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Originally posted by Feynman
Please let me cross the bridge before you cross it. 
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Depends on how much ya weigh there Feynman...
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Juggling them means that he has to throw them
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Actually it doesn't mean that at all; one could do a drop juggle (lifting and releasing bundles) and never have to throw them, merely lift and release...
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The bigger the bundles, larger the movements he has to make and the longer the bundles have to remain into the air.
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Bigger bundles do not matter, I think you might be referring to mass. As gravity is fairly constant across the length of said bridge (and rest of the Earth for that matter), bundles of similar shape would fall (accelerate downward) at pretty much the same change in velocity (delta v)... ;o)
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The longer the bundle have to remain into the air, the faster he has to throw them upwards.
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Not sure what you are referring to here, when juggling 3 objects, you are never in contact with more than one object at any one time. Yes, if you want a 5 stone bundle to reach the same position in the air as a 1 stone bundle, it will require more delta v exerted on it.
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the faster he has to throw them upward, the more reaction will be exerted by his throwing them of into the air.
I.e. the very act of throwing them into the air increases the force he exerts on the bridge (his weight plus the downward reaction from the accelerating of the bundle upward).
I won't get into calculations, but my intuition is that the average weight increase caused by the accelerating the three bundles to launch them into the air is exactly the weight of the three bundles. Assuming you would have constant acceleration and zero delay between the load switch. Accounting for friction and other losses and inefficiencies, it is actually more. And if you have the slightest delay between switching of the loads, the peak reaction will be more than three times the weight.
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Yes, to throw them upwards would increase the force (f=m*delta v) he acts on the bridge, but also the force the bridge acts on him; however, there are many ways that this force could be handled... he could get on his knees or lay on his back and skootch across the bridge... He could time his throws when both of his feet are off the bridge... any number of ways this could be addressed... The MASS of him plus one (or even two) bundles though would never be as great as that of him plus all three bundles... Reading the original question you will see it was geared toward weight (m*g) solution rather than a force equation.
As for the increase of force being too great, perhaps this quick demonstration will paint a clearer picture for you... Step on a bathroom scale holding an object (or two or three if you can juggle), watch the reading, toss an object into the air or begin juggling while looking at the needle... I don't believe it should ever go over your original reading... ;o)
Oh... from information given (at constant temp), the scale would decrease the further the fly moved away from the base of the jar always approaching the true weight (mass * gravity) of the sealed jar.