We introduced packet filtering firewalls. So very simple. They they look at the packets which Pass through the firewall they look at in particular the headers And if you're browsing through your lecture notes, you won't find this here This was in the the extra notes just for this week, but you'll follow a Packet filtering firewall as packets go come to it it looks at IP address of The source and destination who sent it who are they sending it to port numbers Which identify applications so which client application is sending to which server application? protocol number which identifies the transport protocol being used TCP UDP and others and Use that information to determine ship shall we allow this packet or not? Accept or drop There may be other information used as well. We'll see We could potentially use other Information about which interface that arrives on other packet information. So it's looking at the packet headers to determine which one to accept and the packet Filtering firewall is made up of a set of rules that the Administrator of the network creates. So the rules are really conditions based upon this packet information where we can have wild cards or ranges and When a packet arrives the firewall map compares the packet information against the rule if it matches it takes some action So that's what we got to on Tuesday Let's go through some examples to demonstrate those concepts Here's our simple network So Let's go through a different example where we have a firewall in the middle So running on a router that connects an internal network and an external network The internal network has many computers One of them is computer one With IP address one one one one and the other is computer two, but the outside network There are also many computers there. I just draw one computer two So Here's your task set up a firewall such that for the first case Let's say our firewall has a default policy to accept everything We have set up that so that will accept all packets through Let's write down the default policy by default that is if no rules match We will accept the packets So it's a rather open firewall So we want to accept everything but we want to block some things So for an example, let's say you want to block block computer to From accessing the web server on computer one Create the rule rule or rule. So try Computer to needs the We should block computer to from accessing the web server on computer one anyone What are you going to do? This is going to be your task In the quiz in the online quiz and some of you will have the task in labs as well Block computer to from accessing web server on computer one. How? What are you going to do firewall? Yes, but what's the rule for the firewall? Filter the IP and protocol what IP? So here let's let's create the rule here So I've drawn the think of the firewall table contains a set of rules a set of rows Where we look at the source the destination the transport protocol being used and if our packet matches our rule will take some action So we need to specify the rule to block computer to from accessing computer one What's the source IP address? Computer to from accessing computer one This network is an internal network. This is outside Computer one is our web server. We want to allow everyone to access except computer to we don't like them Well, we think they're malicious. So we want to set up the firewall so that they cannot access the web server Source IP would be Compute that of computer to so we'll write the rule should say that if the source IP is Two dot two dot Two dot two in fact, I've just listed the column source here. Remember, there are two things that identify the source the source IP identifies the source computer and The source port number identifies the source application So we'll try and list both of them under this source column and the way that I'll do that is We'll write the IP address followed by a colon followed by the port number We'll come back to the port number Destination address We want to Stop to from accessing the web server on one so the source address match must match that of computer to The destination must match that of computer one What protocol? TCP is the transport protocol because we said to stop access to the web server What protocol do we use for the web? Browsing HTTP, but we're looking at the transport protocol not the application protocol HTTP But the transport protocol that it uses and HTTP Uses TCP so the protocol must be TCP But we're missing some things The source port number we want to write here and the destination port number the easy one first Destination port should be 80 Again stop computer to from accessing web server on computer one Destination port will be that of the web server Which is 80? source port what port number does the Web browser on computer to use Anyone have a computer open your browser and find the port number that it uses Open your browser connect to a website and type in netstat on your terminal easy now open your terminal and you don't need Open a terminal and type in netstat and you'll probably see the list of net, S T A T network statistics, but what And you'll see, to make it easier for you to see, net stat minus t. And he sees a list of values and scroll up, look at the local address, your address, <IP_ADDRESS>.81. Read out those five digit numbers, five one, five one, I'll read them to everyone, five eight, four, four, four, five, eight, four, four, one, these are the port numbers of his web browser. Five, eight, four, three, eight, five, eight, four, two, four, any structure? No, then the browser doesn't use a fixed port number. Okay, the web server uses port 80. We know that. But a browser, the operating system, when you start the browser and it tries to connect, the operating system will assign a port number from some range. It's not random, but it's assigned dynamically. So when user on computer two opens their browser, it will get a port number and try and connect to our web server with port at destination port 80. But we need to configure the firewall rule before they connect. So we won't know the port number used by computer two in advance. There's no way to know that, because today it uses 50481, tomorrow it uses a different number. So the source port number, what will we use here? Any value, star. Okay, so in the firewall rule, when we configure it, we say, if it comes from computer two from any port and going to computer one specifically to port 80 and using TCP, then we'll take some action. So we don't specify a specific port number. We say any value, or I'll write as star, I mean anything matches. We, which is just a range, all possible port numbers. If the packet matches those conditions, what do we do with that packet? We take the action of dropping it easy. User on computer two opens their web browser. It gets some port number 50481. They send a packet to the destination port 80 on computer one. It will get to the firewall. The firewall will look at the packet information, compare it against this preconfigured rule and see that it matches. And therefore the firewall will drop that packet, not allowing it to go to computer one. Computer two wants to connect to the web server, the web browser starts. Let's say it gets port number similar to his laptop, that's assigned by the operating system to the browser, sends a packet, goes across the network, gets to the firewall. The source port is 50481. The source IP is 2222. He's sending to 1111 destination port 80 using TCP as the protocol. Therefore the packet information will match this rule and the firewall will drop that packet, delete it. It doesn't send it through to the destination, achieving our aim that computer two cannot access the web server. Any questions on that, the simplest of firewall rules that you'll see. Okay, let's create a new one then. Let's try a different scenario. Let's go back to our start. Let's try it where we have a different default policy and have a different aim. In that first example we said the default policy was accept. That meant if a packet did not match the rules, we would allow it through, we would accept. Let's try the opposite. Default policy is drop, which is more secure. It's recommended. Meaning let's set up this firewall to drop everything. No one can communicate via the firewall unless we add a rule to allow them. Let's try a different aim. We want to drop everything, that is block everything in the network but let's say we want to allow the person on computer one to access the web server on computer two. Block everything in the network, no internet access at all except computer one can access the web server on computer two. Try, just set up the rule. Computer one access the server on computer two. So look at if computer one tries to access the server on computer two, think about the packet. What would the source IP be? What would the destination be? Protocol, we're still using web browsing, HTTP which is used as the protocol, the transport protocol TCP so that's easy. So just write the rule to stop, no to it, sorry, what did I say? To allow computer one to access the server on computer two. We want to stop everything except computer one accessing the server. What do we do? What are you going to do? You go get a job next year okay or maybe in summer training in the next month or so you go work at a company and they ask you to set up their firewall. If you don't set it up correct and someone attacks their network they fire you. What are you going to do to set up this firewall? Quit the job, nice life you're going to have, just quit the job, give up. Think of the source, who's the source? We want to allow computer one to access computer two web server. Sources, okay so one one one one, okay good. This is what we want to allow to happen. We want one to be able to communicate with the web server on two, okay so web browsing, very simple. So yes, source IP, source port number, port number of your web browser. How about a different challenge? This is you in the lab or in SIT and you have control over the firewall. SIT set it up to block all your internet access but now you want to access your favorite website so what do you do to allow yourself on computer one to have access? What port number is your web browser using? What port number is your web browser using? What's this, sign language? What sign? Star, okay. Star meaning your port number of your browser may be any value. The firewall or the administrator of the firewall doesn't know what it will be in advance so let's set it to be any value. Destination two, this is easy. Destination port 18. Protocol, action, accept, okay. If a packet arrives at the firewall and it's from computer one, any port number, any application and it's going to computer two specifically to the web server on computer two using TCP then let's let it through. Let's accept that packet meaning it can go through the firewall to destination two. Default, if a packet doesn't match that, drop. Easy. What's the problem? We need to allow the response to go back. We need a second rule for the response to come back, okay. So it's not as easy as the first case because this allows my request to go to computer two but of course web browsing is not much fun if you don't receive a response. Computer two sends back some response. Source computer two, does it match the first rule? No, the response. So the first rule doesn't match. There are no other rules therefore the action to take for the packet is to drop that packet. So although we allow the request to go out, we don't allow the response to come back so we need to add a new rule to allow that. In fact it's not the HTTP request and response, it's the TCP send. I have a picture just to remind everyone somewhere. It's just a reminder, a quick reminder of how web browsing works. So computer one wants to connect to server on computer two. They want to send a request. We don't immediately send the request. We first set up a TCP connection. So we computer one sends a TCP SIN segment to computer