more than that but there is lot of thinking that is involved in this problem that what can happen that why is there a range that is coming into picture think about it discuss with your colleagues you can put messages on the chat okay and think through it and then find out what is the range in which range of L by A upper limit and lower limit within which the rod remains stable okay so welcome back I could see that few colleges got the right answer but before I go to the solution of this problem let me discuss what is happening here okay what kind of mechanics is happening here so this was our rod that why is there a range okay this was a rod this is the wall this was the peg this is point A this point B and peg C now the question is why is there this ratio L by A why is there a range that it should be less than or equal to and greater than or equal to such that this system or this entire assembly is in equilibrium what is happening here and a simple thing one simple way to look about it very similar to the ladder problem that we had done earlier okay so think about this suppose what we did there is that under the application of this force P what if there were no friction at this point and this point and in that case clearly you will have a normal reaction only normal reaction coming from here and only normal reaction coming from here now think about it what happens these two normal reactions will interact we will intersect at this point O okay and this point O will lie on this side of the rod with we will lie within this range if A is reasonably small okay if A is too large then it will go out if A is small it will lie here now take the case where A is reasonably small now these two points intersect here now as a result what happens as a result note that this force P creates a counter clock a counter clockwise torque okay on this rod and when this happens the rod will have a tendency okay that when A is very small and the friction is low or friction is 0 then this rod has a tendency to rotate in the counter clockwise direction but now what happens okay this friction that comes here would prevent that motion why because it can exert appropriate torques and balance this force P and it will prevent that motion but what we see here is that that way when A is too small then even the friction that acts there may not be enough to prevent that rotation okay so let us take the first case when A is reasonably small then this can happen and because of this what will be the impending motion of the rod okay when this L by A ratio reaches some crucial value now think about it this if it rotation happens about this point let us say that the rotation happens about this point you will see that this point will have a tendency to move upwards here okay and also inverts but then this inward motion is not allowed okay so what do we do since this inward motion is not allowed what we do is that we take this rod and slide it upwards okay take this slide it upwards and then bring it down such that it will again remain in contact with this peg now as a result what has happened that this contact point has moved a little bit upwards and this contact point has moved a little bit upwards so the slippage okay so this relative slip happening here this point goes up so the friction acting on this will be downwards since this point is forced to move up the friction acting on this is downwards okay now so in the first case when A by A is small okay when the A by A is a reasonably small value then the impending slippage can happen like this where this point tries to move up this point tries to move up and so the friction acts like this in this direction downwards friction act like this in the downward direction so any A when the A becomes smaller than this the system cannot be in equilibrium and then let us say that what is the impending case that why is the impending motion happening so when the impending motion happens then what is the corresponding value of A by L now this I leave it to you look at the equations that are written here you can write down three equations of equilibrium for this now note one thing how many unknowns are present here 1 2 3 4 okay and this value of A phi phi unknowns how many equations of equilibrium we can write 3 in this case moment about b equal to 0 sigma fx equal to 0 and sigma fy equal to 0 so we can write down 3 equations okay but we have phi unknowns so we need slippage at 2 points to understand what is the impending motion and that slippage okay is happening here and simultaneously it is happening here and that is the reason why we should be careful about the direction of the forces because when A is small okay then the tendency of the rod okay will be to rotate in the anticlockwise direction and overall motion will be such the impending moment will be such that this point b moves up this point c moves up and as a result the frictional force here acts downwards frictional force here act downwards and that is the consistent way to choose what are the sign of the friction forces and when we do that we write down these three equations of equilibrium fc is equal to n times mu times nc fb is equal to mu times nb so the only unknowns are A nb nc we solve these three equations we will get an equation of this form okay in terms of mu sin theta cos theta theta equal to 35 degrees and A by L will be like this we substitute all the values and we will see that A by L comes out to be 0.07335 or what is asked that