 Hey everybody welcome to tutor terrific today. I've got another physics video for you in unit one. This is lesson four We're going to be looking at compound unit conversions today And I'm going to give you an introduction to the idea of estimation Doing a lot of estimation as physicists. So let's get started So I want to just practice the last video lesson three We really looked at a lot of single unit conversions. And so I just want to practice some more I have three here. Remember that we are using the factor label method. We start with the units we have and We then multiply that by a conversion factor with the units I want on top and the units I had originally on bottom Thus canceling those units I had and getting to units I want and this works if you have multiple linking units Involved in your factor label method Everything will cancel except your desired unit. So let's look at 1.4 times 10 to the 3 Kilometers, I want to convert that to feet. Well, there's many steps. I need to do in order to make that happen First kilometers needs to be converted to the standard unit of meters. So that's done by Multiplying by 10 to the 3. I've 10 to the 3 meters on top and 1 kilometer on bottom That's a prefix conversion factor that cancels the kilometers and turns it into meters Then I'll go from meters to centimeters because I have a conversion factor from centimeters to inches So I will then put meters on bottom in the next step and Centimeters on top. I know that one centimeter gives me 10 to the minus two Meters using my prefix table that I showed you a couple lessons ago Then if you're forgetting how to get from inches to centimeters I have a huge chart over here for you and we'll go to the length section of this chart And you can see that one inch equals 2.4 Excuse me 2.54 centimeters and they put exactly there for some reason. Okay, somebody was doubting that it is exact So one inch on top 2.4 centimeters on bottom. So centimeters cancel Then I'm gonna convert from inches to feet the last step And I know that there are 12 inches in one foot So put 12 on bottom with the inches all of these linking units cancel Including the units I had originally and my final units will be feet Specifically if you round to the proper sick things you get 4.6 times 10 to the 6 feet That's a lot of feet Considering that the Earth's radius is about 6,380 kilometers Man, there's millions of feet as you go through the earth to the other side. Wow All right, let's convert one year to minutes Okay, pretty straightforward After all One year we need to go to days first because I know that there are 365 days in one year So put 365 days on top and one year on bottom Then convert that to hours because there are 24 hours in one day and then convert Hours to minutes 60 minutes in one hour So all those linking units make sure the years cancel days cancel and hours cancel and you're left with just minutes on top now I Can only put one sick fig. I know from the song 525,600 Minutes I know that there are that many exact minutes in a year But I wasn't very accurate with my year could be one year It could be up to one and a half years. I only have one digit there So I can only round this to one significant figure in scientific notation. That'd be five times ten to the five Minutes that's as accurate as I can be that's how numbers are treated in physics Lastly 0.72 gallons converted to milliliters. Okay, that's interesting We haven't done a lot of volume units yet And I haven't even told you what the SI unit of volume is however. We have This conversion to do now you might need to look at this chart because If there's a conversion from gallons straight to liters We'd be set we'd only have two steps that I could convert liters to milliliters And if you look at the chart down here voila one gallon equals four quarts sure But it also equals three point seven eight five four liters bingo That'll be our first conversion factor that we use As I did here. I converted gallons to three point eight seven eight five four Leaders and so gallons cancel and then I need to convert liters to milliliters with a prefix conversion Millie again stands for ten to the minus three So one milliliter is ten to the minus three liters leaders cancel and I'm left with two point seven times ten to the three Milliliters, okay, that's quite a bit a gallon is quite large All right, so those are single unit conversions There are these things called compound unit measurements Such as meters per second or kilometers per hour. We're gonna learn many quantities that are in compound units gallons per meter or Leaders per foot. There are all kinds of ways you can compound units with the slash and the statement of per in quotes You're gonna work with one unit at a time when you do compound unit measurements Using the factor label method as you're used to however You have to realize that the unit in the denominator if I have to convert it such as this from seconds to hours I have to do it upside down so that the conversion factors have their units canceling for the denominator I'm gonna need to Reconvert in a reciprocal fashion So the unit I want will be on bottom and the unit I'm canceling will show up on top Let me show you an example of that What about seven kilometers an hour? I want to convert that 70 excuse me kilometers an hour I want to convert that to meters per second kilometers per hour to meters per second is one You're gonna do all the time in kinematics. So it's good to get used to it So I'll stop by writing 70 kilometers over one hour like this. Okay, the unit on