two. Computer two responds with a SIN act and then computer one responds with the final act. This is this three-way handshake, set up the TCP connection. Once that connection is established then they can transfer data and the data is computer one sending a HTTP request saying I want this web page and hopefully computer two sending back a reply saying here is the web page. So there may be some further acts that come as well. But remember we actually set up a connection first. So to allow our web browsing we actually allowed that first SIN packet out but we need a new rule to allow the response to come back. So we'll add that second rule now to allow the response. What's the second rule? What do we do? Allow the response. The response is coming from computer two. Port number it's coming from the web server. If I send a request or a web server the response is going to come from that web server. Come from port 80. Destination should be coming to computer one. Destination port don't know star. Remember this is to cover the response to the client from the server to the client and we don't know that the client's the browser's port number still using TCP and we need to accept that. Okay so we need to be careful that we need to allow the request or the packet out and of course all most applications are request response based so we need to allow the response back. Anything that comes from the web server on computer two going to computer one will be accepted anything going from computer one to the web server on computer two will be accepted everything else will be dropped will be blocked and that should allow all of those packets through the firewall. The first seen packet coming from computer one to the web server on computer two. The seen act coming from the web server on two going to computer one that will be accepted and so will the act and the request and the final HTTP response because they all have those same addresses anything hard so far no so a small extension to allow the response what's the problem you've just failed because someone you you configure your firewall and the company fires you because someone hacks into your network what have you done you've opened up a hole somewhere how it's not not an easy one to take advantage of but it's possible if someone sends to two or one so these are the rules everything will be dropped except packets that meet the meet these conditions so what's what have we done wrong or what can we allow there can be a response without a request or there can be a packet there can be a packet from who okay let's say now the user on computer two is some malicious user they want to get a packet through your firewall how do they do it well if they send a packet if their application uses port number 80 this second rule will allow the packet through so let's say the user on computer two is malicious they want to get a packet through the firewall the firewall should only allow web browsing from one to two they shouldn't allow computer two to send arbitrary packets to computer one but it can because what the user on computer two does is they create their application that uses port 80 and they send a packet to computer one and that will be accepted by the second rule so if the user on computer two can create an application that uses port 80 they can get their packet through the firewall defeating our original intentions okay so it assumes that the user can use port 80 I can can you use port 80 on your computer those with computers open do you know how to use port 80 how about this you can do anything you like on your computer okay if you've got control of the computer you can program it to send with an address whatever you like remember this is a packet that is created at computer two and sent out the source address the source ip will be two dot two dot two dot two the source port whatever computer two wants it to be okay because it's under control of the computer two so yes we can send a packet with source port 80 either create an application that uses that port or use a fake port address it's not hard to to use fake addresses so we opened a hole where some unintended consequences of computer two is now allowed to send packets into the network even if it doesn't get a request from the web browser how do you close that hole so you can keep your job how are you going to close the hole before your boss finds out about it delete the rule but then you block web access and your boss will certainly notice then okay we needed this second rule to allow the web server to send a response back computer one is the boss's computer you need to set it up so he can access the website if you delete the second rule he will never get a response and he'll fire you in five minutes but you've got a bit more time now because he doesn't know there's a hole in the the firewall so how are you going to fix it any ideas sorry use authentication well no uh let's say all we have available is looking at the packets okay that's all we have available set the destination port uh okay but what are you going to set it to set the destination port here what value uh but remember this is the configuration of this firewall some device on the network the port number is chosen by this computer so when the boss starts his browser it gets a port number he starts it tomorrow he gets a different port number which one are you going to set it to here well it's going to take many possible values that's why we use star any value but maybe you're on the right track there are different ways set the port again force his browser to use the same port i don't think it will work very well because usually a browser when you open multiple tabs it may use multiple ports okay yep okay we need some other condition that says only accept this packet if it is a response to a previous packet okay that was the intention of this second rule to say if we set send a packet out this is to accept the response coming back it shouldn't it shouldn't match if it's the original packet if it's the first packet so that's the idea and we'll go straight to that is that if we can keep track of what's happened in the past then we can effectively add more conditions to this to say okay if we if we sent a request out then we should allow the response to come back that makes sense because i think most applications need that so keep track of what's happened so that we don't have to we don't allow any packet to match this condition actually two ways one is if you look at the tcp connection setup we could use those values the first packet is a tcp sin segment the packet coming back is a sin ac so that second rule should only match that sin ac or packets that if we can identify our responses to previous ones so somehow we need to identify a response and attach that condition to rule two so it gets a bit harder than we originally thought of allowing web browsing let's go to the easy way to do it we add a new feature to the firewall we add what's called stateful packet inspection and it will simplify our task and make your job much easier when you set up the firewall so far our firewall is what we call stateless in that it doesn't keep track of what happens to the packets in the past but that doesn't work so well especially when we have connections so we'll introduce this new piece of information to keep track of past packets especially past packets that have been accepted so let's use our example to explain how spi stateful packet inspection works the idea is that if we allow this first packet out from computer one to the web server on computer two then we should allow all of these other packets through the firewall we should automatically allow them and that's what stateful packet inspection allows us to do it keeps track if we accept the first one according to the firewall rule then all of the others which are related to that one let's accept them as well let's see how it works let's attach just our first rule and return to that one which was if the source is so this is the same first rule as we had before the source is one one one one any port going to two computer two port 80 protocol tcp accept and our default policy same as before is drop now before we add this second rule but we saw it allowed packets in it gave us a hole so let's not add this second rule and use just the first one but now let's introduce another piece of information or another table of information called our stateful packet inspection table spi table where we'll keep track of packets allowed we'll keep track in some spi table similar source original source original destination protocol and we'll add another column state so this is a second table that we store in the firewall we have our rules but we have this other information stored and let's see how we use it computer one tries to establish the connection and i'm going to flick through but computer one in this case establishes the connection again ip is one dot one and the ip of computer two in this example computer two is a web server running port 80 what port number is our client running well when we start our client it gets a side one let's give it one just a random port number in some range so the first thing we do then when the computer one tries to contact the web server is it sends this tcp sin segment where the source address is 1111 and port 40163 this is just a random one i've chosen the destination ip is 2222 destination port 80 protocol tcp that's the packet information this sin segment goes from computer one and gets to the firewall is it accepted or not so go back to our firewall does that packet get accepted yes or no the first packet in our web browsing from computer one to server on computer two is it accepted the first packet yes because it's from computer one to computer two port number i think i what did i choose 40631 going to a server this rule that matches the packet and therefore we accept that packet so that's normal the normal behavior of our firewall compare our packets against our rules we accept it we allow it to go through to computer two but also because we accepted it we add an entry to this spi table we keep track of the packets we've accepted so let's add an entry that keeps track of that information and let's just remind us so sorry a packet from computer one with source port 40163 was allowed to go through to computer two with destination port 80 that's the sin packet the first one so let's record those addresses and let's write them down here from one one one one four oh what was it 163 destination two dot two dot two dot two port 80 protocol we're still using tcp so that was the packet accepted it has these values in the addresses and we record this information along with what what this packet is related to and that's what this state is this is related to setting up the connection i will not write it here because we'll run out of space and i'll change it quite shortly but the state at this stage is we're trying to set up the connection this one packet was to set up the tcp connection so we record this in this table now the second packet comes back that was for the sin it was accepted through the firewall firewall that got to computer two computer two the web server sends back this sin act source ip is computer two source port is 80 destination computer one destination port 40163 still using tcp it gets to the firewall it gets to the firewall and now what the firewall does is before it looks in the the firewall table it actually compares to the values in the spi table we've recorded these values in the table the packet that came back was from 2222 port 80 and it was destined to 1111 port 40163 and because the values match in its spi stateful packet inspection table the firewall automatically accepts it okay now note that they don't match the source destination it's the opposite because it's the response those values are the opposite that is the source was 2222 port 80 destination was computer one but it still is considered a match with respect to stateful packet inspection because the