   Chapter 9, Problem 21P

Chapter
Section
Textbook Problem

A hot-air balloon consists of a basket banging beneath a large envelope filled with hot air. A topical hot-air balloon has a total mass of 545 kg. including passengers in its basket, and holds 2.55 × 103 m3 of hot air in its envelope. If the ambient air density is 1.25 kg/m3, determine the density of hot air inside the envelope when the balloon is neutrally buoyant. Neglect the volume of air displaced by the basket and | passengers.

To determine
The density of hot air inside the envelope when the balloon is neutrally buoyant.

Explanation

Given info: The density of ambient air is 1.25kg/m3 , mass of balloon/basket is 545kg , and volume of the balloon/basket is 2.55×103m3 .

Explanation: In this event, there are three kind of forces are involved they are weight of the balloon/basket (wBB) , weight of the hot air inside the balloon (whot) , and the buoyant force which is equal to the weight of the displaced ambient air wair . By using Newton’s law of motion, the density of hot air inside the balloon is calculated as follows Fy=mayBmBBgmhotg=0 and the buoyant force B is ρairVBBg and the mass of the hot air inside the balloon is mhot=ρhotVBB . After their substitution in Newton’s equations of motion, the density of hot air inside the balloon is identified.

The formula for the density of hot air inside the balloon is,

ρhot=ρairmBBVBB

• ρair is density of ambient air

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