So the term static equilibrium relates a physical observation that something stays at rest or in motion to a theoretical observation that the forces which cause motion change are equal and balanced. So if something is not in motion, it must mean that the forces acting on it are equal and balanced. So notice a single non-zero force, something sitting alone by itself, cannot be balanced. It's going to create some sort of motion if acting by itself. Two forces, however, can be balanced if they are co-linear. In other words, if they're acting on the same line and opposite in sense. Consider, for example, our Statue of Liberty. We know that the Statue of Liberty has a certain amount of weight. We also notice that she doesn't move very much. We consider her to be in static equilibrium. Well, if she is in static equilibrium, it must mean that there is more than one force. And we've observed that there is a force that she's putting a force on the pedestal, which is acting in a direction that's in line with her weight and in the opposite direction. We know in this particular case that the weight has to be equal to the normal force, where n normal is the force perpendicular to the pedestal surface, and w is the weight of the Statue of Liberty itself. If we do a little algebra here, we can see the relation that the normal force minus the weight is equal to 0. If we consider the normal force to be positive, up is positive, and down being negative. Concurrent vectors are vectors that have lines of action that meet at a single point. For example, if I have some sort of ring with cables tied to it, and all of those cables are aligned in such a way that their point of action meets in the center of the ring, these would be an example of concurrent vectors. And usually, we represent the pole of each of those cables with a letter t representing the word tension. Tension is the word for something that is being pulled on both ends. In two dimensions, these vectors each can be described with two components, one associated with each basis. So in order to view that, I need to create a basis. Let me create a Cartesian basis. We'll call an x direction as positive to the right, and a y direction as positive up and down. And we'll make that at a right angle. And then we can look at each of these vectors as having two components. Let me move them off to the side. This first vector, t1, can be considered to have two components. An x component, we can call t1x. And a y component, we'll call t1y. Similarly, for vector t2, we can have a component t2x and t2y. And finally, for our vector t3, we can have a component t3y and also a component t3x. But notice if t3 is aligned with our y-axis, it may not actually have a component in the horizontal direction. Once we've broken these down into components, we can think of each component as acting along the line of action that is parallel to each basis. For example, we can consider only the components that line up along the x-axis. If we do that, we realize that just this t2x is pointing in a positive direction. And the t1x is pointing in a negative direction. We can say that in the x direction, positive forces must balance with the negative forces. In other words, that t2x, which is in our positive direction, is equal to t1x, which is in our negative direction. Or the other way to express that is to do a little bit of algebra and demonstrate that t2x minus t1x is equal to 0. In other words, that the sum of all the vectors in the x direction is equal to 0. If we are careful and make sure that we keep track of the signs to represent which direction the force is acting in. Similarly, if we do that in the y direction, we take all the positive and set them equal to the negative. We recognize that t1 in the y direction is pointing up, t2 in the y direction is pointing up. And that's equal to t3, which is in the y direction, pointing down. We could say t3y, but that's equal to t3. Or, again, we can do the algebra and express them as a sum of all of them, noticing that ty is positive, t2y is positive, and t3 in a downward direction is negative. So that's equal to 0. In short, what we recognize here is that the sum of forces in the x direction is equal to 0, and the sum of forces in the y direction is equal to 0. Using a notation called sigma notation, using the Greek letter sigma, which means we're adding up all the forces in the x direction and adding all the forces in the y direction. If we're in 3D, we can also recognize the sum of forces in the z direction would also be equal to 0, but most of our examples are going to be in 2D. So these are the conditions for static equilibrium if all of our forces are concurrent, if they're all acting through a common point. Let's consider a practical example, shall we? Here's a stop light hanging from a couple of cables. And each of those cables are attached to rings labeled A, B, C, and D. Actually, A, B, and C, D is actually the connection to the stop light itself. Well, we might be interested in knowing the amount of tension in the cables, knowing how much each cable is pulled, because certain cables can only hold a certain amount of weight, and it might be important to know how much weight that is. Let me go ahead and provide some information about this particular system. First of all, we're probably going to need to know the information about the geometry of the system. So we're going to say in this particular case that this length from A to directly above C is going to be 10 feet, and the remaining length is going to be 20 feet, and that a distance at C is below that straight line is going to be 3 feet. That geometry is going to be important to figure out what's happened. If we decide to change the length of the chain or the position where the stop light is, it's going to change the forces that are inside. We also want to identify how heavy the light is itself, and we're going to say that it has a weight of 30 pounds. So if we want to solve a problem like this, the first thing we're going to do is go ahead and create a free body diagram. So where's the best place for a free body diagram? Well, if we're interested in the tension or how much forces each of the cables, we're going to draw a free body diagram around the ring where all three cables come together. That will separate the ring out, and it will replace each of the cables with a force. Let's take a look at a close-up of that free body diagram. Here we have the tension in each of the three cables. The tension from A to C, the tension from C to B, and the tension from C to D. We happen to know what the tension from C to D is. That's going to be equal to our 30 pounds. The amount that the cable has to pull up