Dimensional Analysis Part 2
These problems involve setting up two conversions in order to reach your goal. The video solves two problems
Unit conversion problem 1. Convert 14 lb/week to ounces/day
Problem 2. 17 centimeters/minute to meters /hour
Welcome to MooMooMath where we upload a new Math video every day. This is part two of dimensional analysis, and completing unit conversion. In the first video we worked on several problems that were a little easier. For instance we worked on converting from feet per hour, and our goal was to convert to miles an hour. The reason that these were easier is if you notice the hour is on the bottom, and we only need to get to complete one conversion and put the feet on the bottom. Next you would put miles on the top and ask yourself which is larger and the miles is larger and place a 1 on top, and then just multiply straight across and you are left with miles an hour. What if you get a question in which you have more than one conversion? Let me show you what I'm talking about. You are lifting weights (this is a pitiful example) and you can lift 14 pounds in one week. You want to know how many ounces a day you are lifting. Our goal is ounces a day. If you look we have week and days, so we can't just go straight across. Don't fear. It is really not that difficult. Let's go ahead do this. The first thing we do is get rid of the pounds by putting pounds on the bottom and put ounces on top. Again. I ask myself "which is larger?" I know a pound is larger than an ounce. If I have 1 pound how many ounces do I have? That will be 16 ounces. We now have the ounces on top. What you may want to do is cover up this term, and now get rid of the week by placing week on top and day on the bottom. I ask "Which is larger, day or week?" There are 7 days in one week. I then just multiply straight across, but before that I will cancel. We are left with ounces and days. Now let's do the Math. 14 x 16 =227, and 1 x1 x 7 =7. Then when you divide 227/7 = 32 ounces per day.
Let's go with one more example. Let's go with, I can travel 17 centimeters in a minute on my bicycle. I want to know how my distance in meters per hour. When I look at this we have minutes and meters so I know I will have two conversions. I need to get meters on top. I will put centimeters on bottom, and put miles on top because that is our goal. I next ask “which is larger, meters or centimeters?" 1 meter = 100 centimeters. Then I need to get hours on the bottom, and get rid of the minute. In order to get rid of the minute I will put minutes on top, and hours on the bottom, and get rid of the minute, and hours on the bottom. Hours are larger than minutes so I will place a 1 by minutes, and a 60 by minutes because there are 60 minutes in 1 hour. Let's see what cancels, and then we have the minutes cancel and we are left with meters and hours. Now we just complete the math and 17 x 60 = 1020, and on the bottom 1 x 100 x 1 = 100. We divide 1020 by 100 and that equals 10.20 meters per hour. There you go, an example of dimensional analysis. Hope that helps. Please subscribe. Remember, MooMooMath uploads a new video every day. Thanks for watching.
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Tagged under: dimensional analysis,unit conversions,converting,Mathematics (Field Of Study),math,maths,moomoomath,word problems,Dimension
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