 Today we are going to do a little demonstration on calculating pressure, in this case the personal standing pressure, or the amount of pressure that you put on the ground whenever you are standing at rest on your two feet. In order to participate along with us, you're going to need a pencil, some graph paper, a ruler, and a stocking foot. We're going to start here by talking about exactly what pressure is. If we want to calculate the pressure, we're going to need to know two pieces of information. To calculate the pressure, we're going to need to know a weight and an area. Well, in order to calculate your personal standing pressure, you'll need to know your own weight. For example, my weight might be 180 pounds today. And then we'll also need to know the area of you standing on two feet. So I'm going to put area of two feet here as something we need to calculate. And that's what we're going to do next, is go ahead and calculate the area that we are in contact with the ground. To do so, I'm going to start by taking my foot and tracing it on the piece of graph paper. I'll orient my foot so it fits on the entire page. Probably have to do so at a bit of an angle depending on the size of your foot. If you have a much larger foot, you may need two pages of graph paper. And then I do the best I can to trace my foot where it's contacting the paper. Now that I've completed that process, I'm interested in figuring out how much area my foot takes or how much area my foot is on when it's on contact with the ground. To do so, I notice that there's a whole bunch of little grids here. That's why I did this on graph paper. So what I'm going to do next step is to go ahead and count the grids. Well, this could be a long time counting all the grids, so I'm going to speed the process up a little bit by recognizing that I can do the grids in maybe larger chunks, larger grid sections. In this case, my graph paper is already conveniently sort of divided into groups of five. So I'm going to go ahead and take advantage of that fact and identify larger five-by-five boxes. Now that I've sort of drawn out where those boxes are, I can identify all the complete boxes where I will know that there are 25 of these smaller grids inside one of the larger complete five-by-five boxes. So I'm going to identify all of those complete boxes by numbering them. You'll notice I had to make an executive decision in here about what a complete box actually is. For example, here on box number eight, you'll notice it cuts off a little bit of a corner, and I'm going to make the decision that any box that has the center of the box inside the outline of the foot is going to count as being inside the area, and any box that doesn't have the center will be considered as outside. So using that basis, I've decided that box number eight here is a complete large 25 box. Similarly with box number 12 and even box 14, which appears to follow right along the line, we're going to consider to be sort of a complete box. Now that I've identified 16 of these larger grids, I understand that there are 16 boxes of 25 smaller grids, but now I also need to count all the other boxes around the periphery, all the partial boxes. So I can do so. I'll pick a starting location here and identify how many boxes are associated in each partial one. For example, here I'm going to count one, two, three. I'll identify that there are three smaller grid boxes there. I will look and notice that there are five, 10, 11, 12, 13, 14, 15, 16, 17. 17 boxes, smaller grids associated with that larger box. And I'll continue to do so all the way around the perimeter of the foot until I've counted all of these parts. Now that I've identified the counts all around the perimeter of the foot, now I need to sum up all the number of grid boxes around the outside. I'll do so basically by adding around the outside here in a clockwise direction. So now that I've counted that there are 242 smaller grid units around the outside, and I recognize that there are 16 times 25 if we count the larger boxes, I can find the total number of grids here. So 16 times 25 is going to be 400 grids plus 242 smaller grid units. So our area of one foot is going to be equal to 642 GU, which I'm going to say are these smaller grid units. So I've now established an area for my foot. However, grid units, small units on graph paper, aren't necessarily standard units. We're going to need to put those into units that other people use so that our communication makes sense. I mean we could calculate using these grid units, but if I wanted to compare the size of my foot to somebody who used the different size grids on their graph paper, it would be hard to make those comparisons. So now we want to sort of convert our grid into a standard unit. Now we're going to need to be a little careful with this because this is a common mistake that students will often make the first time that they're working with area and making conversions to area. So I'm going to start by making a relationship between our grids and our standard unit system. In this case I can choose to do either inches or centimeters. I'm going to go ahead and do inches here because I'm using pounds, which is in an English system, so I'll go ahead and use inches to stay in the English system as well. I'm going to turn my paper here and use this length along the side and draw a line of a known length. I'm going to go ahead and decide that my line is going to be six inches long. So I've identified that this is a six inch line, six inches, and now I'm going to count how many grid boxes are associated with that six inches. One, two, three, four, five, ten, fifteen, twenty, twenty, five, thirty. As it turns out, much graph paper is somewhat standardized. In this case there are five grids per inch. In other cases there are four grids per inch is another sort of standard for measurements of graph paper. But I recognize here that sixty inches is equal to thirty grid lengths, and I'm going to make sure I label that as grid lengths because that's different than our grid units, our grid boxes that we were talking about before. Okay, and that's just important. So I'm going to sort of make a note here that sixty inches equals thirty grid lengths. Well, I'm going to note, I can convert that, that one inch is equal to five grid lengths. Noting the ratio, six to thirty is the same as the ratio of one to five. So there's a conversion. However, this is a conversion of linear length and not a conversion of area. One thing I want to sort of notice here is that it's important that we convert a little bit differently. If I consider an inch, you'll notice it has five grid lengths, but if I consider an inch of area, one inch by one inch, you'll notice that's a total of one, two, three, four, five, five by five equals twenty five grid units is equal to one square inch or inch squared. So our conversion of one to five is not the correct conversion. We need to actually do that conversion twice or recognize that one square inch, one times one is five times five or twenty five of my grid units. So we're going to go ahead and make that conversion to figure out our area of one foot over here. So I'll take my area of one foot, 642 grid units, and I'm going to go ahead and convert it. I'm going to actually use my two linear conversions and recognize that five grid lengths is one inch and five grid lengths is one inch and recognize that a grid length times a grid length is one grid unit. So that will allow me to cancel out a grid unit with a grid length times a grid length and that will give me my answer in inches squared. So now I simply need to do the math, 642 divided by five divided by five and that will actually give me a value 25.68 square inches. Now I have to be a little careful here because I wrote 25.68 square inches because that's what my calculator told me but I also have to realize that I wasn't particularly careful. I wasn't counting down to quite that level of detail when I was figuring out how many dots I have. So we're going to keep the appropriate number of significant figures here. Notice I have three significant figures in my number 642. So that's the most that I can actually keep here. So to be more appropriate, I'm going to actually record this as 25.7 square inches. Now some of you might point out, well what about the five and the five here? You actually have a pretty good point there if you would point out that I only can keep one significant digit with these fives. Although if I go back and if I'm a little more careful about thinking about my measurement of one inch per five grid lengths if I look a little bit more carefully, I can probably record that five grid lengths to at least two more decimal spaces that one inch is within two decimal places, 5.00 grid lengths without doing any rounding. So I still feel comfortable in keeping three significant digits but probably not more than that. Alright so now I've established the area of one foot, 25.7 inches squared. But notice when I'm standing on the ground, I'm actually going to be standing on two feet. So the area of two feet is going to be this area times two. So I multiply that by two, I get 51.4 square inches. Now that I've established that value, I can take it back here to my calculation up here, 51.4 inches squared. And I can do that division, 180 divided by 51.4 gives me 3.50194. I can't keep all of those decimals, I can keep the 3.50. And now my units are pounds per inch squared, which we typically abbreviate as PSI. So the pressure that I exert on the floor when I'm standing on both feet at rest would be 3.5 pounds per square inch.