Centrifugal Force on a Bucket of Water

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SUMMARY

The discussion centers on the determination of the shape of water in a spinning bucket, specifically concluding that the water forms a paraboloid due to the effects of centrifugal force. The participant utilized the equation for centrifugal force, F = mω²r, and integrated it to derive the potential energy associated with this force, resulting in the equation z = (ω²/2g)r². This analysis confirms that the potential energy from centrifugal force balances gravitational potential energy, leading to the parabolic shape. Additionally, the discussion highlights the practical application of this principle in the manufacturing of large parabolic telescope mirrors.

PREREQUISITES
  • Understanding of centrifugal force and its mathematical representation
  • Familiarity with potential energy concepts in physics
  • Knowledge of gravitational force and its effects on objects
  • Basic calculus for integration and solving equations
NEXT STEPS
  • Explore the derivation and applications of the centrifugal force equation F = mω²r
  • Study the principles of potential energy in rotating systems
  • Research the design and manufacturing processes of parabolic mirrors
  • Investigate the relationship between rotational motion and fluid dynamics
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Students in physics, engineering professionals, and anyone interested in the dynamics of rotating fluids and their applications in technology.

BAnders1
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I had a test the other day and it doesn't sound like it will be graded for quite some time (our TA seems to be over his head in classwork). I wanted to see if anyone here could tell me if my answer to one of the questions is correct and justified. Prethanks.

Homework Statement



"A bucket of water is set spinning around its symmetry axis, determine the shape of the water in the bucket"

Homework Equations



F=-mω×(ω×r) (centrifugal force)


The Attempt at a Solution



I first found the centrifugal force on a small mass of water (F=mω²r), then I integrated this with respect to r to find the potential energy associated with the centrifugal force [U=-(mω²/2)r²]. Since the water is bound in the bucket, it cannot attain any kinetic energy, thus in equilibrium the potential energy due to the centrifugal force must cancel the gravitational potential energy U=mgz. Solving for z, I got z=(ω²/2g)r², thus the water forms a paraboloid.

Is my reasoning correct? Thank you in advance.
 
Physics news on Phys.org
Looks good.

In fact large, parabolic telescope mirrors are made by spinning molten glass until the glass has cooled and hardened.
 

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