is equal to the weight that's being pulled down by the stop light. And that same tension is going to be 30 pounds pulling down on our ring. So now that we've created our free body diagram, let's go ahead and think about each of these vectors in terms of components. We're going to recognize that they all meet at a common point. We'll need a basis to create a basis. Let's define the X direction as positive to the right and the Y direction as positive vertically. We'll make it perpendicular. And now we can break each of these up into the component parts. We're going to recognize that CD only has a component in the Y direction. Let's do the components in the X direction for CA. So we have TCA in the X direction. And we have a component here, TCB also in the X direction. And then we have components TCA in the Y direction and TCB in the Y direction. Notice we're also going to need a little bit more information here. Let's go ahead and give the angles the directions of these each a name. This will be theta or angle CA and let's call this theta angle CB. Now that we've identified component vectors, let's go ahead and apply static equilibrium. In other words, let's make the assumption that all the sum of forces in the X direction is equal to zero. Now that we have that sum, we notice that we have a force in the X direction, TCB in the X direction. And we have a force also in the X direction, TCA in the X direction, but in the opposite direction, so we'll give it a negative value. And we know those two together must sum up to be equal to zero. Now that's not particularly useful because we don't know what those values are. However, we can relate those values to things that we do know what they are that we might want to know what they are. We can figure out the angle. So let's go ahead and use a little bit of our trigonometry to recognize that each of these X components is related for the tension itself through the cosine of the angle. So TCBX is equal to TCB times the cosine of angle CB. Similarly, TCAX is equal to TCA times the cosine of the angle CA. We can also then apply the sum of forces in the Y direction. Noticing that TCAY is in a positive direction. We add TCBY, which is also in a positive direction. We also have to include in this case the 30 pounds for TCD, which we recognize as being downward in a negative direction. And when we sum those together, we recognize that they are equal to zero. The sum of forces in the Y direction is equal to zero, so those are equal to Y. We also recognize that their relationship in the Y dimension uses the sine of each angle. So TCAY is TCA times the sine of the angle CA plus TCBY, the yogurt place, is equal to TCB times the sine of the angle CB. We subtract our 30 pounds and that entire sum is equal to zero. So what do we do with this information? Well, now we have to refer to the information we know about the geometry of our system. We have to see if we can figure out what these angles actually are. For example, here is my angle theta theta minus theta. CB, and here is my angle theta CA. See if we can figure out what those angles are by the relationships in the geometry. We'll notice those are both parts of triangles that we know the sides of. I'm gonna do a little calculation here. Let's first of all find the hypotenuse of each triangle. That length AC is going to be a squared plus b squared equals c squared is gonna be the square root of 10 feet, which is that horizontal length right there plus three feet, which is the vertical distance. But in both of these cases, we have to square each of those, a squared plus b squared equals c squared. And we find out that the length of segment AC is about 10.44 feet. If we do a similar calculation for length BC, we find that length BC is the square root of 20 feet squared plus the three feet squared. And we find the length of BC is 20.22 feet. Well, how is that useful? Well, now we can use our trigonometric relationship, socotoa, over here on the left, I'm gonna write some angle relationships that would be useful. For example, the sine of angle theta CA, which we'll use below, is gonna be equal to the opposite. Here's the opposite side, which is the three feet, over the hypotenuse, which is the 10.44 feet. The cosine of that angle is gonna be equal to the adjacent of 10 feet over the 10.4 feet. So that's the adjacent side, so that's the adjacent side over the hypotenuse. We can do a similar thing to determine the sine of angle CB, which is now our three feet over 20.22 feet, and the cosine of that angle, which is equal to 20 feet over 20.22 feet. Notice all of the feet units are going to cancel out here, feet divided by feet, and we just get ratios. But we don't necessarily need to calculate these ratios in a calculator right this moment. We can just simply use those ratios in our formula down below. Or you could type them into the calculator if you would like. But notice we found these not by actually calculating the angle. We don't need the angle. All we really need are the trigonometric relationships. We need to know the sines and the cosines for our formula down below. So let's finish this problem. Here's our two formulas. We have TCB times the cosine of CB. That value is 20 over 20.22 minus TCA times the cosine of angle CA. Well, that's the 10 over 10.44. And we know that's equal to zero. For our forces in the y direction, TCA, the sine of CA, let's see here, this is the CA. So this is going to be the three over 10.44 minus TCB times three over 20.22. That's a plus minus 30 pounds is equal to zero. Now that we've added the geometry into play, we now have an equation where we have two unknowns, TCA and TCB, but we have two equations. Now it's simply a matter of algebra. Two equations in two unknowns. If we solve both of those equations and I'll leave that solution up to you, we come up with the tension in CA is equal to 69.7 pounds and the tension in CB is 67.5 pounds. Notice this tension is significantly more than the 30 pounds, it's more than twice as much as the 30 pounds of the stop light itself, which demonstrates why it's important for us to do this calculation. Because in order to hold this stop light up, the two cables have to both pull up, but at the same time they have to add additional force where they pull against each other. They have to balance the vertical force together, but they have to oppose each other and that additional pulling leads to these additional values. So just to recall, static equilibrium, sum of forces in the x direction is zero, sum of forces in the y direction is equal to zero and that should suffice as long as you have concurrent force vectors, all meeting their lines of action at the same point.


