Extended: Beaker Ball Balance Problem

This is the final installment of the beaker ball balance problem. So if you haven’t seen the first part, you should probably watch that now. The link is in the description.

Now assuming you have seen it, you know that the balance tips towards the hanging acrylic ball when weighed against a beaker with a submerged ping pong ball. But what would happen if, instead of tethering the ping pong ball to the base of the beaker, it was instead submerged by my finger? I posed this question in the last video, and you responded with thousands of comments.

Thirteen percent of you thought that the acrylic ball beaker would be heavier. Twenty-nine percent thought the ping pong ball beaker would be heavier. And 54 percent of you thought that they would be balanced. So now let’s see what actually happens in three, two, one. Perfectly balanced.

But why is this the case? Well, just as in the previous experiment, both balls displaced the same amount of water and so they experienced the same upward buoyant force equal to the weight of water they displace. Therefore, there are equal and opposite downward forces on the water, making both beakers heavier by this amount.

And our answer could stop here. But if you are wondering why this result is different from the previous case, consider that in the first part, the downward force on the ping pong ball side was counteracted by the upward tension in the string. But not anymore, because there is no string.

Instead, the downward force from my hand is equal to the buoyant force minus the weight of the ping pong ball. So that overall both beakers get heavier by the same amount. It is just the weight of water displaced by the ping pong ball or the acrylic ball because it has the same volume.

I hope you enjoyed this experiment. If you have got another way of explaining this, please let me know in the comments.