   Chapter 9, Problem 23P

Chapter
Section
Textbook Problem

A spherical weather balloon is filled with hydrogen until its radius is 3.00 m. Its total mass including the instruments it carries is 15.0 kg. (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?

(a)

To determine
The buoyant force acting on the balloon.

Explanation

Given info: The density of air is 1.29kg/m3 , acceleration due to gravity is 9.80m/s2 , and the radius of the balloon is 3.00m .

Explanation: The buoyant force on the balloon is B=ρairgVballoon=ρairg(4πr3/3) .

The formula for the force acting on the balloon is,

B=ρairg(4πr3/3)

• ρair is density of air.
• g is acceleration due to gravity.
• r is radius of the balloon.

Substitute 1.29kg/m3 for ρair , 9

(b)

To determine
The net force acting on the balloon and its instruments after the balloon is released from the ground.

(c)

To determine
The increase of radius of the balloon as it rises to higher altitude.

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