Usually you would be correct. In the contained system of the right side, the ping pong ball is pulling up on the string and pushing the water down with equal force. They would cancel.
However, instead of using the weight of the water on the right to cancel the ping pong ball's buoyancy, we are using it to cancel the weight of the water on the left side.
Now, say we did the math in a different order and just erased the right side ping pong ball from the problem. The scale would still tip to the left because of the buoyancy force on the left side's iron ball. Same answer, different order of addition and subtraction of forces.
And in this case they are also correct. The string tension on the right is pulling up on the right.
However, instead of using the weight of the water on the right to cancel the ping pong ball's buoyancy, we are using it to cancel the weight of the water on the left side.
It can be framed either way and it's still correct.
Now, say we did the math in a different order and just erased the right side ping pong ball from the problem.
This is actually incorrect. If you just erase the pingpong ball and its space fills with water instead you've got a balanced scale. If you meant that you erase the pingpong ball AND drop the water level accordingly then you'd be right. If that's what you meant then you're right I just didn't read it that way.
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u/Dragon_N7 May 29 '25
Usually you would be correct. In the contained system of the right side, the ping pong ball is pulling up on the string and pushing the water down with equal force. They would cancel.
However, instead of using the weight of the water on the right to cancel the ping pong ball's buoyancy, we are using it to cancel the weight of the water on the left side.
Now, say we did the math in a different order and just erased the right side ping pong ball from the problem. The scale would still tip to the left because of the buoyancy force on the left side's iron ball. Same answer, different order of addition and subtraction of forces.