The objective of this paper is to find the tension acting on a line that anchors a buoy submerged just beneath the surface of the ocean. Since the problem statement only gives the geometric shapes and dimensions of the buoy, we must use calculus to find its volume and surface area through integration of the volumes and surfaces of revolution formed by the specific parts of the buoy along an axis. The volume and surface area determine the buoyancy force and force of gravity, the two forces acting on the buoy that affect the tension in the line. After calculating this data, we were able to conclude that the tension affecting the line would be approximately 78 kN if the buoy was made of 1% carbon steel with a thickness of 6.35 mm. This problem is useful in several engineering disciplines.
"Buoy Dynamics in Subsurface Zones,"
Undergraduate Journal of Mathematical Modeling: One + Two:
2, Article 5.
DOI: http://dx.doi.org/10.5038/2326-36188.8.131.52 Available at: https://scholarcommons.usf.edu/ujmm/vol1/iss2/5
Arcadii Grinshpan, Mathematics and Statistics
Scott Campbell, Chemical & Biomedical Engineering
Problem Suggested By:
Elliot Findley, Mathematician & Physicist