Purchase Solution

Paraboloid of revolution

Not what you're looking for?

Ask Custom Question

(Parabaloid of revolution)

Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W.

Hint: consider a particle of liquid located at (x, y) on the surface of the liquid.
The forces acting on the particle are m*W^2*x in the x direction and -m*g in the y direction.

As the particle is in radial and equilibrium the resultant vestor is normal to the curve.

Please solve by writing and solving the appropriate 1st order equation and show how the curve containing the particle is found.

Purchase this Solution
Solution Summary

The problem is solved by considering various forces acting on a particle of liquid on the surface and the conditions for its equilibrium.

Solution Preview

Please refer attachment for solution.

Solution

Y

ω

P(x,y)
F1
θ θ
Liquid surface A B C
F2 R

X

Let us consider a particle of liquid at point P(x,y) on the surface of the liquid. It will be ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Surface Integral of a Paraboloid of Revolution

    105354 Surface Integral of a Paraboloid of Revolution Let S be the closed surface of the paraboloid of revolution z = ±(4 − x2 − y2 ) where −2 x, y +2.

  • Volume of solids of revolution

    339913 Volume of solids of revolution.. Volume of solids of revolution.. 1. A paraboloid dish (cross section ) is 8 units deep. It is filled with water up to a height of 4 units.

  • Volume of Region between a Paraboloid and a Cone

    127045 Volume of Region Between a Paraboloid and a Cone Find the volume of the region between the paraboloid z = 2(x^2 + y^2) and the cone z = 2 sqrt(x^2 + y^2). Please see the attached file for the complete solution.

  • Leval Curves of a Cone and a Paraboloid

    121908 Level Curves of a Cone and a Paraboloid Show that the level curves of the cone z = ( x^(2) + y^(2) )^(1/2) and the paraboloid z = x^(2) + y^(2) are circles. Proof.

  • Paraboloid volume

    Find the volume inside the paraboloid Z = X^2 + Y^2 below the plane Z = 4 Thank you. Please see the attachment. This shows how to find the volume inside a paraboloid.

  • Quadratic equation

    C. elliptic paraboloid D. parabolic cone E. hyperbolic paraboloid ANSWER: B. hyperbola Because, diagonal matrix has 1/alpha^2 and -1/beta^2.

  • Volume of a solid

    The system looks like: Since the plane is above the paraboloid , the volume captured between the plane and the paraboloid is: The limits of integrations are determined by the curve where the plane intersects the paraboloid.

  • Sketch the surface of a spheroid inside a parabaloid and evaluate the surface integral.

    63361 Sketch the surface of a spheroid inside a parabaloid and evaluate the surface integral. The surface S is that part of the spheroid .... which lies inside the paraboloid az = x2 + y2; here a is a constant.

  • Gradients : Elliptic Paraboloid and Vector Fields

    are investigated with respect to an Elliptic Paraboloid and Vector Fields.

View More Related Solutions