# Archimedes' Principle Buoyancy?

• munchy35
In summary, the conversation discusses a question regarding the work done by the buoyant force on a flotation device as it ascends from being fully submerged in water to floating on the surface. The solution involves using both Archimedes' equation and the equation for work, with the final answer being found through integration.
munchy35

## Homework Statement

A flotation device is in the shape of a right cylinder, with a height of 0.500 m and a face area of 4.00 m2 on top and bottom, and its density is 0.400 times that of fresh water. It is initially held fully submerged in fresh water, with its top face at the water surface. Then it is allowed to ascend gradually until it begins to float. How much work does the buoyant force do on the device during the ascent?

## Homework Equations

Fb=mf*g or Fb = density*Volume*g

## The Attempt at a Solution

Fb=dwVg, where dw is the density of the fluid (water).

The net force is the difference between the buoyant force and gravity, Fg=mg=rVg, where r is the density of the cylinder’s material. Since the cylinder’s density is smaller than that of water, the upwards buoyant force has larger magnitude than the downwards gravity force, and the net force will be upwards, with magnitude Fnet=Fb-Fg=(rw-r)Vg.

Using Newton’s law, the net force is Fnet=ma, so the acceleration is upwards, and equal to a=Fnet/m=(rw-r)Vg/m=(rw-r)g/r=(rw/r-1)g=(1/0.4-1)g=1.5g.

i don't know how to answer the question.

The force varies from a large value initially to zero when it reaches its equilibrium point with 60% of its volume out of the water, so you need an expression for the force as a function of h, the height that is above the surface. If you know calculus, you can integrate Fdh from h=0 to h=0.6H. If not, you can sketch the graph of F vs h and the work will be the area under the graph from 0 to 0.6H. Here H is the total height of the cylinder, which I think you can find from the given information.

i'm just confused.

what equation should i be using to find the answer. the Archimedes' equation or the equation for work.

Both! You need an expression for the force (gravitational + buoyancy) as a function of h (height above the water). Then W = integral of F*dh.

## 1. What is Archimedes' Principle Buoyancy?

Archimedes' Principle Buoyancy states that the upward buoyant force on an object submerged in fluid is equal to the weight of the fluid that the object displaces.

## 2. How does Archimedes' Principle Buoyancy work?

When an object is submerged in a fluid, the fluid exerts an upward force on the object that is equal to the weight of the fluid that is displaced. This force is known as the buoyant force and it acts in the opposite direction to the force of gravity. As long as the buoyant force is greater than the weight of the object, the object will float.

## 3. What is the relationship between density and buoyancy?

The density of an object determines how much fluid it will displace when submerged, and therefore affects the buoyant force acting on the object. Objects with a higher density will displace less fluid and experience a smaller buoyant force, making it more likely to sink.

## 4. How is Archimedes' Principle Buoyancy used in real life?

Archimedes' Principle Buoyancy is used to explain why objects float in fluids such as water. It is also used in the design of boats, ships, and other watercraft to ensure they have the correct buoyancy to stay afloat. In addition, it is used in industries such as oil and gas and underwater exploration to calculate the weight of submerged objects and structures.

## 5. What is an example of Archimedes' Principle Buoyancy in action?

An example of Archimedes' Principle Buoyancy in action is when you fill a bathtub with water and place a rubber duck in it. The duck floats because it is less dense than the water and therefore displaces more water than its own weight. The upward buoyant force acting on the duck is equal to the weight of the water it displaces, allowing it to float on the surface of the water.

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