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Question: If a person has a bucket with water in it and they swing it around with their arm, what shape does the water take? Is it flat to the bottom of the bucket, or is it tilted to the side since there are two forces pulling at it?
This is a question that at first glance seems to be easy to answer, but then, on further thought, there is the realization that the answer is not as simple as you might think. So, this is a really good question because it is thought provoking.
I must assume that the two forces, mentioned in the question, are the force of gravity and the force of the bottom of the bucket pushing on the water. Also, assuming that the bucket is moving in a vertical circle, that gravity does not change over the diameter of the circle, or over the diameter of the bucket, then we can say that the surface of the water will be parallel to the bottom of the bucket. This is the simple answer with a lot of assumptions, which sometimes happens in the teaching of science. A lot of assumptions are made so that the explanation can focus on a major concept, but some of the reality of the situation is lost in trying to simplify. Let's explain further.
When the person's arm is extended straight up, both the force of gravity and the force of the bucket on the water are in the same direction. The water does not fall out because, if the person is moving the bucket fast enough, the bucket is falling around the circle at that point with a greater acceleration downward than the water. At just the right speed, the force of the bucket on the water can actually be reduced to zero.
When the bucket is at the bottom of the circle, the force of gravity on the water and the force of the bucket pushing up on the water are in opposite directions. No trouble at this point understanding how the water stays in the bucket.
In these first two situations, it is safe to say (but might not be entirely accurate) that the surface of the water is parallel to the bottom of the bucket. Now we must consider some other positions of the bucket, the arm extended straight out and straight back. This makes the bottom of the bucket vertical.
Let's do a little thinking. Stretch a piece of plastic wrap over the top of the water in the bucket so that there is no air space between the plastic and the water. Glue it so that the water can't leak out. Now tip the bucket so that it would be in the same position as when the arm of the person is straight out or straight back. What happens? We see a bulge at the bottom of the plastic wrap. Gravity is pulling the water down more at the bottom of the water than at the top and the weight of the water at the top is pushing down on the water at the bottom. You might say "What if we used stiff plastic rather than plastic wrap?" Well, gravity would still be pulling down more on the bottom of the water and the weight of the top water would be pushing down on the bottom water, we just would not see the effect because the stiff plastic would not bend as much.
What would this difference in pull do to the water in the open bucket? It would make it bulge slightly (very slightly) on the side closest to the ground. This bulge should be changing as the bucket goes around the circle. Increasing as the bucket approaches the horizontal (front and back) positions and decreasing as it approaches the vertical (top and bottom) positions. So, the surface would be ever so slightly not parallel to the bottom of the bucket through most of the circle.
There is another force acting between the water and the bucket that we haven't talked about yet. It is the adhesive force. This is the force that makes the surface of the water creep up along the edges where the water meets the bucket. This gives the surface a slight curve, especially at the edges.
And then there are the hydrogen bonding forces that make it difficult to break the surface, and gives drops of water on a flat surface their curvature. Sometimes these forces are called surface tension.
So, at first glance, it may look as though the surface of the water is parallel to the bottom of the bucket, but if you could make some closer observations and measurements, you might find out that it's not. Thanks for the thought- provoking question. It has really raised a lot of questions in my mind. What happens if you put the water in a balloon instead of a bucket? What happens if you put a hole in the bottom of the bucket? Or put the hole in the side of the bucket? Why are there holes in the side of the washing machine tub and not just in the bottom? Why is there a spin cycle?
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