Hey, welcome back everybody. Jeff Frick here with theCUBE. We're in downtown San Francisco at Twitter's World Headquarters. It's a beautiful building. Find a reason to get up here and check it out. But they have data privacy day here today. It's an all day seminar, session, series of conversations about data privacy. And even though Scott McNeely said data privacy is dead, get over it, everyone here would beg to differ. So we're excited to have our next guest, Eva Velasquez. She's the president and CEO of ITRC. Welcome. Thank you. Thank you for having me and for covering this important topic. Absolutely. So what is ITRC? We are the Identity Theft Resource Center. And the name exactly what it is. We're a resource for the public when they have identity theft or fraud, privacy, data breach issues and need help. So that begs an interesting question. How do people usually find out that their identity has been compromised? And what is usually the first step they do take? And maybe what's the first step they should take? Well, it's interesting because there isn't one universal pathway that people discover it. It's usually a roadblock. So they're trying to move forward in their lives in some manner. Maybe trying to rent an apartment, get a new job, buy a car or a house. And during that process, they find out that there's something amiss either in a background check or their credit report. And at that point, it creates a sense of urgency because they must resolve this issue and prove to whoever they're trying to deal with that actually wasn't me. Somebody use my identity. And that's how they find out, generally speaking. So you impact their credit score or something in a way that they had no idea is how they, what usually triggers that? Right, right. Or a background check, appearing in a database. It's just when we think about how pervasive our identity is out there in the world now and how it's being used by a wide swath of different companies to do these kinds of background checks and see who we are, that's where that damage comes in. So we're talking about security and security breaches at a lot of shows. It's many hundreds of days, usually, before companies know that they've been breached or a particular breach. I think now we just assume that they're breached all the time and hopefully they've minimized damage. But on an identity theft, what do you find as kind of the average duration between the time something was compromised before somebody actually figures it out? Is there kind of an industry mean? It's really wildly inconsistent from what we see because sometimes if there is an issue, let's say that a wallet is stolen and they're on high alert, they can often discover it within a week or 10 days because they are looking for those things. But sometimes if it's a data breach that they were unaware of or they have no idea how their information was compromised and especially in the case of child identity theft, it can go on for years and years before they find out that something's amiss. Child identity theft. Now what's going on? I've never heard of child identity theft. They usually don't have credit cards. What's down to the story on child identity theft? Or is it just their PayPal account or their Snapchat account? Well, you're right. Children don't have a credit file or a credit history, but they do have a social security number and that is being issued within the first year of their life because their parents need to use it on their tax returns and other government documents. Well, because of the Social Security Administration and the credit reporting agencies, they don't interface. So if a thief gets ahold of that social security number, that first record that's created is what the credit bureaus will use. So they don't even need a legitimate name or date of birth. Obviously, the legitimate date of birth isn't going to go through those filters because it's for someone who's under 18.  And as they get out and start doing things like applying for student loans, which is one of the really common ways we see it in our call center, then they come to find out, I have this whole credit history and guess what? It's a terrible credit history and they have to clean that up before they can even begin to launch into adulthood. Okay, so when people find out, what should they do? What's the right thing to do? I just get rejected on a credit application, some weird thing gets flagged. What should people do first? There's a couple of things and the first one is don't panic because we do have resources out there to help folks. One of them is the Identity Theft Resource Center. All of our services are completely free to the public. We're a charity nonprofit funded by grants, donations and sponsorships. They should also look into what they might have in their back pocket already. There are a lot of insurance policy writers for things like your homeowner's insurance, sometimes even your renter's insurance. So you might already have a benefit that you've paid for in another way. There are a lot of plans within employee benefit packages. So if you work for a company that has a reasonably robust package, you might have that help there as well. And then the other thing is if you really feel like you're overwhelmed and you don't have the time, you can always look into hiring a service provider and that's a legitimate thing to do as long as you know who you're doing business with and realize that you're going to be paying for that convenience. But there are plenty of free resources out there. And then the last one is the Federal Trade Commission. They have some wonderful remediation plans online that you can just plug in right there. And which is a great segue because you're doing a panel later today, you mentioned with the FTC around data privacy and identity theft. You know, what role does the federal government have? And what is cleaning up my identity theft? What actually happens? Well, the federal government is one of the many stakeholders in this process. And we really believe that everybody has to be involved. So that includes our government that includes industry and the individual consumers or victims