Archemides principle/ Center of buoyancy

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Homework Help Overview

The discussion revolves around a problem involving Archimedes' principle and buoyancy, specifically related to lifting a rock using a cylindrical drum submerged in water. The scenario includes calculations of buoyant force, volume, and density, with a focus on determining the maximum mass of a rock that can be lifted.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using Archimedes' principle to relate the buoyant force to the weight of the rock and the drum. There are attempts to calculate the volume of the drum and its implications for lifting capacity. Questions arise regarding the interpretation of terms like "AIr" and the calculations leading to unexpected negative results.

Discussion Status

Some participants have provided guidance on calculating the maximum lift from the drum and the relationship between the weight of the rock in water and air. There is an ongoing exploration of the calculations, with some participants questioning the validity of negative results obtained in their computations.

Contextual Notes

Participants have noted potential errors in volume calculations and are clarifying terminology. There is an emphasis on ensuring accurate definitions and assumptions related to the problem setup.

huffy
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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.

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Homework Equations



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?
 
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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
 

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