   Chapter 9, Problem 25P

Chapter
Section
Textbook Problem

On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of 3.35 km (11 000 ft) powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about 0.50 m and an estimated mass of 0.30 kg. (a) Estimate the total buoyant force on the 600 balloons. (b) Estimate the net upward force on all 600 balloons, (c) Ashpole parachuted to Earth after the balloons began to burst at the high altitude and the system lost buoyancy. Why did the balloons burst?

(a)

To determine
The estimation of the total buoyant force on the 600 balloons.

Explanation
The total buoyant force on the 600 balloons would be Btotal=600Bballoon and the buoyant of force of a single balloon is Bballoon=ρairgVballoon=ρairg(4πr3/3) . By using these expressions, the total buoyant force on 600 balloons is calculated.

Given info: The radius of the balloon is 0.50m , the density of air is 1.29kg/m3 , and acceleration due to gravity is 9.80m/s2 .

The formula for the total buoyant force on balloon is,

Btotal=600[ρairg(4π3r3)]

• ρair is density of atmospheric air.
• g is acceleration due to gravity

(b)

To determine
The estimations net upward force on all 600 balloons.

(c)

To determine
Burst of balloons at high altitude.

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