themselves. So on the government end, things like frameworks for how we need to treat data, have resources available to folks, build an understanding and a culture in our country that really understands the convenience versus security conundrum. Of course, industry needs to protect and safeguard that data and be good stewards of it when people give it to them. And then individual consumers really need to pay attention and understand what choice they're making. It's their choice to make, but it should be an educated one. Right, right. And it just, the whole social security card thing is just, I find fascinating. It's always referenced as kind of the anchor data point of your identity. At the same time, you know, it's a paper card that comes after you're born. And people ask for the paper card. I mean, I got a chip on my ATM card. It just seems so archaic. The amount of times that it's asked in kind of common every day, kind of customer service engagements with your bank or whatever just seems almost humorous in the fact that this is supposed to be such an anchor point of security. Why, you know, when is the Social Security Administration or that record either gonna come up to speed or do you see is there a different identity thing with biometrics or a credit card or your fingerprint or your retina scan? I mean, I have clear, I go through the airport, I can look in my eye. Is that ever gonna change or is it just always, it's such a legacy that's so embedded in who we are that it's just, it's not going to change. It just, it seems so bizarre to me. Well, it's a classic case of we invented a tool for one purpose and then industry decided to repurpose it. So the Social Security Number was simply too entitled to social security benefits. That was the only thing it was created for. Then as we started building the credit and credit file industry, we needed an initial authenticator. And hey, look at this great thing. This is a number it's issued to one individual. We know that they have, there's some litmus tests that they have to pass in order to get one. This is a great tool, let's use it. But nobody started talking about that. And now that we're looking at things like other government benefits being offered and now credit is issued based on this number. It really kind of got away from everybody. And think about it. It used to be your military ID and you would have your Social Security Number painted on your rucksack there for the world to see. It's still on our Medicare cards. It used to be on our checks. A lot of that has changed. That's right, it was on our checks. It was, it was. So we have started shifting into this, at least the thought process of if we're going to use something as an initial authenticator, we probably should not be displaying it ready for anyone to see. And in the big conversation, you were talking about biometrics and other ways to authenticate people. That's one of the big conversations we're having right now is what is the solution? Is it a repurposing of the Social Security Number? Is it more sharing within government agencies and industry of that data so we can authenticate people through that? Is it a combination of things? And that's what we're trying to wrestle with and work out right now. But it is moving forward, albeit very, very slowly. Yeah, the two-factor authentication seems to have really taken off recently. You get the text and here's your secure code and at least it's another step that's relatively simple to execute. So. Something you are, something you have, something you know. There you go. That's kind of the standard we're really trying to push. So on the identity theft bad guys, how is their behavior changed since you've been in this business? Is it, has it changed dramatically? Is the patterns of theft pretty similar? How's that world evolving? Because generally these things are a little bit of an arm race. And oftentimes the bad guys are one step ahead of the good guys because the good guys are reacting to the last thing that the bad guys do. How do you see that world kind of changing? Well, I've been in the fraud space for over 20 years, which I hate to admit, but it's the truth. We'll talk about it. And we do look at it sort of like a treadmill and I think that's just the nature of the beast. When you think about the fact that the thieves are, you know, they're doing penetration testing and we as the good guys trying to prevent it have to be right 100% of the time. The thieves only have to be right once. They know it. They also spend an extraordinary amount of time being creative about how they're going to monetize our information. The last big wave on new types of identity theft was tax identity theft. And the federal government never really thought that that would be a thing. So when we went to online filing, there really weren't any fraud analytics. There wasn't any verification of it. So that first filing was the one that was processed. Well, fast forward to now we've started to address that it's still a huge problem in the number one type of identity theft. But if you had asked me 10 years ago, if that would be something, I don't think I would have said yes, it seems, you know, so how do you create money out of something like that? And so to me, what is moving forward is that I think we just have to be really vigilant for when we leave that door unlocked, that these are gonna push it open and burst through. And we just have to make sure we notice when it's cracked so that we can push it closed. Because that's really, I think the only way we're going to be able to address this is just to be able to detect and react much more quickly than we do now. Right, right, because they're kinda coming through, right? Exactly, they are. There's no wall, there's no wall, pick it up, right? Right, and like you said, they only have to be right once. Nothing's impenetrable. Right, crazy. All right, Eva, we're gonna leave it there and let you go off to your session, have fun at your session, and thanks for spending a few minutes with us. Thank you. All right, she's Eva Velasquez, president and CEO of the ITRC. I'm Jeff Frick, you're watching theCUBE. Catch you next time.