Mass on a Spring semi-submerged in a liquid

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SUMMARY

The discussion centers on the physics of a mass on a spring that is semi-submerged in a liquid. The participants explore the relationship between variables such as spring constant (k), height (h), fluid density (ρ), gravitational acceleration (g), and volume (V). The conclusion reached is that the definitions of the variable d can be adjusted, yet they yield equivalent results when substituting into the equations governing the system. The emphasis is on the correct application of these variables to derive the same outcome.

PREREQUISITES
  • Understanding of Hooke's Law and spring mechanics
  • Basic principles of fluid mechanics
  • Knowledge of gravitational forces and buoyancy
  • Familiarity with algebraic manipulation of equations
NEXT STEPS
  • Study the principles of buoyancy and Archimedes' principle
  • Learn about the mathematical modeling of oscillatory motion in fluids
  • Explore the effects of damping in spring systems submerged in liquids
  • Investigate the relationship between spring constants and fluid density
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Physics students, mechanical engineers, and anyone interested in the dynamics of oscillating systems in fluid environments.

MatinSAR
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Homework Statement
According to the figure, the metal cylinder with mass M and volume V is connected to a fixed point from above by a spring with spring constant k and it floats inside a liquid of density p so that half of its height is inside the liquid. What weight should we put on it so that two-thirds of the height is inside the liquid?
Relevant Equations
Fluid mechanics.
Hi , Can someone tell me wether my answer is corrrect or false ?
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I'm getting something different from you. The difference is I define ##d'## in terms of ##d## and ##h## differently. Actually, they work out equivalently. If you just eliminate ##Mg## via your first equation, and put ##L## in terms of ##d## and ##h## , I think we will get the same result.

My end result is purely a function of ##k,h,\rho,g,V##
 
Last edited:
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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