Water in a spinning bucket: a better explanation

[fisico30]

Hello Forum,

we all know about the experiment of the spinning bucket full of water. The water does not fall if the speed of the bucket is right (at least equal to the critical speed or larger than it).

If there was no bucket the water would not fall on our heads either if the water moved at the critical speed. But the water would move in a parabolic path. The higher the speed the larger the parabolic path would be an the farther it would fall. Like when a water jet comes out of a water hose and we don't get wet...

What the bucket does is to keep the water trajectory in a circular path of fixed radius: once the water made it beyond the highest point of its trajectory it would continue to move parabolically.The bottom of the bucket prevents the water from doing that and keeps it in the circular path...

The water does not fall on our heads because it is moving tangentially to the circular path faster than it is moving downward due to gravity. Gravity pulls it down but at a rate that is matching the tangential speed.
So the force of gravity, allowing the water to move in a circle is the main component of the actual centripetal force. If the speed is larger than the critical speed the contact force of the bottom of the bucket, pointing towards the center, helps the water stay in the circular path. Otherwise the water would climb up to follow its natural parabolic path...

So these two force, gravity and the contact force are what produce the circular path, hence they are together the net centripetal force...
Any flaw with my explanation?

thanks
fisico30

 

[Skrambles]

This is supposed to be a better explanation than what exactly?

 

[fisico30]

:) than the ones I generally read...:)

they put too much emphasis on the formulas and not enough on the real concept...

anyway, am I correct or not really?

 

[rcgldr]

I think the easiest way to explain this is if the bucket is accelerating downwards equal to or faster than 1 g, then the water will stay in the bucket because the bucket accelerates as fast or faster than gravity accelerates the water.

 

[fisico30]

True.

I have been trying to explain this common example to someone without knowledge of physics, forces, etc...

But itself water would follow a parabolic path that would move it farther and out of the circular path. The role of the bucket is to constrain the water motion to a circular path. The inertia of water causes a contact force with the bottom of the bucket that points inward (part of the centripetal force).

At critical velocity, the water at the top point of the trajectory is still falling down but not on our heads because the distance traveled downward is matched by the bucket which is always moving in sync with the water and catching it...
If the bucket moves faster than the critical velocity the water would have the tendency, by inertia to move even farther out of the circular path. It is the bucket that keeps it from doing that (pressure at the bottom of the bucket).
If the bottom of the bucket breaks water spills out radially...

Simple problems but interesting to look at it in details, I think.

The equation is simple (m v^2/r= n+mg) but does not shine enough light on the actual concept...

 

[Bobbywhy]

fisico30, You have tried to put into your own words the phenomonem known as "Newton's Bucket" for a "better explanation of what I generally read". What do you think of Newton's description?

“If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; after, by the sudden action of another force, it is whirled about in the contrary way, and while the cord is untwisting itself, the vessel continues for some time this motion; the surface of the water will at first be plain, as before the vessel began to move; but the vessel by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little, and ascend to the sides of the vessel, forming itself into a concave figure...This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavour. ... And therefore, this endeavour does not depend upon any translation of the water in respect to ambient bodies, nor can true circular motion be defined by such translation. ...; but relative motions...are altogether destitute of any real effect. ...It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space in which these motions are performed, do by no means come under the observations of our senses.”

— Isaac Newton; Principia, Book 1: Scholium
http://en.wikipedia.org/wiki/Bucket_argument

 

[HallsofIvy]

I don't believe that is what fisico30 is talking about. From his description, he is talking about swinging a bucket of water in a circle over his head. Newton was talking about spinning a bucket of water around its own axis.

 

[Bobbywhy]

Oops! Excuse me, I misread the OP.

 

[fisico30]

still interesting...
so, physically, why does the water surface curves towards the edge as the bucket is rotating?

Conceptually, how can this be explained in terms of the viscosity of water and the adhesion with the bucket's walls?
thanks
fisico30

 

[HallsofIvy]

Partially but more importantly the water "particles" want to move in a straight line so they move to the side of the bucket which the stops it. The water "builds up" at the sides of the bucket.