by Bill Graham

Does the juggler get wet?

Throwing a one-pound nugget several feet into the air requires the man to apply a force significantly greater than one pound in order to accelerate the nugget upward.

Sir Isaac Newton (one of my heroes) stated in his second law of motion that Force = Mass times Acceleration (f = ma). According to the third law of motion, every force has an equal and opposite reaction force.

So, the tossed nugget is creating a downward force on the juggler and on the bridge. Besides, every time the juggler catches the nugget, it exerts a significant downward force on him.

If you watch a juggler with three balls, you'll note that the juggler is only holding one ball at a time. Two balls are in the air. As each ball is caught, it must have its downward motion changed to an upward motion, and this acceleration must counter the acceleration of gravity as well.

The best possible scenario for the juggler is that the acceleration while in a hand is constant and that each nugget is in the air exactly two-thirds of the time. For ease of calculation, assume that the catch and release heights are the same. If the release speed is v, the the catch speed is -v. The time to reach the top of the trajectory for a nugget is simply t = v/g. The speed of the caught nugget must change by 2v in that time, making the acceleration 2v/t = 2g. Thus, the force on the juggler is the mass times this acceleration plus the acceleration of gravity or 3mg, which is three times the weight of the nugget or three pounds.

As you can see, the juggler cannot escape the laws of physics. Even with perfect juggling, not an ounce is saved. Imperfect juggling would create an even larger force. The total weight of the juggler and nuggets remains at least 201 pounds. He is definitely going to get wet.

Birds in a cage and a scale

The force of the air on a bird’s wings necessary to keep the bird in the air is equal to the bird’s weight. The birds’ wings are pushing down on the air, and the some of that air is pushing down on the bottom of the cage.

If the cage is a closed box, the force of the air pushing down on the bottom of the cage would equal the weight of the birds in the air. However, since the birds’ flight isn’t perfectly constant and level, the weight of the cage would vary slightly more and less than 25 pounds with the average being 25 pounds.

Because the air can get out of the sides of an open cage without exerting force on the cage bottom, the weight of the cage would certainly be less than 25 pounds. The weight would exceed 20 pounds by an amount which depends on the geometry of the cage and birds. That’s the theoretical answer. I wonder if anyone has ever tried this experiment?

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Contents copyright 2005 by Bill Graham and ParaComp, Inc. All rights reserved.
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