There is a popular riddle that you may have heard about traveling in a boat with 3 heavy balls such that the total weight is more than the boat can handle. The “solution” is to juggle the balls so that one is always in the air, which will make the total weight low enough for the boat to handle.
When I heard this riddle as a kid I though it was very clever. Once I had learned some physics I began to wonder if it was really accurate. Once I had a decent intuition, it struck me that this idea could never work. But it wasn’t until this morning that I actually calculated anything — I think I had a dream about this last night that inspired this activity.
Heuristic #1: When you’re juggling, you have to apply an upward force to the ball to throw it and during this time the ball is perceived as heavier. The same goes for stopping the ball when you catch it. The fact that the ball in the air contributes nothing is counteracted by these other two forces.
Heuristic #2: The boat with the traveler and the balls is a closed system. It can’t get lighter unless it’s acted on by an outside force. This trick is like picking yourself up off the ground.
I’m pretty sure someone taking a freshman physics class would have the tools to bust this riddle. Imagine a piston that periodically launches and catches a ball. It’s straightforward to calculate the perceived weight of the ball during launching and catching and, including the zero weight during the flight of the ball, find that the time averaged weight of the ball is just the gravitational weight.