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Calculate the weight of air at $20^{\circ} \mathrm{C}$ in a room that measures$5.00 \times 4.50 \times 3.25 \mathrm{m} .$ Give your answer in newtons and in pounds.

$859.95 N=859.95 N \times \frac{0.2248 \mathrm{Ib}}{N}=193.32 \mathrm{Ib}$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

McMaster University

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this problem asked us to find the weight in both new ins and pounds of a massive air at 20 degrees Celsius and were given the dimensions of that mass of air. In order to solve this problem, there's a few things that we're going to need to know. In addition to what's laid out in the problem, we know that the density other materials equal to its mass divided by its volume. We can look up that the density of air at 20 degrees Celsius, which is what's relevant to our problem, is equal to 1.2 kilograms per cubic meter. We can also, um, know that we're going to need to convert whatever mass we figure out from that density equation into a weight. To deal with that and new ins, we can know that weight in new ends is equal to mass in kilograms times acceleration due to gravity in meters per second squared, and then we can also take that weight in new ins and use the fact that one knew in is equal to £0.2248 those air provided by our texts, we can look that conversion up should we need to? The first thing we're going to need to do is we're going to need to find the volume of this air to do so where it is going to multiply out. Our three dimensions were given length with and height. So to find volume of our air, I'm going to do a 5.0 times 4.50 times 3.25 meters. I do that and I end up with a volume of 73.12 five cubic meters. I'm not going to round quite yet until we get to the end of my problem. Um, I also do already know from the information I gathered before I started my problem, that the density of air is equal to 1.2 kilograms per cubic meter. And now what I'm going to do is I'm going to rearrange our density equation so that I can solve for mass. I know density is equal to mass divided by volume. I can multiply by volume on both sides and I end up with mass is equal to volume times density row. Now I can calculate the mass of this air to do that. All I need to do is take my volume, which we just found 73.1 to 5 cubic meters and I went to multiply it. By the density of our air, we could do a quick dimensional analysis to double check of This will give us the quantity that we want and it will because our meters cubed will cancel out and we will be left with a mass of 87.75 kilograms. Now that is our mass. We need to find the weight of this air first to find the weight of this air in new ends going to do the Newmans calculations in red. We know that weight is equal to mass times gravity. So I'm just going to do my mass 87.75 times acceleration due to gravity, which is 9.8 meters per second squared gives me a weight off 8 59.95 new ones. And now to find it in pounds, what I know from my conversion chart in my text I know that one knew in is equal to 0.2248 pounds. So all I need to do is multiply my weight in new INS, which was 8 59.95 times that conversion factor. And that will give me this weight in pounds of 1 £93.317. And if I would like, my initial dimensions were given with three significant digits, so I can put thes each with three significant digits as well. So my final rounded answers to three Sig figs is 8 60 noons and 1 £93.

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