L by A is equal to 13.6 degrees now the question is that that this is one value we obtained why can't we just stop that this is the value of A by L any value of A by L when it becomes lesser sorry this is the value of A L by A if your L by A for example becomes or your A by L becomes smaller than this value or L by becomes larger than 3.46 you are done why is there a necessity of the second limit and the necessity of the second limit comes because if you increase this A if you increase this A then what happens is that just think about it if you increase A this is the vertical wall okay then what can happen is that if the peg is moved really upwards here then the normal assume then for example the friction is not there then what happens the normal reaction will have a line of action like this this normal reaction will have a line of action like this and this will be the instantaneous center of rotation for this slippage now think about it if you apply a force P like this then about this point what is the moment that it will create the moment will be a clockwise moment okay and then consistently what will happen is that that because of this clockwise moment if the friction is not enough then the rod will have a tendency to rotate in the clockwise direction like this and in order to cover this gap okay this point moved downwards in order to cover this gap what do we need to do we need to bring this downwards okay this entire rod now is slip downwards and then taken here perpendicularly so what you see is that that this entire infinitesimal movement what it does is that that this point C okay this point C it tends to slip downwards and this point B it tends to slip downwards what does that mean that previously because both of these points had a tendency to slip upwards at impending motion the resulting friction force acted downwards and here also downwards but in this case if you increase a then the tendency of the rod at some critical point is to rotate overall in the clockwise direction and in order to maintain compatibility which means contact at all the points this point C will tend to move down this point B will tend to move down and as a result the friction force will act upwards this friction force will act upwards and in other words what we can say is that because we had taken that the friction force is nothing but mu times NB we do not need to re-solve the problem again with plus and minus mu what with by reversing the directions and solving it again we can just note that since mu s times NA NB is equal to FB and mu s times NC is equal to FC since the direction of FB previously was up was downwards and this one okay was also downwards in the second case when l by when a becomes larger then this value this just become upward and this becomes upward so rather than re-solving the problem again okay so mu s NB is equal to FB previously it was downwards mu s NC is equal to FC previously it was downward in this case it becomes upwards so rather than solving it I can just say that we replace mu s with minus mu s and so the direction of friction forces are automatically so we just replace mu s with minus mu s and so that will switch the directions automatically okay and put mu equal to minus mu and we will get a second value of a by l which is larger or l by a which is 3.46 and what we see is that that that is the second limit that if you go beyond a which is larger than this value 0.29 okay or ratio l by a which is smaller than this value 3.46 then you will have an impending slippage which is in the anticlockwise direction and that will make the rod unstable so that is the reason that why we have this limit that at this point okay 13.6 the impending motion of the rod is such that is overall clockwise and downwards so and upwards whereas at this point the overall impending motion is in the clockwise sense and upwards and between these the rod will be in stable equilibrium under the application of force P you go beyond this and beyond this the rod will be unstable okay so what we will quickly do is there is another problem which I wanted to discuss okay is this so we will discuss it for 5 minutes and then we will move on to the quiz so this is a wedge problem so what do we have here we have a cylinder we have a wedge the coefficient of friction is given as 1 by 4 between this contact is given as 1 by 4 between this contact and what we are asked to find out is if the coefficient of friction is 1 by 4 for all surfaces determine the force P required to move the wedge that when you apply some force P what is the force minimum force that you require to move this wedge now this problem just remember that how many unknowns we have here we have 2 unknowns here normal reaction friction we have 2 unknowns here normal reaction and friction 4 and 1 P 5 how many equations of equilibrium we can draw we can write equations of equilibrium 3 for this 2 for this so we need 1 extra equation and that 1 extra equations so we have 3 plus 2 5 okay so we should have slippage exactly at one point and these are the different modes in which the slippage can happen okay you can convince yourself that what will happen is that when this point is moved inside this cylinder will tend to slip here you put the direction of slippage downwards and then put the appropriate forces and then you can solve this problem okay there isn't enough time to do this problem fully if you have any questions you can ask I can pose the answers on the moodle