On October 21, 2001, Ian Ashpole of the United Kingdom...

On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of $3.35 \mathrm{~km}$ (11 $000 \mathrm{ft})$ powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about $0.50 \mathrm{~m}$ and an estimated mass of $0.30 \mathrm{~kg}$. (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?

Key Concepts

Gas Expansion and Balloon Bursting

At higher altitudes, the external atmospheric pressure decreases. According to the ideal gas law, if the temperature and the quantity of helium remain constant, the helium expands as it rises. This expansion increases the internal pressure of the balloon until it exceeds the elastic limits of the balloon material, causing the balloon to burst. This process explains the failure of the balloons at high altitude.

Net Upward Force

The net upward force on the balloons is found by subtracting the total weight (gravitational force) of the balloons and their contents from the total buoyant force. This concept is important in determining whether the system will accelerate upwards when the lift from the buoyant force exceeds the opposing gravitational force.

Buoyant Force Calculation

The buoyant force on an object, such as a balloon, is determined by the volume of air it displaces and the density of the air. This force is calculated as the product of the displaced volume, the density of the air, and the acceleration due to gravity. This calculation is central when estimating the total upward force contributed by multiple balloons.

Archimedes' Principle

This concept states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. It is fundamental to understanding why objects, including balloons, rise in air. In the context of the problem, it explains how the helium-filled balloons displace air and thereby generate lift.

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