Archimedian Principle and Vibrating Cylindrical Buoy Analysis

In summary, the Archimedian principle states that the buoyancy force is equal to the weight of the water displaced by a body. In this conversation, a cylindrical buoy with a diameter of 60cm is discussed, which is floating in water with its axis vertical. The question is posed about the buoy's weight, and the solution involves using the period of its vibrations and setting up a differential equation to solve. The conversation also mentions the involvement of math and physics in this problem.
  • #1
kasse
384
1

Homework Statement



The Archimedian principle stetes that the bouyancy force equals the weight of the water displaced by the body (partly or totally submerged). A cylindrical buoy of diameter 60cm is floating in water tiwh its axis vertical. When dupressed downward in the water and released, it vibrates with period 2 sec. Ehat is its weight?

2. The attempt at a solution

The period is 2*pi/w, so that w=pi. But what then?
 
Physics news on Phys.org
  • #2
Model the system. You know the forces acting in it (a function of displacement) so you have a differential equation to solve.
 
  • #3
This must be the first time I've seen m g dabbling in physics and diff eqs..
I hope he won't neglect the pure math section. :smile:
 

What is the Archimedian Principle?

The Archimedian Principle, also known as the buoyancy principle, states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This principle is named after the ancient Greek mathematician and scientist, Archimedes.

How does the Archimedian Principle apply to vibrating cylindrical buoys?

In the analysis of vibrating cylindrical buoys, the Archimedian Principle is used to calculate the buoyant force on the buoy, which is an important factor in determining its stability and motion. The principle helps in understanding how the buoy reacts to external forces such as waves and currents.

What is the significance of studying the vibrating cylindrical buoy analysis?

The study of vibrating cylindrical buoy analysis is important for various applications such as offshore structures, marine transportation, and ocean energy conversion. It helps in designing efficient and stable buoys that can withstand different environmental conditions.

What are the key components of the vibrating cylindrical buoy analysis?

The key components of the vibrating cylindrical buoy analysis include the buoy's geometry, material properties, fluid properties, external forces, and boundary conditions. These factors are used to develop mathematical models and simulations to analyze the behavior of the buoy.

What are some limitations of the vibrating cylindrical buoy analysis?

Some limitations of the vibrating cylindrical buoy analysis include assumptions made in the mathematical models, which may not accurately represent real-world conditions. Additionally, the analysis may not account for all external factors, such as extreme weather events, which can affect the buoy's behavior. Further research and development are needed to improve the accuracy and reliability of the analysis.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
18
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
4K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
7K
  • Introductory Physics Homework Help
Replies
9
Views
7K
  • Introductory Physics Homework Help
Replies
8
Views
6K
  • Introductory Physics Homework Help
Replies
2
Views
11K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Calculus and Beyond Homework Help
Replies
1
Views
8K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Back
Top