How Is the Density of the Rock Determined in a Buoyancy Problem?

Click For Summary
SUMMARY

The density of the rock in a buoyancy problem can be determined using the principles of buoyancy and the submerged fractions of a cork in two different liquids. Given a cork density of ρC = 0.24 g/cm³, when submerged in liquid 1 (ρ1 = 0.80 g/cm³) with a submerged fraction f1 = 0.75, and in liquid 2 (ρ2 = 0.89 g/cm³) with a submerged fraction f2 = 0.67, the density of the rock can be calculated using the equilibrium of forces acting on the cork and the rock. The derived equation will involve the densities of the liquids and the fractions submerged.

PREREQUISITES
  • Understanding of buoyancy principles
  • Knowledge of density calculations
  • Familiarity with algebraic equations
  • Basic physics concepts related to fluid mechanics
NEXT STEPS
  • Derive the equation for buoyant force in fluid mechanics
  • Explore Archimedes' principle in detail
  • Learn about the relationship between density and buoyancy
  • Investigate real-world applications of buoyancy in engineering
USEFUL FOR

Students in physics, engineers dealing with fluid mechanics, and anyone interested in solving buoyancy-related problems will benefit from this discussion.

xgoodtimesx
Messages
4
Reaction score
0
One end of a light thin string is attached to a cork with density ρC = 0.24 g/cm3. The other end is attached to a rock. When the arrangement is placed in liquid 1 with density ρ1 = 0.80 g/cm3, a fraction f1 = 0.75 of the cork becomes submerged. When the arrangement is placed in liquid 2 with density ρ2 = 0.89 g/cm3, a fraction f2 = 0.67 of the cork becomes submerged. What is the density of the rock?


Please derive a equation to solve this problem
 
Physics news on Phys.org
Welcome to PF!

Hi xgoodtimesx! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 

Similar threads

Optimizing Mass for Vertical Rod Buoyancy in Unknown Fluid
  • · Replies 29 ·
Replies
29
Views
3K
What is the tension in the string connecting a cork and a cube in water?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Structure of Earth, pressure and density model
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Astrophysics project gone wrong: why isn't the moon tearing the Earth apart?
  • · Replies 4 ·
Replies
4
Views
4K