Determining scale readings given different densities

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SUMMARY

The discussion focuses on calculating the scale reading of an object suspended in oil with a density of 800 kg/m³, given its readings in air and water. The scale reads 200 N in air and 150 N in water, indicating a buoyant force of 50 N in water. The volume of the object was determined to be 0.015 m³ using the formula d = m/v, leading to a calculated mass of 12.24 kg when submerged in oil, resulting in a scale reading of 120 N. The calculations and methodology presented are accurate and follow the principles of buoyancy and density.

PREREQUISITES
  • Understanding of Archimedes' principle and buoyancy
  • Familiarity with the formula for density (d = m/v)
  • Basic knowledge of weight and force measurements
  • Concept of displaced liquid volume in fluid mechanics
NEXT STEPS
  • Study Archimedes' principle in detail
  • Learn about buoyancy calculations in different fluids
  • Explore the relationship between density and volume in fluid mechanics
  • Investigate the effects of varying densities on scale readings
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Students in physics, engineers working with fluid dynamics, and anyone involved in buoyancy-related calculations will benefit from this discussion.

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Connected by a string to a scale is an object and when suspended in air, the scale reads 200 N. The scale reads 150 N when the object is suspended in water (d = 1000 kg/m^3). What does the scale read (in N) when the object is suspended in oil having a density of 800 kg/m^3?

I determined that the volume of the object was .015 m^3 from using the d=m/v formula in the H2O portion of the problem. I just substituted the volume into the oil density and determined that the mass was 12.24 kg. and then converted that to 120 N. Did I do this correctly?
 
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I determined that the volume of the object was .015 m^3 from using the d=m/v formula in the H2O portion of the problem.

Loss of weight in liquid is equal to the weight of the displaced liquid.
In the problem loss of weight in water is 50N. Then what is the volume of the object?
 

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