the response packet belongs to the connection identified by these values so that packet is automatically accepted so the idea is that once we allow a connection using our firewall all subsequent packets related to that that connection are also allowed so our responses are allowed the the sin act the act and so on are allowed without having specific rules in the firewall what does the state do the state is used to indicate or what part of the tcp connection set up are we in so the first one we were setting it up eventually it would become established and it would store some values saying the connection is established tcp connections go through different states but the the one that once we've set up the connection and we can send data is called established so once we have this value or entry in the spi table any packet that matches these conditions is accepted automatically we don't check the rules if it doesn't match these conditions we go back to checking the rules if it doesn't match any of them we go to the default policy of dropping this greatly simplifies our firewall rules we just need our original one rule we don't need to deal with the response spi automatically does that for us so actually we now have two tables of information the rules and the connections questions on stateful packet inspection so you can impress your boss when you go get that job so think of it as an extension of the basic firewall the basic firewall we just have the rules but with stateful packet inspection we can simplify the rules by keeping track of the connections that we've already allowed note that a connection in the internet is uniquely identified by these five values when your browser talks to a web server then there should be in the internet no other browser using the same source ip and the same port number talking to the same web server those addresses identify that unique connection in the internet therefore if we ever see a packet that matches these either the source matches this and the destination this or the opposite way if it's coming from two and going to one then we can accept it because we accepted it from here so in practice stateful packet inspection is commonly used one way to think of it is now we have two tables a packet arrives at the firewall first check in the spi table doesn't match if so except if not let's go to our rules in the firewall and take the action if it matches if it doesn't match take our default action drop so you can think there's sort of three steps spi table first the rules otherwise the default action any questions all easy quiet means easy correct let's go back to our lecture notes then and see what we've missed so we said just going back that we've got packet filtering firewalls this basic concept of look at the packet header information we can extend that with stateful packet inspection there are some other type of firewalls called proxies but we're not going to introduce them okay we're going to keep it simple and stay with the basic ones but they're still important but we'll just stick with packet filtering firewalls so that you can be experts on that we saw that the most common information that's used to filter packets is IP address port number protocol number but you can use other information you can use what interface did it come in on the firewall you can use MAC addresses you can use TCP flags is it a sin segment is it a sin act so you can use other information but these are the five common ones which are important rules are processed in order in our firewall so always think of them as a packet comes in compare against the first rule if it matches take the action and you're done if it doesn't match move to the second rule and keep going and there's usually some either some rule down the bottom that captures everything or just a default rule default action to take where do you find firewalls in software most operating systems have inbuilt firewall software we'll use IP tables so you'll get some experience with IP tables in Linux for firewall setup you can install your own software so you can download some software to install firewall on your computer but that's more so well that's for say firewalls on the end computer but in large networks usually the firewalls are installed on network devices with the aim of protecting the entire network rather than having to have a firewall on every computer so most routers most large routers when you buy them may include some firewall capabilities or you can buy dedicated hardware that acts as a firewall if you need to have a fast processing speed packet filtering firewalls are quite simple we just set up the rules transparent to users meaning the firewall doesn't modify anything it either blocks or accepts the simplest terms it doesn't change anything so the user right if it's blocked the users will know but if it's accepted the users won't know the other types of firewalls that we go through using proxies may change the data as it passes through the firewall so it's not transparent it may modify the data they're very fast because they the functionality is not much different from a typical network device like a switch or a router so they can do things process packets very quickly and they don't delay packets much some attacks some malicious software for example firewalls cannot prevent a simple packet filtering firewalls cannot prevent so if they're just looking at the header fields they don't look at the data if this packet contains a virus or spam our simple packet filtering firewalls won't detect that they're just looking at who's sent it who's coming to a few other things how do we use our packet filtering firewall to allow one user to access a website but allow other stop other users from accessing the same website how can we do that allow me to access a website but stop all the students from accessing the website from sit how could we set that up the port that is in sit from my office computer i need to be able to access some website facebook but no students in sit can access facebook what would we do at the sit firewall okay we need some way to identify the user but packet filtering firewalls generally don't consider that okay yes you're right we could do that what's a simpler way maybe not as bad good but ip address configure the firewall if it knows my office computer's ip address say everything from steve's computer with this ip address let it go from all our ip addresses block it okay so in simple firewalls we can use ip addresses but more advanced features of today i'm using one ip address but in my laptop i have a different ip address so how do i allow that that's when we need some more advanced way to identify the user simple packet filtering firewalls don't do that normally we need more advanced features as with any firewall if you set it up wrong you could have a compromise in the security of your network if you add the wrong rules you make a typo when adding those rules then maybe something is allowed in that shouldn't be and stateful packet inspection keep track of the connections except everything relating to those connections that have already been accepted the problem with packet stateful packet inspection is that we need to keep track of many connections sometimes let's to close on those to let's show an example it's hard to see here's one computer and we'll look at the firewall i have to zoom out a bit we're not explain all of it but you'll see these are rules in a firewall so if you look at a particular line you see this firewall says accept packets which are using tcp coming from this source address and this is a special value meaning any source all zeros coming from anywhere so think of a star going to computer 192 168 122 dot 10 so that's the destination ip address and destination port dpt the destination port is 80 so this is saying this firewall is set up to say anyone who contacts the web server on this computer 10 the packet will be accepted okay and there are some other rules to allow access to secure shell servers 22 email servers 25 secure web browsing HTTPS port 443 okay so just an example of some rules in this software or this firewall stateful packet inspection is enabled using this special rule to say record the established connections so remember there are two tables the list of rules and another sbi table that keeps track of all the connections that's stored separately it's hard to see because it's hard to see because it's quite large but we'll try the software keeps track of connections called nf contract connection tracker again it's wrapped across lines but let's just highlight some values this is so every line is one connection that it's tracking this firewall at this point in time and we see some values that this connection is established that's the state the source is computer 192 168 1 2 2 dot 11 destination 150 address source port 80 destination port 539 68 so this is the sbi table any packet that comes into the firewall that matches those values where the source and destination can be in either order will be automatically accepted that's the idea here and there are many different values if we scroll through okay so just an example that we keep track of many connections over a period of time the way the state of those connections may change the idea is that if there's no packet sent along those connections for some period of time delete it from this table so timeout value so we have two tables the firewall rules that you the administrator creates someone has to set this up and the sbi table or the the the list of connections that is automatically created by the firewall you don't have to manage that add blockers add blockers software that what do they do they do filtering yes so yeah they use similar concepts filtering based on they look at addresses and domains I think but they also look at content more than a packet filtering firewall that in this firewall we don't really look at content whether the the web page contains this text or not add blockers will look at content any other questions on firewalls that's we're going to stop there on firewalls what we will not go through the proxies there's only a few slides on the proxies firewall locations where do you put them well in practice in large organizations you you don't put them on the end user computers or they may be on the end user computers but the firewalls are usually located on network devices routers and switches or special network devices so that they cover all traffic for the network and we don't need to set up a firewall on every computer in the organization we can do it on one central location it's common to separate the internal network into zones two zones the internal network for all the the workers or the computers and the internal network that has servers which should be accessed from outside like web servers email servers so we can think inside sit there's a sit web server which is inside our network but people from outside should be able to access it but then there's my computer which is inside the network people from outside should not be able to access it so we separate them out and the concept or the terminology you may hear is that we put the those public facing servers the ones that people from outside need to access in a demilitarized zone a DMZ some part of the network which is separated from the rest of the internal network for example is our internal network office computers and so on no one from outside needs to be able to access them so here's outside the router is this red one out here is the rest of the internet no one outside should be should be able to access our internet our internal network but in this DMZ is our web server for sit our email server and again they are part of our internal network but they need to be able to be accessed from people outside so we actually separate them into two zones this zone which is separate from internal and external the DMZ and this green box is the firewall it should be set up to say if someone sends in to one of our servers send it into that zone if someone sends in to one of our something that's not a server block it so it's easy to set that up and if you want to be extra secure you can use two firewalls if someone sends in the first file will direct it into the DMZ nothing will go from the first firewall to the second firewall to the internal network unless it's a response to what came out and having two firewalls adds extra security because if there's a an attack on one of them and it's compromised or it's misconfigured someone sets it up wrong then we have the second one as a backup so if there's an attack on the first firewall and that an attacker can get their packets through it then the second one if it's configured correctly will block those packets to the internal then similarly if there's a misconfiguration in the second one the first one should block and not allow anything through let's stop on firewalls just a quick


