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A hot-air balloon has a volume of 2200 $\mathrm{m}^{3} .$ The balloon fabric (the envelope) weighs 900 $\mathrm{N} .$ The basket with gear and full propane tanks weighs 1700 $\mathrm{N}$ . If the balloon can barely lift an additional 3200 $\mathrm{N}$ of passengers, breakfast, and champagne when the outside air density is $1.23 \mathrm{kg} / \mathrm{m}^{3},$ what is the average density of the heated gases in the envelope?

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0.97$k g / m^{3}$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Nnkel N.

May 3, 2021

wtf bro

Cornell University

Simon Fraser University

University of Sheffield

University of Winnipeg

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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all right in this problem, we want to figure out the density of gas in a hot air balloon and were given that the volume of the balloon is 2.2 tens tend to the three cubic meters. The density of air is 1.23 kilograms per meter. Cute. And the principle that we want to use here is that if the balloon, um is just a tte the threshold for being ableto lift, then the buoyant force should be equal to the force of gravity on it. So let's write out expressions for you to these two forces. So the buoyant force is going to be given by row air times v balloon times, the gravitational acceleration G and then the force of gravity. It will be the way of the gas in the balloon, plus the weight of everything extra that they give in the problem. And this F extra is 900 close 1,700 plus 32 100. So now it's just a matter of plugging in the various values and solving for on row gas, so row gas will be ro air the balloon time's cheek minus of extra over the balloon times G

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