Archimedes Principle: Calculate Outer & Inner Radii

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SUMMARY

The discussion focuses on applying Archimedes' Principle to calculate the outer and inner radii of a spherical aluminum ball with a mass of 1.48 kg and a concentric cavity. The key equation used is the buoyant force equation, which states that the buoyant force equals the density of the fluid multiplied by the volume of the object and gravitational acceleration (g). Since the ball barely floats, its effective density is nearly equal to that of water, allowing for the calculation of the outer radius and the radius of the cavity using the density of aluminum.

PREREQUISITES
  • Understanding of Archimedes' Principle
  • Knowledge of buoyant force calculations
  • Familiarity with density concepts, specifically for aluminum
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the outer radius of the aluminum ball using the buoyant force equation
  • Determine the inner radius of the cavity based on the mass and density of aluminum
  • Explore the properties of buoyancy in different fluids
  • Study the implications of density variations in floating objects
USEFUL FOR

Students studying physics, particularly those focusing on fluid mechanics and buoyancy, as well as educators looking for practical applications of Archimedes' Principle in problem-solving scenarios.

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Homework Statement


A spherical aluminum ball of mass 1.48 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water.
A. Calculate the outer radius of the ball.

B. Calculate the radius of the cavity


Homework Equations


Buoyant Force = density of fluid * Volume of object *g


The Attempt at a Solution

 
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If the ball barely floats in water, then it's effective density must be vey nearly equal to water. So, equate the mass of the ball to the buoyant force. Also, vol of water = vol of the ball.
 
You'll need the density of Al.
 

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