Diameter 0.8 m height 1.2 m floats in water

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SUMMARY

The discussion centers on calculating the submerged volume of a cone with a diameter of 0.8 m and a height of 1.2 m floating in a liquid with a density of 1360 kg/m³. Participants emphasize the importance of using the buoyant force equation and establishing a relationship between the dimensions of the cone and the submerged depth. The key insight is to express the radius or height as a function of the submerged length to determine how far the cone sinks in the denser liquid.

PREREQUISITES
  • Understanding of buoyant force principles
  • Familiarity with geometric properties of cones
  • Knowledge of density and its impact on floating objects
  • Ability to set up and solve ratios and proportions
NEXT STEPS
  • Study the principles of buoyancy and Archimedes' principle
  • Learn how to calculate the volume of a cone
  • Explore the relationship between density and buoyancy in different liquids
  • Practice solving problems involving submerged objects in fluids
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This discussion is beneficial for physics students, educators, and anyone interested in fluid mechanics and buoyancy calculations.

darkmagic
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Homework Statement



Given:
diameter 0.8 m
height 1.2 m
floats in water
how far will it sink in a liquid (density =1360 kg/m^3)

Homework Equations



Buoyant force

The Attempt at a Solution



In the attachment
I'm stuck on how to find the volume of the submerged cone in the liquid
please help
 

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You are doing well, so far. Hint 1: Write d (or r, or x) as a function of L.
 


This what I think: since the liquid is more dense than water, then the cone will float a little. From triangle, 0.8 becomes 0.8+y and 0.4 becomes 0.4-y. The ratio and proportion becomes 0.4/1.2 = x/(0.8 + y). Am I correct? or the cone will sink a little?
 
No. Hint 2: 0.4/1.2 = x/L.
 

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