What, what, what, what in the world, what, what in the world can I do for you today? What's up guys? Today I'm going to give you four magic questions to help you build real relationships with your clients. Okay. Welcome back to my channel. I'm Ricky Caruth and if this is the first time you're seeing me, I'm a 16 year real estate agent. I've written two books. I speak nationally to real estate agents and I coach for absolutely free. Why am I coaching for free? Because I actually want to help. I want to give back to the real estate industry. My overall goal is to help reduce the failure rate because it's so crazy high. They say 87% of agents fail in their first couple of years in the business and I think that is absolutely a tragedy when real estate is so simple. You just talk to people, you create relationships, you find out what you can do to help them, you make a connection and then you put a system in place to stay relevant forever in their life and they always use you as their agent. They refer everybody they know to you. Every prospect that you create a relationship with is worth 10 to 20 deals to you over the life of your career. So regardless if they buy or sell today, if you begin that relationship, they could be worth 10 to 20 deals to you over the life of your career. I have a complete free course from top to bottom exactly how I do this. It's at ZeroToDiamond.com. As soon as you sign up, you'll start getting my emails as well and we're doing live training sessions every other week. It's live right here on this YouTube channel so be sure to click subscribe and hit the bell so you get notified when I post new videos and when we do our live training sessions. Last week I made live calls for an hour and a half. This week we're going to do lead conversion. I'm going to go through my entire lead conversion process and take all of your questions. I want you to take your business to another level. So let's get into these magic questions that I ask and I'm talking to prospects that enables me to begin a relationship. You see the problem is that most of the training out there is designed to figure out what the client can do for the agent. I want to teach agents how to find out what the agent can do for the client. That's where all the money is made. That's how you actually help people. That's how you succeed big time in this business. So the questions I don't want you asking every single person you run into is do you want to buy or sell? And if not, who do you know that wants to buy or sell? Because all that tells that prospect is that you're looking to do a deal just like every other real estate agent and you're not really looking out for what's best for them. What do they want? How can you help them? So that brings me to my first magic question. What in the world can I do for you? Good man. I don't want to take up too much of your time but there was a house right around the corner from you that just sold and I didn't know if there's anything in the world I could do for you today. This has been a game changer for so many agents. They jump into my zero to diamond coaching program and this is the first thing that really stands out to them is that I'm very low pressure and I'm not trying to see if they want to buy or sell something right now. And most agents if the prospect doesn't want to buy or sell right now they move on to the next one and they just forget about that person. And I want to begin a relationship with every single person that I can regardless if they want to buy or sell right now because chances are they're going to buy or sell later and if we're talking right now in the present anyway why not make that connection for the future and that deal is going to turn into repeat business referrals and referrals of referrals. This is how I got to 100 deals a year as a single agent. This is how I make a million dollars a year as a single agent in South Alabama because I want to know what I can do to help the prospect. So this is a big, big question. It's my money maker and what happens is it opens up so many opportunities. When you ask that question people realize right then you're out for them, not for you and they're not used to that. They feel different. They don't feel like they're talking to a real estate agent. They feel like they're talking to a friend or family and that's what you want. You want to get that sensation that they feel comfortable with you, that they like you, that they know that you're going to be their form, work hard form, you're professional, dependable, you do what you say, you're confident, you're consistent and you want to know what you can do to help them. So when I finally realized this about eight years into my career that this was the question to ask, not if they want to buy or sell or who do they know. It was a complete game changer and I said to myself, man, I wish somebody would have told me this when I started selling real estate. I would have been so much further ahead of where I am right now if I'd known that from the beginning. The second magic question is, is there an agent that you would work with if you were to do something? I got you. I got you. Well, look, is there an agent in the area that you would work with if you were to do something? This is a big, big question because it establishes where you stand in the relationship. Where are we? Are we going to be their agent? If they decide to do something, do they already have a relationship in place? Is their mother a real estate agent? Is their cousin best friend from high school? A lot of agents have a great conversation with the prospect and they say to themselves afterwards, man, I just had this great conversation. Everything's going good. This future client, everything's awesome, but they didn't ask them if there's an agent that they would work with if they were to do something and their mom is an agent. Right then and there, it doesn't matter how much they like you. They're never going to use you as a real estate agent. It's just something to throw out there very casually that establishes where you are. Then when they give you their answer, if they do have an agent, then you can make a decision if you want to still stay in the game or if you want to back off. A lot of times I back off if they already have an agent, especially if they sound very confident and this is just their agent for life. This agent did so much for them. They sold them the house that they're in and did all this stuff for them. Great. That's a good agent. I know that agent. You're in great hands. Look, if there's ever anything I can do for you, let me know. Have a great day. I'll just think if they don't, if they say they don't have an agent that they would deal with, that they were to buy or sell something, look at where you are. Now you know for sure that the door is wide open to begin that relationship and start nurturing that and cultivating that into a future prospect who's not only going to do deals with you, but it's going to send you everybody they know. I also like to use this when I run into somebody who does want to buy or sell. They say that they want to buy or sell right now pretty soon in a month or two or three. Okay, cool. Do you have an agent that you're going to work with on that? Okay. If they want to buy right now today, like, yeah, we're thinking about doing something. We want to go look at houses tomorrow. Okay, great. Is there an agent that you're already working with on that? I like to get that out there quick because I want to establish what's going on. That way there's no misunderstandings later. The third magic question is I want to know why. Why are you buying? Why are you selling? When I finally get to somebody who wants to buy or wants to sell, I want to know why. What's going on in your life that's causing you to make this decision to buy or sell? Did somebody die? Was somebody born? Did you lose a job? Get a new job? Are you relocating? Are you downgrading? Are you upgrading? Is it investment? What is going on in your life that's causing you to make this decision? We're going to just buy properties and sell properties for the heck of it, okay? Something's going on bigger. There's a bigger picture going on in their life that's causing this, and we want to know what it is, and when we know what it is, then we can really go deep. We can really help them with what they're really trying to accomplish, which is not just to buy or sell a house. There's something bigger, and we want to help them accomplish that bigger goal, whatever's going on. Make that be the focus, not necessarily the sell or the buy of a property. The fourth magic question is, is it okay if I stayed in touch with you? Would it be all right if I stayed in touch? I like this because once they answer it and say yes, and they've committed to you staying in touch with them, then you can say, okay, cool, what's your email address? I like to ask for the email address after they commit to saying it's okay that I stay in touch with them, they're more apt to give me their email address. Of course, everybody who's in my program knows that my follow-up system is the weekly email that goes out every single Wednesday. You can go to zerododiamond.com and go to the section about my weekly email. There's a video tutorial. There's an example of my email, and everything you need to get started with that, if that's something that you want to do. What I don't want to do is come out and just ask, can I have your email address? Or, hey, do you want to be on my email list or do you want to start receiving my market reports? I never want to say any of those things because it makes them feel like they're just another number on this big list that's just going to get this huge bulk blast email. I don't want them to feel like that. I want them to feel like, hey, I want to stay in touch with you. You want to make it feel personal even though you are sending a bulk email. I create my email so there's personality behind my bulk emails. So even though they know it's bulk, it still has that Ricky feel. And so when I'm asking for email addresses or I'm asking to stay in touch, I want to simply say, hey, is it hard not to stay in touch with you? Okay, cool with your email address.  Having a mindset like this where you're laid back and low pressure and you have a high volume of people that you're contacting is the secret. That is the way to the top. That is how you build your business to do 100 deals a year as a single agent. And I hope that you use one or two or all of them in your daily business to help you build that bond with your clients that you need to get to the top of the mountain. Leave a comment below and let me know which one you like the best. And if there's anything in the world that I can do for you.


Aquias ZN-based batteries represent a viable and cost-effective technology for electricity grid storage. Here, the authors discuss the most challenging aspects to bridge academic and industrial research and accelerate the adoption of this class of devices on a large scale. This article was authored by George Zampardi and Fabio Lamantia.


