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 $3.35 \mathrm{~km}(11000 \mathrm{ft})$ 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 the Earth after the balloons began to burst at the high altitude and the buoyant force decreased. Why did the balloons burst?

On October $21,2001,$ Ian Ashpole of the United Kingdom achieved a record altitude of $3.35 \mathrm{~km}(11000 \mathrm{ft})$ 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 the Earth after the balloons began to burst at the high altitude and the buoyant force decreased. Why did the balloons burst?

Key Concepts

Net Upward Force

Net upward force is the result of the upward buoyant force minus the downward gravitational force (weight) acting on the system. For the balloons, while the buoyant force provides lift, the system's overall weight, including the mass of the balloons and any additional load, reduces this net lifting force. Evaluating the net force helps determine whether the system will accelerate upwards or fall.

Volume of a Sphere

The volume of a sphere is determined by its radius using the mathematical formula V = (4/3)?r³. This calculation is essential in determining the displacement of air by each balloon and, subsequently, the buoyant force acting on them. It forms the basis for estimating how much air is displaced when dealing with spherical objects.

Gas Expansion and Atmospheric Pressure

Gas expansion in response to changing atmospheric pressure is a key concept in the behavior of balloons at high altitudes. As the balloons rise, the external pressure decreases, causing the helium inside to expand. If the pressure difference becomes too great, the increased volume can lead to the structural failure of the balloon envelope, resulting in bursting. This concept explains why balloons might rupture when the buoyant force decreases due to bursting at high altitude.

Buoyant Force

Buoyant force is the upward force exerted by a fluid on an immersed object, which is equal to the weight of the fluid displaced by that object. In contexts like this, where balloons displace air, it provides the lift that allows the balloon to rise. Understanding this concept is crucial for determining how much lift is generated by the displaced air volume relative to the weight of the balloon and any additional payload.

Archimedes' Principle

Archimedes’ principle is central to understanding buoyancy; it states that any object fully or partially submerged in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. This principle is used to estimate the force the helium-filled balloons produce, relying on the density of the surrounding air and the volume of helium in each balloon.

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