Really, this doesn’t tell us much. All it says is that the upward-pulling tension has to be equal to the two downward forces (gravity and the other tension).
But what about the sum of the torques? If the object is in equilibrium, you can pick any point on the object to calculate the torque. I’m going to pick point o, where the upward-pulling string is attached. And I’ll say clockwise torques are negative values and counterclockwise are positive.
To get the torque resulting from each force, remember that τ = Fr. But since the distance (r) for T1 is zero, this tension results in zero torque.
So now, with only two other forces, the only way for their torques to offset is for one to pull clockwise and the other to pull counterclockwise. T2 is pulling down on the right side, which creates a negative torque around point o of T2 r2. But the gravitational force mg also pulls down—we can’t change that. That means the center of gravity of the top platform has to be on the other side of the central support string. So here’s our equilibrium torque equation:
That’s the key to the whole thing: The center of gravity of the “floating” tabletop and the downward force T2 need to be on opposite sides of the central suspension string. It’s actually not that complicated, right?
Build Your Own Floating Table!
Now that you understand how it works, you can build one yourself. In this video, I’ll show how to do it with just the kind of ordinary Lego pieces you probably have at home.
In theory, you could also build a floating table with only the upward pulling string in the middle, if the center of gravity was exactly above the point where the string is connected. But it would be unstable. With just a tiny push, the center of gravity would shift to the side and the whole thing would topple over.
Could you stack whatever you want on the top of this table? Nope—there’s a limit to the maximum tension in the string (and in that little support hook). As you add mass on top, the downward pulling string might have to increase in tension to prevent it from tipping over. Then the upward pulling string has to compensate for the added load as well as the extra tension pulling down to balance it. If this force is more than the string can handle, that’s it—it will break and crash.
What about a super-sized floating table that could support a car? Would that be possible? Yup. You’d just need to make sure both the platform and the cables are strong enough to exert enough tension without breaking. It would be pretty cool to see.
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