What is the force that keeps water in a bucket when you swing it in a circle?

Question

My fiance says it's G-Force but I say hell no. I know what the word is but I can't think of it. I think it starts with a C but I need some help here. I have 500 dollars riding on this.

Answer 1

"centrifugal force" is not really correct -- it implies that there is a
force by the water that keeps it in the bucket.

"centripetal force" is the correct word - the force you pull on the
bucket to keep it traveling in a circle.

Answer 2

You are thinking of "centrifugal force," but that itself is only what applied mathematicians DO, and physicists SHOULD, call a "pseudeo-force." If you work in an inertial, non-rotating frame (the only secure frame in which to apply Newton's equations of motion with no additional jiggery-pokery), when you whirl the bucket around in a circle at a constant speed, it (the bucket) is ACCELERATING INWARDS towards the centre of the circle. Inertia would make the water go in a straight line at any stage. However, the sides of the bucket are FORCING it, too, to accelerate inwards. All this is REALLY happening because YOU are applying a CENTRIPETAL FORCE --- a "centre-seeking force." (Without that REAL, honest-to-God force, applied by YOU, the bucket would NOT be travelling in the circle in the first place!)

But if, INSTEAD, you now look at it from the point of view of moving with the bucket, you have moved you attention INTO an ACCELERATING FRAME (if only mentally). In that case, d'Alembert's Principle says that in an accelerating frame, everything behaves as though there is a "body-force" on every piece of matter, exactly equal to the mass of the matter times the NEGATIVE of the acceleration in inertial space. But that's just like gravity behaves! So, if it pleases you to think that way, you can think of it as a pseudo-gravitational effect with the unusual properties that it (i) points AWAY from the centre [really ; central axis] and (ii) increases linearly with distance from that axis.

In summary, then, you can view the water as behaving in the bucket exactly as if it were in an (outwardly directed!) gravitational field with forces acting on each bit of matter, just as calculated from the corresponding "centrifugal force."

What this means is that, appropriately interpreted, there is a way of looking at the resolution of this problem in which both you and your fiancé are right!

So why don't the two of you celebrate being so in sync. by making love and sending ME the $500 ?!

Live long and prosper.

Answer 3

ditto