Question

please explain briefly, step by step.

z() Consider a bucket of water spinning with constant angular speed w. We interested in finding the shape of the water's surface, z(r). We do this by first noting that in the rotating frame of the bucket, a small water elem mass m on the surface of the water is in static equilibrium. The figure shows the three forces acting on the water element: Centrifugal force Fc, gravity Fg and the normal force n of the rest of the water on the water element. a) Find the angle o as a function of r, the distance from the axis of rotation. We are interested in the curve describing the water surface height, z(r). b) Given that the normal force is perpendicular to the surface, express the slope dz/dr in terms of $. c) Combine the results of a) and b) to find z(r). Does it make sense, and why?

Answer 1

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