Finding the density of a liquid with buoyancy

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SUMMARY

The discussion focuses on calculating the density of a liquid using buoyancy principles, specifically through the equation B = ρ(fluid)ghA. The rectangular block's apparent weight (W_app) is analyzed as a function of depth (h), with the relationship W_app = W - B being central to the calculations. The participants confirm that the equation is appropriate for determining fluid density and discuss the implications of the slope of the graph representing W_app against depth. The connection between the slope and the constants in the buoyant force equation is also highlighted.

PREREQUISITES
  • Understanding of buoyancy principles and Archimedes' principle
  • Familiarity with the equation for buoyant force B = ρ(fluid)ghA
  • Knowledge of how to interpret graphs in physics
  • Basic algebra for manipulating equations
NEXT STEPS
  • Research the derivation of Archimedes' principle and its applications
  • Learn about the relationship between pressure, depth, and buoyancy
  • Explore how to analyze linear graphs in physics for slope interpretation
  • Investigate different methods for measuring fluid density in laboratory settings
USEFUL FOR

Students studying fluid mechanics, physics educators, and professionals involved in material science or engineering applications related to fluid density measurements.

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http://spock.physast.uga.edu/prtspool/bearhug_uga_printout_1163471689_22380_10.pdf
A rectangular block is gradually pushed faced-down into a liquid. The block has height d; on the bottom and top the face area is A=5.67 cm^2 . Also shown is a graph that shows the apparent weight W_app of the block as a function of the depth h of its lower face. What is the density of the liquid in units of g/cm^3

Originally I used the equation B=p(fluid)ghA and solved for the density of the fluid. First of all, is this the right equation to use?
 
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I can't for some reason post the figures but if anyone can still give me some help without the use of the figures would be greatly appreciated.
 
Apparent weight W_a is actual weight W minus the buoyant force B.

W_a = W - B

I assume your graph starts with W_a = 0 at some h and then goes down as h increases. The buoyant force is the Area of the face times the pressure (ρgh), as you have written it. Everything in B is a constant except for h, and W is a constant. The equation above is the equation of a straight line. There is a connection between the slope of that line and the constant factors in B. What is that connection?
 

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