# Archimede's Principle and Work due to buoyant force

• Blooch
In summary, the conversation discusses a problem involving a flotation device in the shape of a right cylinder, with a given height and face area, and a density that is a fraction of fresh water's density. The question is how much work the buoyant force does on the device as it ascends from being fully submerged to floating. The attempted solution involves finding the mass and buoyant force, but there is uncertainty about how to translate these values into work. The key is to draw a free body diagram and consider the submerged volume needed to provide enough buoyant force to balance the device's weight.
Blooch

## Homework Statement

A flotation device is in the shape of a right cylinder, with a height of 0.323 m and a face area of 4.81 m2 on top and bottom, and its density is 0.460 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?

Fb=mg
Rho=M/V
V=Ah
W=Fd

## The Attempt at a Solution

I solved to find that the mass is 714.6698kg through manipulation of the density formula and then I solved to find the Buoyant force to be 7003.76404N. I'm not quite sure how to translate these two values that I found into Work(in joules). I know the equation for work is Force x distance and I know that, fully submerged the distance is at least .323m + whatever portion of the device floats above the surface of the water(my guess is either (.323/2)m or (.460*.323)m. Please help! Thank you!

Blooch said:
I know the equation for work is Force x distance and I know that, fully submerged the distance is at least .323m + whatever portion of the device floats above the surface of the water(my guess is either (.323/2)m or (.460*.323)m. Please help! Thank you!
No, that's not right, draw pictures of it's start and end position. Where would the cylinder be if the distance is greater than 0.323 m?

Draw a free body diagram of the floating cylinder, you need to find the submerged volume required to provide a buoyant force equal to force due to gravity.

## 1. What is Archimedes' Principle?

Archimedes' Principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In other words, an object will float if the weight of the liquid it displaces is greater than its own weight.

## 2. How does Archimedes' Principle relate to buoyancy?

Archimedes' Principle is the fundamental concept behind buoyancy. It explains why objects float or sink in a fluid, and the magnitude of the buoyant force acting on them.

## 3. What is the formula for calculating the buoyant force?

The formula for calculating the buoyant force is FB = ρVg, where FB is the buoyant force, ρ is the density of the fluid, V is the volume of the fluid displaced by the object, and g is the acceleration due to gravity.

## 4. Can Archimedes' Principle be applied to gases?

Yes, Archimedes' Principle can be applied to gases. It states that the buoyant force acting on an object in a gas is equal to the weight of the gas displaced by the object.

## 5. How is work related to buoyancy?

Work done by buoyant force is equal to the product of the buoyant force and the displacement of the object in the fluid. This work is done against the force of gravity and is responsible for the upward movement of the object.

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