# Archemides principle/ Center of buoyancy

• huffy
In summary, the conversation discusses a method of moving a large undersea rock using a closed, empty oil drum and the use of Archimedes' principle to determine the maximum weight of a rock that can be lifted. The conversation also includes a discussion on calculating the weight of the rock in air.
huffy

## Homework Statement

One way of moving a large undersea rock or mooring is to fasten a closed, empty oil drum to the rock while at low tide. As the tide comes in the drum is drawn down into the water increasing the buoyant foce acting on the system of the rock and drum. Suppose a cylindrical drum of radius 25 cm, length 100cm, and mass 20kg is used. What is the maximum mass of a rock (of density 5.0 x10^3) that the drum can lift from the bottom? Assume the density of sea water is the same as that of pure water.

http://imgur.com/Y4Qrhjq

http://imgur.com/2wD4OpR

PfVs=PoVo

## The Attempt at a Solution

So to solve this I am trying to use archimedes principle which is the density of a fluid times the volume submerged=the density of the system times the volume of the system (PfVs=PoVo). I know That Pf=1000kg/m^3 because its pure water and I know that the Po is approx 102.4 because i can use m=PV to find the density of the drum and add it to the density of the rock. I also know that the volume of the system is Vdrum+Vrock.

I end up with the formula 1000kg/m^3*Vsubmerged=102.04(0.196+(Mrock/5.0x10^3) where 0.196 is the volume of the drum and 5.0x10^3 is the density of the rock.

Rearranged I get that Mrock=(1000kg/m^3-20.04/102.04)*5.0x10^3

What do i need to do to find the volume of the submerged?

First find the max lift from the drum = volume of drum x density... minus weight of drum

This is the weight of the rock (WHEN IN WATER) that can be lifted ...from this calculate weight of rock in AIr... and from this mass of rock

What does Alr stand for?

Whoops, it looks like I calculated the volume of the drum wrong. It's actually 19.63

anyone know what alr is?

OH THAT SAYS air

oz93666 said:
First find the max lift from the drum = volume of drum x density... minus weight of drum

This is the weight of the rock (WHEN IN WATER) that can be lifted ...from this calculate weight of rock in AIr... and from this mass of rock
When i take the volume of drum x density... minus weight of drum i end up getting -176.2, would that be right? I don't see how it would be a negative number

## 1. What is Archimedes' principle?

Archimedes' principle states that the upward buoyant force on an object immersed in a fluid is equal to the weight of the fluid that the object displaces. This means that if the weight of the object is less than the weight of the fluid it displaces, the object will float; if the weight of the object is greater, it will sink.

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

Archimedes' principle explains how buoyancy works. When an object is placed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid that the object displaces. This force, known as buoyant force, is what keeps objects afloat in water.

## 3. What is the center of buoyancy?

The center of buoyancy is the point at which the upward buoyant force acts on an object. It is typically located at the geometric center of the displaced fluid, which is also the center of mass of the fluid displaced by the object.

## 4. How is the center of buoyancy determined?

The center of buoyancy can be determined by finding the centroid, or geometric center, of the displaced fluid. This can be done mathematically by considering the shape and volume of the displaced fluid, or experimentally by measuring the position of the object in the fluid and the change in water level.

## 5. What factors affect the center of buoyancy?

The position of the center of buoyancy can be affected by the shape, size, and weight distribution of an object, as well as the density and viscosity of the fluid it is immersed in. It can also change as an object moves or rotates in the fluid.

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