top You know it before the slash Goes on top and the unit after the slash goes on bottom now the next two steps This first step is to convert the top unit to meters. Okay normal everything normal right now It's a prefix conversion ten to the three meters for every kilometer cancel the kilometers Next I want to convert hours to seconds I do not put the seconds that I want on top now I put it on bottom and I put hours on top so that they cancel. Okay, so that's reciprocal fashion and One hour is 3,600 seconds. I'm starting to truncate the two-step Conversion into one because you're gonna use it so many times one hour is 3,600 seconds Then you have this calculation to do and You end up with in the calculator your answer is proud 19.44 meters per second But you cannot use that answer because you only had one technically one sig fig to start with one And so I can only have one sig fig in my answer this number would round to 20 or 2.0 times 10 to the 1 meters per second. You cannot use all the sig figs you want. Please do not forget that All right, so let's practice with some compound unit conversions Ones that I made up that allow you to use this chart Okay, one meters per second Converted to kilometers per hour. Okay, very similar to the one that was shown on the previous page One sig fig one more time. I want some more practice with that Remember guys that when we're doing this we're working with one unit at a time And we're continuing to use the factor label method But we're gonna note that the unit in the denominator will be converted upside down in a reciprocal fashion Meaning the units were going towards on the bottom So one meters per second one meter over one second Then I'm going to convert the meters to kilometers Okay, and so I put kilometers on top and ten to the three meters on bottom so the meters cancel So the top unit's finished. It's converted now the bottom unit seconds to hours. So I'm gonna place seconds on top in the next iteration of this factor label method and I'm gonna put minutes that I want or I'm going towards on bottom The seconds will cancel 60 seconds in one minute. Then I'm gonna do it again to go from 60 minutes to one hour You know, sometimes I'm doing it in two steps sometimes in one you could go back and forth from seconds to hours two minute to two steps or one step and When I multiply one by 60 type 60 and then divide by a thousand You never need to multiply the ones because they don't change anything. You would get a number close to Four three point six to be exact But I only had one sig fig in my initial measurement So I can only have one sig fig in my answer four kilometers per hour Next we're gonna do 32 gallons per hour converted to liters per second okay Gallons to leaders will occur first and I already know what my special conversion factor is Down at the bottom of this table 32 gallons in one hour. Well, I'm gonna convert that gallons to leaders 3.7 8 5 4 liters in every gallon put gallons on bottom and that number with leaders on top cancel the gallons Okay, the top is finished now. I'm gonna do this hours to seconds in one step Notice how I put the seconds on bottom this time and Hours on top with the correct conversion factor in here So it looks like I'm did multiply 32 by 3.7 8 5 4 and then divide by 3600 and that gives me a number that I will round to two sig figs scientific notation 3.4 times 10 of the minus 2 liters per second Now this last one here is many steps many steps indeed 7 1.7 times 10 of the minus 4 miles per kilogram Now don't ask me why I just made that unit up doesn't really make a lot of sense Converted to meters per gram. Okay miles to meters is quite a few steps So we start with miles we start by writing 1.7 times 10 of the minus 4 miles over one kilogram Notice how I always put the denominator as one the per unit the one on bottom just gets a one next to it Okay, we start by converting miles to feet because I know that there's 5,280 feet in one mile. That's also on the the length conversion factors list up here, which you could definitely Take a screenshot of this and keep for your records if you wish So that will cancel miles now. We're in feet and we're gonna convert to inches 12 inches in one foot Cancel the feet and convert to centimeters 2.54 centimeters exactly in one inch So we're gonna cancel the inches now, then we'll go to Using a prefix. We're gonna go to regular meters from centimeters 10 to the minus 2 meters every centimeter So cancel the centimeters. Okay. Finally. We got to meters from miles in the numerator Going from kilograms to grams in the denominator will be one prefix type step We'll put the old kilograms we had on top this time and we'll put the grams we want 10 to the three of them Down on bottom when we multiply all these numbers on top divide by 100 and divide by 1000 we get the following result in sig figs scientific notation 2.7 times 10 to the minus 4 meters per gram again, don't ask me how I came up with this unit All right. Good job guys. Let's move on All right estimation now. I'd like to introduce this topic by discussing the following thing Measuring tools have other limits than accuracy accuracy. We know from a while ago in my lesson two for this chapter this unit that Accuracy is limited. Your ability to be accurate is limited with each measuring device you use You can improve your accuracy with higher caliber measuring devices But there's another problem and i'm going to illustrate this problem with this story Let's say you were at fallen leaf lake the beautiful fallen leaf lake just south of