Pressure, Force, and Density Calculations for Immersed Objects

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SUMMARY

The discussion focuses on calculating pressure, force, and density for immersed objects, specifically a cylinder and a metal cube. For the cylinder, the pressure at a depth of 15 cm is calculated using the formula P = ρgh, where ρ is the density of water. The force on the cylinder's ends is derived from this pressure, and the loss in weight when immersed is also determined. For the metal cube, the density is calculated based on its mass and volume, and the apparent mass when immersed in a liquid of density 850 kg/m³ is discussed.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically pressure calculations.
  • Familiarity with the formula for pressure: P = ρgh.
  • Knowledge of density calculations, including mass and volume relationships.
  • Ability to apply Archimedes' principle for buoyancy effects.
NEXT STEPS
  • Study the derivation and applications of the pressure formula P = ρgh in various contexts.
  • Learn how to calculate buoyant force using Archimedes' principle.
  • Explore density calculations for different materials and their implications in fluid dynamics.
  • Investigate the effects of immersion on weight and apparent mass in various liquids.
USEFUL FOR

Students in physics or engineering, educators teaching fluid mechanics, and anyone interested in understanding the principles of pressure and buoyancy in fluids.

LongFTW
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Homework Statement


Q1.A cylinder of length 10cm and radius 4cm has its axis vertical and its top end 15cm below the surface of a large beaker of water.
Calculate:
a) the pressure on the upper and on the lower ends of the cylinder due to the water
b) the force on the upper and on the lower ends of the cylinder due to the water
c) hence state the loss in weigh of the cylinder when immersed in water.

Q2.A solid metal cube, each side 3cm long has a mass of 207.8grams.
Calculate:
a) the density of the metal kg m^-3
b)the apparent mass of the cube when immersed in a liquid of density 850kg m^-3

I am completely stumped about these 2 questions and have no idea how to obtain the formula. So if anyone can just post the formula for me would be great.

Homework Equations





The Attempt at a Solution

 
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Welcome to PF!

Hi LongFTW! Welcome to PF! :wink:

Pressure at depth h is ρgh, where ρ is density (of water).

That should enable you to do Q1 …

show us how far you get, and where you're stuck, and then we'll know how to help! :smile:
 
Never mind, I figured it out with some notes in my book, thanks for the help anyways.
 

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