Buoyancy of a Balloon

This Demonstration shows the relationship between the buoyant force and the force of gravity acting on an object. A spherical balloon, for which you can vary the radius and the density of the enclosed gas, is attached to a box, which you can vary in mass. For the system to rise, the buoyancy must be greater than the weight.


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Snapshot 1: The buoyancy of the balloon (around ) is greater than the weight of the box (around ) due to the increased radius of the balloon, so the system rises. The balloon has risen from its initial point with the increase in the time slider.
Snapshot 2: The buoyancy of the balloon (around ) is again greater than the weight of the box (around ), mainly due to the increased density of the gas within the balloon, so the system rises. 
Snapshot 3: The buoyancy of the balloon (around ) is less than the weight of the box (around ). The entire system stays in the same position due to the weight of the box.
The density of the balloon cannot be less than the density of hydrogen at 1 atmosphere (). The density within the balloon varies from to .
[1] L. Taylor. "Practical Buoyancy Control." (May 17, 2014) www-personal.umich.edu/~lpt/practical.htm.
[2] C. Ophardt. "Density Applications with Gases." (May 17, 2014) chemistry.elmhurst.edu/vchembook/imagespdb/123Adensitygas.html.
Special thanks to: The University of Illinois NetMath Program and the Mathematics Department at William Fremd High School.
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