In a previous video, we introduced the idea of the three parallel alternatives. We had LPP, the elliptic parallel postulate, we had EPP, the Euclidean parallel postulate, and we had HPP, the hyperbolic parallel postulate. The elliptic parallel postulate says that there are no parallel lines. The Euclidean parallel postulate says that parallel lines exist and are unique. And the hyperbolic parallel postulate says that parallel lines exist and are multiple. There's more than one parallel line. And play here. Now it turns out that these three parallel postulates, they're alternatives, you can't have more than one of them. You don't even have to have any of them. But if you take the four actions of incidence geometry and you equip one of these parallel alternatives, then you get a consistent geometry. The Euclidean parallel postulate plus the incidence axioms gives you a consistent geometry. There exist geometries that we've seen in this lecture series to have their incidence geometry with Euclidean parallel postulate. The elliptic parallel postulate, if you equip it to the incident axioms, you get a consistent system. There exist incidence geometries that satisfy the elliptic parallel postulate. We have listed some ourselves. And then finally, if you take the hyperbolic parallel postulate and equip it to the four incidence axioms, you do get incidence geometries with satisfy the hyperbolic parallel postulate. We've seen some examples of that as well. Hand shaked geometry is a good example of that. And so what this tells us is that these parallel postulates with the incidence axioms is a consistent logical system. It also tells us that parallelism is independent of the incidence axioms. The incidence axioms are insufficient to tell us what is true about parallel lines. Maybe there's no parallel lines. Maybe there's one, maybe there's more than one. Maybe you have a hybrid of these things like we saw in a different example of five point geometry. But importantly, the parallel axioms are independent of the incidence axioms. Therefore, when you want to further develop your theory, because we've basically gone as far as we can with incidence theory, if you wanna develop the theory using parallelism, you have to accept one of these parallel alternatives or again, maybe some hybrid of them and then start approving the theory with that. And so that's what then leads to our definitions right now. So we say that an incidence geometry is affine if it's additionally satisfies the Euclidean parallel postulate. So if you take the four axioms of incidence, line determination, secancy, point existence, and non-colinearity, if you also give it EPP, the Euclidean parallel postulate, those five axioms together give us affine geometry. And affine geometry is gonna be the titular topic for lecture eight. Another important geometry that's an incidence geometry we get is projective geometry. An incidence geometry is projective if it satisfies the elliptic parallel postulate and, that's a big and, all lines contain at least three points. So if we take incidence geometry equipped LPP and this other strengthening of secancy, because secancy says you only need two points on a line, why not to be a projective geometry, we need at least three. We'll talk about projective geometry later on in this lecture series. Take a look for that lecture, but it's gonna be a while from now, so sorry. We're gonna do projective geometry in tandem when we talk about elliptic geometry because projective geometry, elliptic geometry are projective, projective is more broad. But again, that'll be stuff we talk about later. Why not, why do we need at least three points? Now I should mention that phano geometry is a projective geometry. So if we draw our deathly hollows right here, real quick, like so. So we remember we have our seven points, our seven lines, and we have our resurrection stone, cloak of invisibility and three elder wands. Phano geometry is an example of a projective geometry. It does satisfy the elliptic parallel posture that was actually actually five of phano geometry. It's an incidence geometry, we've talked about that. And all lines contain at least three points and phano geometry, all lines have exactly three points. But you could have a projective geometry with more than three points per line. You have to have at least three. Now it sort of begs the question, why do we need at least three? Now let me kind of give you an example here. What if we looked at our three-point geometry before? This is the only three-point incidence geometry. And notice here that it is an incidence geometry, like I said, it also satisfies the elliptic parallel posture because all lines intersect each other. There's no parallel lines here. So this would be a projective geometry except, you know, there's at least three points, right? The lines in three-point geometry, they're only handshakes, they only have two points each, not three points. And it feels like projective geometry is defined in the following way. It feels like a projective geometry is an incidence geometry that satisfies the elliptic parallel posture that's not three-point geometry. It's like, what? Why can't I join the club? It's kind of like, you know, no girl's allowed sign on the clubhouse or something. It's like, that's really rude. There's no reason why we shouldn't include this. Well, it's not just some arbitrary, sexist, racist distinction. No, no, no, we're not intentionally segregating our geometries just for superficial reasons. There is a reason why we don't want to consider three-point geometry as a projective geometry because in so many ways, it doesn't behave like a projective geometry. It behaves differently and so it does need to be excluded and those reasons will be more apparent when we talk about projective geometry in the future. So then if this point, if three-point geometry is not a projective geometry, where does it belong? It is a handshake geometry, but the parallel alternatives for handshake geometry can be a little confusing. For three-point geometry, it's actually satisfied the elliptic parallel postulate. All right, handshake geometry pretty much always is hyperbolic. The only exception is three-point geometry and then the four-point geometry we defined earlier. Right, with four-point geometry, it actually satisfies the Euclidean parallel postulate. So this is actually an affine geometry and so four-point geometry really is the start of affine geometry, which we'll talk about in the next one. So it is a handshake geometry, but we really want to think of it as an affine geometry. And then all of the handshake geometries, five and above, they're hyperbolic, those all belong together. This three-point geometry, we could consider it a handshake, but kind of like four-point geometry, it's somewhat degenerate in that regard. It should be something else. The family of geometries that three-point geometry should belong to is actually what we call fan geometry. Now, fan geometry, which we'll call the fan geometry with endpoints fn, this is the geometry that's constructed by the following scheme. Okay, five point, excuse me, fan geometry looks something like this. You have a line, whoops, you have this line. And this line contains every single point in the geometry, except for one, because if all the points were on this line, it would violate non-colonarity, but there's exactly one point that is not on this line. And then by line determination, there must be a line between all these other, there has to be a line between this point off the mega line, the mother line, and all the points on the mother line. But to avoid an intersection more than one, these all have to be handshakes. And so fan geometry looks something like this. You have this line that hosts all the points, except for one, and then the one point off of the line, there's handshakes from that point to all the other points. And so three-point geometry is really just f3. It's the fan geometry with three points. F4 would look like this picture right here. And it turns out that up to isomorphism, there are only four, there's only two four-point geometries. One is the fan geometry F4, and the other one's what we've been calling four-point geometry. It's the four-point handshake geometry, but really it's the four-point affine geometry, which we'll talk about more of those in the future. And then also for a little bit more exposure, this is a diagram for the five-point fan geometry. This would be F5. So I want you to note here that in an electric series, now I've seen three different five-point geometries. There's the handshake geometry, H5. There's fan geometry right here, which of course the reason why this is called fan geometry is because of the shape. It looks like this hand fan that you wave at yourself if you wanna cool yourself down. We also had this other five-point geometry that looked like a diamond that we saw in a previous video. It looks something like this. Right, these are all distinct. We get five, so far we have three different. Classifying all of the five-point, six-point, seven-point geometries turns into a very, very fascinating question, which can get a little bit technical the more and more points you get. And so that's not something we're gonna dive too much into this lecture, but I just wanna point out here that fan geometry is an incidence geometry, right? When you look at your picture here, non-coloniality was sort of like the motivating factor here. Point existence, right? As long as n is greater than three, you'll have three points or more. Line determination also kinda gave us all these handshakes here. That's why they are there. And then the last one, see, can't see. All the handshakes have exactly two lines and then the master line, the mother line there, it has more than two points in general. It has at least two though. So it is an incidence geometry. And also by construction, fan geometry satisfies the elliptic parallel postulate, okay? And for which all lines intersect each other because if you're two handshakes, if you're two handshakes like these ones right here that intersect at this point off the mother line, but if you're the mother line and a handshake, one of these children, then they intersect at that point that you see right there. So we do have the elliptic parallel postulate, no lines are parallel in fan geometry. So the reason why projective geometry has this rule that lines need at least three points is that projective geometry is different. It doesn't include fan geometry. And the three point geometry is really F3, the three point fan geometry. That's a distinction that I wanted to point out to you as we in this lecture talking about the parallel alternatives. I do appreciate you watching this video. If you liked what you saw or learned something, give these videos a like, post any questions in the comments below if you do have any questions. I'd love to see that and I'll answer them as soon as I can. And of course, see more videos like this about geometry and other advanced mathematics. Subscribe to the channel and you'll get updates regularly.


