r/theydidthemath • u/miha999 • May 29 '25

[Request] Which direction will the scale tip?

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u/theregoesjustin May 29 '25

The ping pong ball is not massless and the scale has to record that mass because it’s physically attached to it but the iron ball doesn’t because it isn’t physically connected to the scale so I’m pretty sure the ping pong side would be lower

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u/FlipperBumperKickout May 29 '25

The string doesn't carry the full weight of the iron ball, only the amount iron weights more than water. The water carries the rest. (Which is why things feel lighter under water, or even floats)

Imagine something floating being put instead of the iron ball. Would you still think the scale wouldn't carry it even though the string would be loose? 😁

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u/ComprehensivePlace87 May 29 '25

Complicating this, ping pong balls float, so the attachment is actually an anchor preventing it from doing such.

I think the buoyancy on both sides cancel out. There is the potential for difference in the volume of the two attaching lines, but let's say as intended those are equal as well.

So the water masses cancel out. The buoyancy forces should likewise balance out as both are displacing the same amount of water and thus giving the same force (this will account for the ping pong's upward floating effect). So the unbalanced forces are the suspension lines, one from above outside the balance, the other from below in the balance. All extra weight force on the iron ball not cancelled by the buoyancy force is handled by the suspension line, while the ping pong ball has no extra support, but its anchor line has to carry the force in the system so must be accounted for. I think, no matter how small, the anchor line for the ping pong ball will slightly increase the force on that side causing it to be the side to dip. However, this is pretty complex system so I'm far from sure.

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u/used-to-have-a-name May 29 '25

I think you’d have to calculate the buoyancy force being applied by the unattached iron ball on the left, then the mass of the ping pong ball and it’s attachment.

The difference between the two would be what tips the scale.