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Space station. You are designing a space station and want to get some idea how large it should be to provide adequate air for the astronauts. Normally, the air is replenished, but for security, you decide that there should be enough to last for two weeks in case of a malfunction. (a) Estimate how many cubicmeters of air an average person breathes in two weeks. A typical human breathes about 1$/ 2 \mathrm{L}$ per breath. (b) If the space station is to be spherical, what should be its diameter to containall the air you calculated in part (a)?

$200 m^{3}, 7.26 m$ respectively,

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

02:16

You are designing a space …

07:00

07:14

Four astronauts are in…

01:59

Four astronauts are in a s…

09:47

04:52

BIO Four astronauts are in…

02:49

03:23

. Breathing oxygen. The de…

05:35

Breathing Oxygen. The dens…

04:33

The density of air under s…

05:31

Respiration A human breath…

03:22

The air that we breathe is…

07:57

The space shuttle environm…

this's chapter one problem. 30 in part. They were looking for the volume of air briefed by a human in two weeks, and he wanted to keep with meters. So let's start with what we're given, which is that a single breath has a volume of half a leader or no 0.5 liters. And now, if we want to know how, that's volume per breath. If you wanted the volume breathes in two weeks, you're going to know how many breaths are taken in two weeks. Well, a typical respiration rate is about 12 breaths per minute, using BR here to denote breaths. So here, 12 breaths in a minute, or not equal one of the number of breaths and one of the unit of time but their equivalent. So if we multiply here, we're going to get a respiration rate and leaders per minute. Now I want to know how many breaths in two weeks, So let's convert that minutes. We've got 60 minutes in one hour. He's a CI for a knauer, got 24 hours in a day, and here thes this fraction of one before it aired, a standard unit converting fractions where we're writing a fractions equal to one. But the top and the bottom, the top of the bottom are truly equal. But they're expressed in different units. And now we've got 14 days in two weeks. Great. So breaths cancel minutes. We're going to cancel hours. You're going to cancel days. I'm going to cancel. And so now this would give us the number of leaders breathed in two weeks if we leave that to attach the weeks instead of dividing the whole rest of the numerical stuff by it. But we want this in terms of cubic meters, so we're gonna have to convert from leaders to keep it meters. And so for this we can look up that there are 1,000 leaders in one cubic meter. And so those leaders are going to cancel. We could multiply everything here out except Lesley. That too, alone in two weeks. And we get about 100 human meters ofher breathed in two weeks, and I'm rounding here to the nearest 100. Since we're estimating, we don't need to be more precise than that. So that's part a in part B. We're looking for the diameter of a space station that can contain this much air so basic and the space station we're told is spherical. So basically, we're given the volume of a sphere. 100 meters cube is the volume and we're looking for the diameter. So we know a volume of a sphere and how it relates to the radius. So let's find the radius first and then just double it to get the diameter. So if a volume it is 4/3 pi are cute. But now I got to rearrange it for if we know the volume finding the radius So let's well distraction over. We have three v pfieffer volume divided by four pi. This thing is equal to r cubed. So let's take the cube root of the whole thing and that is going to be equal to a radius. And so if we take our 100 meter cubed, plug it in for the volume, we can calculate that out and find a radius of about three meters. And so remember we're asked to find the diameter, so we have to double the radius to the diameter of the space station that we need is about six meters

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