Density Example 1

Jules Bruno
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So here in this example question, it says if the density of an unknown metal is 21.4 g per centimeters, cube express its density in pounds per feet. Cute. Alright. So here that the information they're giving to us is not a given amount. It's actually a conversion factor. It's 21.4 g per one centimeters cute, and they're telling us that we need to get to our end amounts, which will be pounds per feet. Cute. We can set this up as a dimensional analysis type of question because all we're doing is setting things up with conversion factors, allowing them to cancel out and wind up with end units or end amounts. All right, so we need to find a way of changing grams to pounds and changing Centimeters Cube to feed. Cute. So let's do the easier one first. Let's go from grams to pounds here. We're going to use a new conversion factor. Where would he starting out with our first conversion factor? This question actually doesn't have a given amount. Ah, unit by itself. That can happen now. We know that there is a connection between grams and pounds when We talked about the different types of conversion factors. We said here that £1 was equal to 453.59 g grams go on the bottom so that they can cancel out like this. So we've done the easy part. We've converted grams to pounds. Now it's up to us to convert Centimeters Cube 2 ft. Cute. All right, So what we're gonna do first is we're going to say that there is a connection between centimeters and inches. We want to get rid of these centimeters, which are on the bottom. So we actually have to put centimeters here on top. Centimeters and inches air connected, and the relationship is that one inch is equal to 2. centimeters. However, this is cube, and these centimeters here are not. So you would cube the whole thing. We'll come back and see what effect that has on our numbers. So basically, centimeters cubes or cancel out. Now we have inches cube. We want to get rid of inches, so we put inches up here. We want feet. Remember, there's a connection between ancient feet, and that's 1 ft is equal to 12 inches, these inches air cubed. But these air Not so I'd have to cute this whole thing, and this would represent my conversion factor for inches. Cancel out in just cubes. Cancel out. So what I'd have at the end is pounds over Feet Cube. Which of the units I'm trying to isolate. Let's come down here and see what effect with all of this. Have so we have 21.4 g, and then we have on the bottom one centimeters Cube. We'd have £1 for 4 53. g when we do. 2.54 cube. That's 2.54 times 2.54 times 2. That comes out to 16. centimeters. Cube over one cube is just one over inches. Cube and then 12 cube is 12 times 12 times 12, which is 17 28 inches. Cube over 1 ft cube. So conversion factor and four Counseling. All the units will give us what we need for end amount, which will be in pounds per feet. Cube. If we look, it would be 21.4 times 16.387 times 17 28 divided on the bottom by 453.59 So we get initially is we would get 35.97 But remember the number of sick fixing your your answer is based on the digits given within the question 21.4 has within it three significant figures. So our answer needs three significant figures. To get that, I'd have to convert it to scientific notation. So I go 123 spaces, and this will come out to be 1.34 times 10 to the three pounds per feet cube as our final answer. So this would be a way of converting the units of density from one set of values toe another set of values. Remember, it's treated like a dimensional analysis question. Use conversion factors in orderto isolate your and amounts at the end. It just happens to be here that are end amounts are two units those of pounds and feet cube