If a bucket of water spins about a vertical axis with constant angular velocity (in

Chapter 9, Problem 65

(choose chapter or problem)

If a bucket of water spins about a vertical axis with constant angular velocity (in radians per second),forces act on a particle located at a distance x from the vertical axis: the gravitational force mg acting downward and the force of the bucket on the particle (transmitted indirectly through the liquid) in the direction perpendicular to the surface of the water. These two forces must combine to supply a centripetal force m2x, and this occurs if the diagonal of the rectangle in Figure 11 is normal to the waters surface (i.e., perpendicular to the tangent line). Prove that if y = f (x) is the equation of the curve obtained by taking a vertical cross section through the axis, then 1/y = g/(2x). Show that y = f (x) is a parabola.