lake tahoe And let's say you wanted to measure the volume of this lake And let's say you were trying to figure out how to do it You weren't very uh savvy and you just had to get a bucket and you said this to your friend Hey, let's take this gallon jug and measure the amount of water in this lake by dumping out the water one gallon at a time And just keep your track one gallon two gallons and then maybe a million years later We'd finally be done. That's kind of stupid. Okay, you'd also get in huge trouble if you were caught doing that repeatedly so That's not the best measuring tool for the device the problem with this Issue this this problem is that no measuring device can really do this job So what we do in this type of situation? Is estimation estimation is the use of logical approximations and mathematical physical experience To answer numerically based questions. We are not measuring with measuring devices. We are in fact estimating Using logical approximations using our experience our mathematics and physics experience to really get a good approximation To the question in a numerical form So let's say I asked you to estimate the volume of water in fallen leaf lake I'm going to give you a little bit of information to get you going I'm going to tell you that it's one kilometer across. I know that's not really accurate But let's just say on average It's one kilometer across At its deepest point. It's 66 feet deep. It's not a very deep lake compared to Lake Tahoe Now I want you to logically approximate its surface first We need in order to estimate something like this to approximate the shape of this lake What's the cue to that the fact that we are finding the volume? We're going to use some geometric formulas if we can approximate the shape of this lake as something What would we then approximate? It's average depth as these are two questions We really need to answer if we are going to be able to estimate this a lot of estimations You'll do in physics involve you approximating obscure or abstract or amorphous shapes as a simple geometric shapes So with this given information, we are going to do that Okay So let's start with this Based on the average depth and the surface shape approximations Such as the average length across the lake is one kilometer and it's average It's deepest point is 66 feet. I think of a cylinder. That's what I think of a right Circular cylinder the volume formula for a circular cylinder is the area The base which would we assume is circular times the height of the cylinder That's going to be related to the depth and the base is pi r squared So pi r squared h is the volume formula we will use we need a radius and we need a height for the cylinder All units that we use must be the same And si units you must use si units. These are all length units. So they all need to be in meters Okay, what will be our approximation for the radius? It will be exactly half the approximation for the diameter, which was one kilometer or a thousand meters So our radius will be half of a thousand meters 500 meters Also, what are we going to approximate as our average depth? One good approximation to make for a leg Which is kind of like a cone in a way That's a very rough problem rough estimation. You could you might get a little cringy in this this a process But realize we're roughing it here. This is an estimation and it's okay to be inaccurate You're making the most probable accurate models of these shapes And so i'm going to approximate the depth is about half The average depth is about half the deepest depth Maybe that's not very accurate, but we're going to go with it 33 feet And the deepest point I said was 66 feet So I need to convert 33 feet into meters Okay, and it's done by this set of three Steps in the factor label method convert feet to inches. They convert inches to centimeters Then convert centimeters two meters. Okay Sometimes I would put one centimeter equals 10 to the minus two meters or I could put one meter equals 100 centimeters same difference So I'll multiply 33 by 12 and 2.54 and then divide it by 100 and I get approximately 10 meters What we normally do In estimation when it comes to sig figs is we use one or two at the most preferably one Because we know we're being inaccurate. So let's not assume we can have all these significant digits in our Approximations. Okay, so I could round this to two sig figs I'm choosing to round all these numbers to one that I'm actually going to plug into this formula Which I'm ready to do now. I just want to show you a picture of what I'm approximating the lake as 500 meter radius 10 meter depth It's about what we're dealing with here I know it doesn't look like this, but that's about the same volume based on my estimating prowess And so when we compute this boom boom boom Pi times the radius squared 500 meters times the height h we get about 8 million cubic meters 8 times 10 to the 6 meters cubed and that's the unit of volume that would arise from meters squared from r squared and times another meter that would be meters cubed Again, see how I'm rounding to one sig fig 8 times 10 to the 6 meters cubed I'd be there a long time with a gallon jug for sure a meter cubed is giant It's a meter On a side so think of a cube That's the length that each edge is a meter long a gallon jug I'd be there for years and I'd probably die before I finished so Realize that estimation is super powerful. All right guys. Thanks for watching this video lesson five the final lesson in this chapter is soon to come Stay tuned. This is for now falconator signing out