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Explained: Beaker Ball Balance Problem

2m read
·Nov 10, 2024

You have made your prediction, and now it is time to see what happens when I release the balance. Ready? In three, two, one.

The balance tips towards the right, towards the hanging, heavier ball. But why does this happen? Well, the best way I can think of to explain this is that both balls displace the same amount of water. So they both experience the same upward buoyant force, which is equal to the weight of the water they displace. That is just Archimedes' Principle.

But by Newton’s Third Law, that means there must be equal and opposite forces down on the water in both beakers. So you would think that both beakers would get heavier by this same amount. Now, for the hanging ball, the beaker does get heavier by this amount because the buoyant force is now supporting some of the weight that used to be supported by this tension in the string. But it is now reduced, and so the beaker actually has more weight.

But for the ping pong ball, the downward force on the water is almost entirely counteracted by the upward force of the tension in that string on the bottom of the beaker. Therefore, the weight of this beaker only increases by the weight of the ping pong ball itself, whereas for the hanging ball, the weight increases by the weight of the water it displaces. So, obviously, this beaker is going to end up being heavier.

Now I want to propose an additional experiment. What if instead of tethering the ping pong ball to the base of this beaker, I just got a free ping pong ball and submerged it with my finger, just barely under the surface of the water? In that case, what do you think would happen when the scale was allowed to rotate? Would it tilt down A) towards the hanging acrylic ball or B) down towards the ping pong ball, which is now just barely submerged under the water or C) would the balance remain perfectly balanced?

So I want you to make your selection, make your prediction by leaving a comment starting with either A, B, or C, and then giving me your explanation. And I will tally up the votes and let you know the answer next time.

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