Welcome to JSATV, the newsroom for tech and telecom professionals. I'm Jamie Scott-Cataya of JSA here at Telecom Exchange LA in Beverly Hills. Joining me, my good friend, Mr. Todd Coleman, he is the president and CEO of eStructure. Todd, welcome to JSATV. Jamie, thanks as always for having me. Pleasure to be here. You are one of our top industry thought leaders, speakers. It's a pleasure and honor to have you here. And you've got more news every day, every time I talk to you. Tons of news coming out. You've obviously expanded your company out of Montreal and Westward to Vancouver this year, notably. How has this experience been serving these two unique markets? Yeah, I mean, it's been interesting. You know, I've, in prior businesses, I've worked in around Vancouver, so it's not foreign to me as I like to describe it.  The real estate prices are through the roof. It's very disaggregated from a competition perspective. All attributes that we like a whole lot, reasons why we've gone into the market. As I like to tell everyone, look if it was easy, everyone would be there. So it requires a bit of work. And so for us, it's about knowing where it's similar and where it's dissimilar. So for us, you know, we're all about driving scale from a process perspective, engineering standards, how we operate, but then having to localize it from a customer touch and a sales perspective. And so those attributes are different. You know, we one of the biggest reasons why we went into Vancouver is good reason and our customers took us westward, right? We had cloud providers and a number of carriers asking us to go west. We have a significant ecosystem in Montreal with the VFX community, the film studios doing rendering, et cetera. And so, you know, us migrating from Montreal to what's now called Hollywood North was a natural progression. And so we're currently building out that team, looking to go deeper into the market. You know, Vancouver is a smallish data center, two and a half megawatts, sitting right in the Mount Pleasant neighborhood. But we didn't go there just to operate that facility. And so it's causing us to look deeper into the market, understand why we're there, what we're going to do, and how that's either the same or slightly nuanced from what we're doing in Montreal. But we're finding that the markets are more similar than dissimilar, but still keeping that local touch and that local knowledge. And what new trends are you seeing in Montreal and Vancouver that's really driving the way you are serving your verticals? Yeah, look, the trends are playing out every single day for us. You know, number one trend is we're seeing greater power densification within our data centers. The types of applications and the amount of power demand is only increasing, which from our perspective is a great thing.  And so that means densification.  You know, what we used to consider high density was six, seven, eight kilowatts a rack. And now if you're not 20 plus, you know, we're working with our customers to say, how do you fill up that rack? How do you take that 42U or 48U rack and fill it up to the greatest extent possible as opposed to spreading it out, which is sort of the old school data center mentality? You know, beyond that, you know, other trends, you know, we're finding, and I've spoken to you about this before, understanding the needs of our customers down to the application level is becoming more and more critical.  We look at our customer applications to understand what do they need? What do they need from a power perspective? What do they need from a redundancy perspective? Do they even need generator backup? Do they need UPS backup? What's the level of security? And so I think that's going to progress. We're seeing that trend play out.  Even the VFX community that we have within our data center ecosystem is a big proponent of understanding where they're at. They have three month project cycles and then they go down for a month. What does that mean from a capacity perspective? And so it requires a unique knowledge base within our customer set. And I think I see that trend continue to evolve regardless of location, whether it's Montreal or Vancouver. And then the OTTs, completely different beast. Completely different beast. The other fortunate or unfortunate trend within the OTTs and the hyperscalers is there's an inconsistency of requirements. We're understanding where they're at and they have different needs, what level of redundancy. They've got different security requirements. Some like raise force, some don't like raise floor. It's, again, working with them. And for us, I guess the underlying trend there is to keep it flexible. It's not a one size fits all. And the more that we can be flexible in our designs while still driving operational scaling standards is going to be important as it plays out. Also last time on JSA TV when we interviewed E-Structure, one of your colleagues, we talked about potentially building out a channel partner program. Any updates for us on that front? Yeah, I mean, there's no potential. We are building out a channel partner program.  We've all had past experiences, some positive, some negative, but we learned from those experiences.  I'm a massive believer in putting on as many feet on the street that are telling our story and reaching out to prospects and customers alike. And so we are absolutely building out a channel partner program. We're, you and I are sitting here in Beverly Hills. I was in Manhattan Beach earlier today meeting with a master channel partner. And so that is in the throws. That is a massive 2019 initiative for us to dedicate our own resources internally to go develop the channel more broadly, make everyone aware of what E-Structure is doing in and around Canada.  When we're looking out into 2019 and beyond, do you have any news maybe on the future expansion front that you can share with us? Well, look, we're constantly expanding. I'm not going to give away any secrets. I mean, look, as you know, we've been equisitive. We're going to continue to be equisitive where we can find the right opportunities. It's got to meet our unique requirements. We're not looking to just buy anyone and roll anyone up, but it's got fit within our model. Unique footprint, right age of equipment, technology, density, location, network providers, all those things come into play, but we continue to expect to be active in the consolidation of the marketplace. Second bit is expansion. We got significant expansion already underway, and we continue to see that play out. We acquired our first acquisition back in February of 2017 already, and we immediately announced a five-megawatt expansion. It's working in a multi-tenant building, so it took a little longer to get that done, but that's actually rolled out and fully live, bringing in a massive utility expansion, cutting over to generators, new generators, new mechanical, and more than doubling the white space. As you know, we acquired the former Montreal Gazette printing building. We literally have 15 megawatts of new power showing up at the end of November. The full 30 megawatts is going to be there by the end of April, and our first pod is coming online by the end of November, so no shortage of stuff going on. Pretty excited about all the things that we're doing from a technology perspective. It's funny, when I started this company, I used to say, hey, we're not in the technology business. We don't take technology risk, and I still believe that, because at the end of the day, we're infrastructure people. But we work with new technology, and we're working with great partners. I'll give you an example. We're working with Verdev to bring in their latest and greatest cooling technology that can do 500 kilowatts a unit, and we have literally the first of their units that are coming off the manufacturing queue and are going right to Canada into our data centers. So we're excited about that. We're working with new floor partners, which doesn't sound overly exciting, but how you handle cabling and airflow within a 150,000 square foot data center is really, really important. And so we're excited about the partners that we work with and the new technologies that we're bringing on board with these data centers. We're excited to watch you as you are on this tear up, so which we always knew. Todd Coleman, of course, once again at it, East structure, thank you, Todd, for joining us. Thank you for having me, as always. I appreciate it. We love having you, and thank you viewers for tuning in to JSA TV. Happy networking.


So, let us start with problem number 1, ok. So, we will do it for around 15 minutes. So, we have a simple mechanism in this problem. What we have is this is a device which is used to supposedly trim various things. So, this is where this is the blade this vertical portion this is a frictionless guide in this problem it is frictionless. And what we are asked to do is that this knife is connected by a 2 force member db to this to this full member abc. And what we do is that if you apply a force here then that force get transmitted here. And in the end at point e the force gets transmitted to the plate which then get sheared. So, what we are asked in this question is it for this very simple system we are asked to find out what is the vertical component of force exerted by the blade at d, ok. So, what is the vertical force here and because there is no friction between these 2 rigid supports this vertical force automatically imply what is the shearing force. And second we want what are the reactions at c, ok is the problem clear, ok. So, let us solve this problem, ok. So, this will be here, but what is the logic, ok. For example, what then in the yesterday's class is we ask ourselves a question if you want to know what is the force in member db the simple question we ask is what if we remove db. So, we know if we remove db then whatever force you apply here, ok there is nothing balanced about c. So, what we know is that this db is providing a counter balance for this force about point c. So, immediately we know that the thing we want to do is take this free body diagram and take moment about point c in order to find out what is the force in this 2 force member. We know what is the orientation of this member why because we know this 2 distances. So, we know what is angle. So, the moment we know this angle we immediately know if the force in db is given vertical and horizontal force is immediately obtained, ok. So, I think I forgot time p let me p is not unknown p is missing let me tell you what p is, but even then you can obtain the answer in terms of p, but let me quickly tell what the value of p is, ok get the answer in terms of p and then report what the value is. p is not a it is a it is a hinge between d and b, but member abc is a full rigid body, abc is a rigid body and it is connected by pin joint to member db at point b. At point b. Point b. Point b pin bb, ok. Right. So, abc is a whole rigid body it is pinned about point b with respect to member db. So, member db is a 2 force member member abc is north, ok. So, load is equal to 400, load is 400. So, use the load as 400 and tell what the answer is. 26. Yeah. It looks fine dy, right 2675. 2534. 2534 Newtons. So, between those like approximately similar value, but not exactly load is p is 400, ok please take p is equal to 400 I am sorry. Answer 2.7 kilo Newton for dy 2856 yeah 2.8 kilo Newton, 2.8 kilo Newton yes. Yeah, yeah, yeah. That is vertical reaction at d, yeah 2.86, 2.86 is the vertical reaction at d, good. 2 force member. I have found that as a db that rdb member comes 3.076 Newton. Ok maybe, but we are asked. Yeah, but what is the vertical reaction? Because that is what is asked in the question and it has miraculously disappeared. You may be right, but what I want is what is the vertical reaction at d? That is what the problem demands, ok at vertical reaction at d. Your like force in member db is fine, ok. So, do you think I can just briefly show the solution and we move on, ok. So, let me just quickly show the solution and we can move on, yes please. Then I got answer 2.83. 8386, ok that is fine. 2.8. Yeah, depends on how, where did you truncate decimal places is fine. 2.8 kilo Newton approximately is the right answer, ok. So, just simple, ok very straight forward problem we begin with a simple problem. We will move on to little bit more difficult problems. So, this is the entire free body diagram. We have replaced the force in member db, ok, along the because db is a 2 force member. This is a line of action of the member. Take moment about point c, ok for the entire free body diagram. You will get an equation like this. Note one thing that the inclination is such that dy by dx, ok is equal to 60 divided by 25. The dy by dx is equal to 60 divided by 25 and when we say that this is the direction of the force which is provided by member db, we are assuming implicitly that db may there is a compression, ok. There is a compression in db is what we are implicitly assuming. So, it will push the other member, ok. We solve this, ok because we are interested in dy what we can do is that while taking the torque of member d, of horizontal force dx about point c, we just replace dx in terms of dy here and we solve this equation we get dy. Then what we do simply that for this complete free body diagram abc, take equilibrium of the force in the horizontal direction. We can immediately then find out what is fcx reaction at point c in the horizontal direction. Similarly taking equilibrium in the y direction, ok. We can immediately find out what is the vertical reaction, ok at point c. The total effective reaction is sigma fx square plus fy square and the angle will be just tan inverse of fcy by fcx, ok because both are negative means we have taken the direction fcx to be upwards sorry fcy to be upwards fcx to be in the horizontal direction, ok and both come out to be negative which means that the direction that we had assumed are exactly opposite. So fcy is downwards fcx is to the left and so the effective angle will be 68.5 in this direction for the force. Any doubts can we move on to the next problem? So what we have is the same kind of a plier what we are asked to find out that what is the clamping force q in terms of the parameters what are the parameters in this system? The parameters in this system are c, e, alpha, b, a. There are 4 dimensions of the system and for this system, ok and there is an angle alpha. So for these dimensions what we are asked to find out is given this p what is the clamping force produced at the clamping points q. Question straight forward just 2 lines question, ok. So let us solve this problem, ok using the symmetry arguments which we had done yesterday little bit difficult problem not too difficult. Which one is alpha? Ok so let me mention that properly here. What is alpha is if you look here focus on these 2 pins these 2 if you take a line joining the centers of these 2 it is not perfectly vertical it makes an angle alpha with respect to the vertical, ok. So that line is at some inclination and you see because of that that angle is also reflected like this because this dotted dashed line is perpendicular to this so that also becomes alpha, ok. Is the geometry clear? What alpha is? Yeah so let us solve this problem. Any question, ok. So you can ask me just note one thing is that even though the geometry looks all curved bars and so on if you can just replace that with straight lines, ok. That will really simplify the problem because all the intricate details of the geometry handles being curved and everything is completely irrelevant to the problem. If you replace it with a nice straight lines problem it will become very straight forward and use little bit of symmetry arguments not much of what we did yesterday. This is even simpler than what we did yesterday. In this problem, ok a simple hint is that, a simple hint is that take this line this horizontal line is actually the line of symmetry in the sense that you take the plier and turn it around about this axis you will see exactly the same thing, right. So what does that mean that at this point of intersection two of these bodies are meeting, ok. This top handle and the bottom handle. They are intersecting at this center point let us call it O and in that case because of Newton's law as we saw yesterday the reactions will be equal and opposite but by the symmetry in the problem about this axis they should also be equal and mirror images of each other. So that will dictate as yesterday that the horizontal force, ok when you remove those two will be 0. You will see that and that is the only symmetry you need to use in this problem. Why? Because then you can just disassemble this portion, disassemble the top portion and we know from symmetry that the horizontal reaction here is 0. Same goes for this one that this pin is common to the top jaw and the bottom jaw, ok. So by Newton's third law when you disassemble these two the reactions from one to the other should be equal and opposite and it is a pin joint, ok. So these two degrees of freedom are restricted rotation is free. So there will be vertical reaction there is horizontal reaction Newton's third law will dictate that they will be equal and opposite but the mirror symmetry about this axis will dictate that they are mirror images of each other and if you just draw those arrows you will immediately see that even at this point the horizontal reaction is 0. And then you are left with two very simple problems you have to analyze this jaw sorry this handle and this jaw, ok. And you will immediately realize that what is this handle doing? This handle is trying to after applying these two forces P these two handles tend to rotate about these two points both the bottom one and the top one, ok. So we know that somehow the torque about this point has to be involved for this free body diagram. Similarly what about the jaw? Even in the jaw you can see that the jaw tends to rotate about this point. When we do principle of virtual work we will solve this exact problem using principle of virtual work and you can actually visualize what the displacements are but here in very hand waving or qualitative terms you will see that the top jaw and the bottom jaw tend to rotate about this point. So the immediate equation that would come to your mind is for this free body diagram torque about this point, ok. So that is the overall idea and by symmetry what did we achieve? We made sure that for the top free body diagram at this point of intersection there is no horizontal reaction. For the jaw, the top jaw if you draw the free body diagram then at the point of intersection there is no horizontal reaction and we simplified the problem we got rid of two unknowns immediately, ok by using symmetry arguments. You do not need to use symmetry argument but then you will end up solving the complete all four free body diagrams and that is not desirable if you can use the symmetry in the problem simplify the problem why not, ok. So that is the idea, ok. So if you can work on it for other five minutes, ok. Now with this extra piece of information if you have not already used it, ok. So what is A? Ok maybe I, this line we saw is the line joining the centers of these two, ok. Now what you do is that you draw this line, this line is parallel to this line. So these two lines are parallel to each other, ok and where these two lines intersect like at this point, ok. So this angle is also alpha, the angle that P makes with this line here is also alpha, ok. And from that point, ok, this distance is A. So for example I can say that P cos alpha into A is the torque of produced by this force P about this inch, ok. This angle here is also alpha. So P cos alpha into A is the torque for this free body diagram, ok of this force about this because the other component will just pass through this. So that is the reason that for example if this entire curved assembly if we reduce it into just straight lines, then the problem will be greatly simplified because all those details are extraneous. Sir I have a doubt. Yes. When we apply the load, we have two hinges in the line of symmetry. Two hinges in the line of symmetry but we, yes. The distance between that reduce when we apply the load. No, no, no, see this right now we are not looking at a mechanism. So for example if there were no material to clamp, then you apply the load of course the distance will change. But in this configuration when you are about to apply load, ok and the presence of the material between the clamps is keeping the system in equilibrium, ok. So we have put some rigid clamps, ok or whatever some material at the clamps. So the system currently is in equilibrium in that configuration and what we want to know is that in that configuration, ok what is the force that is acting at the clamp given the force that handles it. In the diagram of any of that. Yes. Component, we still have a horizontal component at the hinge. At which hinge? The symmetric hinge, the hinge on the line of symmetry. There can be horizontal component if you disassemble those two, ok but only thing that by symmetry. What is symmetry that you take this here, you rotate about the center line, ok. It will look the same. Let us just think about it. You just flip it, you will exactly get the same figure. So there is a symmetry about the center line joining the two center hinges. And that symmetry ensures that there is no horizontal reaction, ok that will add those two, both connection points. And now on watch free world diagram, both top free world diagram and the bottom free world diagram. Can you see this, ok. So what we have done is we have just made a simple caricature. This is the center point, ok. Back to this. This point is this. This center point is this, ok. So all the extraneous details we got rid of. And what we did is that, that this entire handle, we can just replace it by a nice straight of, a pair of straight lines. So this is one line, ok. This is this particular line EB, ok. This line EB is just this. Line joining the center of this and the center of this, ok. I will pose this, ok. You can use these figures if you wish to. So this is EB. And from the dimensions given in this figure, what we have seen is that this line, ok, is perpendicular to EB. Similarly for the top figure also, this line will be perpendicular to EB. So this distance is A. This is the right angle. Now from symmetry we saw that there is only vertical force, no horizontal force. Can everybody see this figure? Is it clear? Ok, no horizontal force. So there is only one vertical force. At point B, there is a possibility of having two forces, ok. There is a possibility of getting two forces. But for this free body diagram, if you take sigma FX equal to 0, you immediately see that FBX has to be 0. And then for this free body diagram, if you take moment about point E to be equal to 0, ok. Then you immediately get what is the value. But what is the moment about point A? So it will be P A cos alpha, ok. Because we want this horizontal distance which is A cos alpha. So P A cos alpha will give you distance, horizontal distance between this point and B. Minus B sin alpha will essentially give you that what is the horizontal distance of the line of action of P from E, ok. So P A cos alpha minus B sin alpha, ok, should be equal to FBY times B sin alpha. So that is an equation. You can immediately find out what is FBY. Now come to this free body diagram. What we know is that, that what is happening is the clamping force, ok, is trying to rotate this free body diagram, from the jaw about point C. And if you then immediately see that, if you take torque about point C to be equal to 0, or the moment balance about point C, similarly since FBX is 0, this goes away. So FBY into E, this is E, is equal to clamping force into C. So you just use these two equations and you will immediately see that Q will be given by P E by C A by B cos alpha minus 1, ok. Which I think very close some answer, some people got it, because we are doing this problem in a hurry. I am sure that if you do it at some leisure, then you will exactly get this answer, ok. It is ok, because there are so many distances and we are doing it in a hurry, ok. If you do it at leisure, ok, everything will work out fine. Is the overall idea clear to most of you? Q is equal to P or less than or greater than? It will have to be more than P. More than P. Yes, because it is a machine. So the advantage is that, why are we doing this? Why don't we just go there and hold it like this?  A is very large, ok. So what you can say that A is extremely large, you can throw away that 1, ok. And then A will essentially win over everything. Take some extreme limit. So that is the mechanical advantage you have. Otherwise I can just go and hold it like this, right. But that is too much force. So there is one thing that I can tell immediately is this. The solution looks like this. E by A, A by B, ok. So what you can see here is that, that you can have double advantage is what I can tell you. That A by B is a number which is more than 1. E by C also if you ensure is a number more than 1, then you are getting more advantage than just having one plan, ok. Less force will be applied. So for less force because we are multiplying 2 numbers which are more than 1, ok. So that may be one of the reasons, ok. But again that is speculation. Because if you look here there are 2 ratios involved. E by C, ok. And it is A by B, ok. And alpha, if you keep to be very small, then just note that cot alpha will be very large when alpha is very small. So you are getting a significant amount of advantage, ok. Mechanical advantage with this one. Because when alpha becomes small, ok, cot alpha becomes large. When alpha becomes close to pi by 2 and becomes very large, cot is just inverse of alpha. So when tan is small, cot is large. So it is a huge advantage that we get here. E by C greater than 1. A by B greater than 1. Cot alpha very large. One you can almost forget actually, ok. So one would be very negligible compared to A by B cot alpha. Actually there are numbers for this problem, ok. So this is, I got it in symbols because it is very easy to display the solution. Because numbers what happens is that like you do something, you may do two mistakes and you get some number which is very close to the actual value. With symbols you cannot lie with the symbols. Numbers you can always fudge. There is idea clear but there is significant amount of mechanical advantage that is coming in this one. Can we move on to the next problem before we start the quiz? This is from the older version of Bear and Johnston, ok. So if you get hold on older version of Bear and Johnston, it has some really interesting problems, ok. So what we have here is an assembly. So like in many problems which we had done yesterday, we have a rigid post which is nicely bolted. So for all practical purposes we can take it to be a rigid body. Nothing to do with no free world diagram that is involved. But what is happening here is that we have a hoisting mechanism to hoist this truss. Now all these details of the truss are extraneous. We do not really need them. How are we hoisting it? We have two parallel members ABC, DEF. We pin this member DEF at point F to the truss. We pin ABC to point C, ok, to the truss. And for simplicity what the textbook tells us is you assume, ok, that the pin at C can only transmit horizontal force, no vertical force. This is only to make the structure statically determinate. That at C there is no vertical reaction even though it is represented as a pin, ok. But what I am telling you is that if you think about it that restriction is not required, but it simplifies the problem, ok, that at point C, ok, even though it is a pin, ok, only horizontal reaction, no vertical reaction can be transmitted. It is written in the statement of the problem. Now this assembly, what are we doing is for this assembly we are hoisting it using this hydraulic cylinder which is attached to this main portion at point H. Now how are we raising or lowering? Look in this position, if you increase the length of this arm, this parallelogram can deform go up and the assembly will go up. If you reduce the length of this arm then the parallelogram which is like this will come back and the entire assembly can be lowered. This 5 kilo Newton, ok, is the weight that we are lowering or raising and what we are asked that for this particular configuration, ok. So for example what I have seen is that some of you are asking that the system will move. So what I have to tell you again is that in this particular course what we are interested is if you are cosy statically lowering or raising or if you are holding this assembly in a particular position then for that position what are the forces and what we are asked here is that given this is the geometry of the problem what is the force that is exerted by this hydraulic cylinder at point H, ok and all the dimensions are given to you. So there is one, a naive way of solving this problem, there is an elegant way of solving this problem, ok. So why do not you have a go at it? Any questions you can ask me. Towards then I will flash the solution, ok. What we are asked, ok, just think about the problem. Is the hydraulic cylinder is attached to the main vertical wall or the main vertical pillar at point H. So what are the forces exerted by the hydraulic cylinder at point H? So we are going to find out FHX and FHY for simplicity and all the dimensions are given. The problem from old Beer and Johnson, get that book if you have, there are many, many nice problems. The new one does not have that many good problems. Problem clear, is there any issue with the problem statement? Only thing that is not clear from the figure is that at point C which is at the top even though it looks a pin joint just for simplicity in the textbook it is given that point C can transmit only a horizontal force, no vertical force. But I assure you that even if that restriction is not there you can still solve this problem. A B is not a two force member. Again see, A B C is a whole rigid member. A B is not a two force member. Similarly D E F is a full member. But B E which is a vertical link, that is a two force member and of course the hydraulic cylinder is also a two force member. Strictly speaking it is not because of the weight but the weight is generally smaller as compared to the other quantity, other forces involved. No H X is not 5. Okay, H Y is how much? 5. 5, H Y is not 5. H X is 5, H Y is 5. No. See note one thing, there is a consistency in H X, H X and H Y both are 5. Then the inclination of that member should be 45 degrees which is clearly it is not. So you know that H X and H Y cannot be both equal. Okay, but the member in the middle portion is 12.5, that is fine. Also for example, if you report that, it is a two force member you should in principle also report its compressive or tensile. But in this case it does not matter because that is not the final goal of this problem. So the consistency check even without going into any details is that H X and X Y should not have the same values because angle is tan inverse of 1.2 by 0.8 with respect to horizontal and not 45. So let me quickly go over okay because we are running out of time. So the way, so everybody can find out force in link B. Everybody can right? Or is there any doubt about finding force in link B? Yeah, you can say something. Okay, let me put it this way. Most of you, can you not solve force in member B? You can solve? Yeah, yeah please. Okay, let me do that okay. So the way I can explain okay. So let me just flash this thing here. Okay, you can see that if you draw a free body diagram okay, for the truss okay, free body diagram for the top member what you will see is at point C according to the problem there is only horizontal force okay. Let me go again here. So point C there is only horizontal reaction. Point F, there can be two reactions both vertical and horizontal. Then by drawing the free body diagram of this okay, we can find out all these three forces fcx, ffy, ffx. You agree with me? Okay, you can find all the three forces. Find simple equilibrium. You can talk about point F, find out fcx, equilibrium in the horizontal direction, find ffx and p will be equal to f of fy, straight up, straight forward. So all three are obtained. Now what we do okay is coming back to this problem again. We know what are the reactions at point C and point F. One horizontal reaction, horizontal and vertical. So we look at this member okay, member ac. We look at member ac. Then what you see is that there is an internal member be. What is that member doing? If the be were not present then what will happen is that this fcx will have nothing to balance its torque for member abc about point A, right? So from that as a few of you obtained, you can obtain what is a member force in member be. Note that we have taken the line of action from member be on to rod abc downwards. So what we have implicitly assumed that member be is in tension. Okay, member be is in tension, it is downwards. So we can solve for this. And as few of you obtained that fbe will be in 12.5 kilo Newton in tension. Now what we do is look at the bottom member bef. Now this fbe will act equal and opposite. Okay, it is a tensile force. It will act, provide a pulling force at point B. There is ffy, ffx. If this force were not present then there will be nothing to balance the moment for this free body diagram about point D from this okay. But what is additional constraint that we have here? Okay, we have the additional constraint we have is that there is a hydraulic cylinder which is attached at point E. So now how many unknowns do we have? We have one unknown. The direction of that unknown is known. Okay, so we can have the horizontal and vertical components easily. ffx, ffy are known. So for this free body diagram, taking moment about point D, we can immediately find out what is fhx and what is fhy. Okay, and there is an even more elegant method to solve this problem. Okay, I will quickly flash that. And this follows. What we do is this, like using the trick which we used yesterday for the top truss. Okay, for the top truss, take your x and y axis which are not straight but which which are inclined. Because then the y axis is along, since then the x axis is along the member ABC, the inclined axis. And this is the y axis. So what we will do is that, that for this top free body diagram, take equilibrium in this inclined direction. Okay, you can immediately say that you have fxy. Okay, this is y. Plus fy is equal to p cos theta. Immediately, p can be written as p cos theta. Now for these two, we just have equal and opposite reactions when you just go along. And you can take for this free body diagram you will get one equation like this. Second free body diagram, take moment about point D. You will again get an equation like this, both in terms of fbe, fcy, ffy. Now just add these two equations. What you will get is a simple equation of this form, ffy plus fcy which is nothing but p cos theta into all the momentum will be equal to the force in the hydraulic cylinder. So in four steps, you can solve this problem. Okay, and get the answer to that. Think about it. That instead of resolving the forces in x and y direction as horizontal, you keep your x and y axis which is tilted. How much is the tilt? The tilt is along the direction abc which is the same as the direction of the ef. Think about it, try it. If you got it, it's great. If not, you can talk me afterwards or just think about it. It will come over. What you will realize is that that we can just write three and four equations and without solving anything, it will be a very transparent answer and it will be extremely transparent answer because you immediately know a simple relation between the applied force, angle of this link, applied force, and all the distances. Very transparent answer will come which will not be clear from the earlier procedure which is simple but a bit convoluted. So idea is that again by choosing appropriate coordinate axes you can really make the problem much simpler than it was.