Date: Thu Dec 20 14:46:16 2007

Author: William McNairy

Subject: Re: two questions

This sounds like a demo opportunity for Dick Berg!

There was a comic several years ago on the same topic: "Shylock Fox"
wanted to cross a suspension bridge with three rocks that, with his
weight, exceeded the capacity of the bridge. The answer to the riddle
was to have him juggle the rocks while crossing the bridge... Oops,
another physics error. (Did anyone catch the error in "Garfield" a few
weeks ago? See for one
version of the incorrect holiday optics. I added this one to my final
exam this semester as a multiple choice question...).

If one neglects air drag, then the average force on the system should
not change from having everything at rest as the center of mass does not

However, in the presence of air drag, then I think things change as the
average speed of the mass(es) will be greater on the way up than on the
way down, so the drag force will be greater. How does this affect the
total impulse, however? I think the juggler has to provide more impulse
to the balls to throw them up than s/he does to catch them (delta v in
this case for the balls has a greater upward term than the negative
downward term), so I would think the average force on the air by the
balls is directed UP. Thus I would expect the measured average weight
of the juggler+balls to increase while the balls are being juggled.

Dick, can you rig up a water pump with a vertically directed jet, having
a catch basin/reservoir, all on a sensitive scale to test this out?? (I
assume one can neglect the mass lost due to evaporation for short
experimental runs-- I'd shudder to think you'd try it with mercury....)

Cheers to all.


PS I noticed that Dick didn't use the 330 lb capacity of the scales in
his video-- he barely used half of it (if indeed that was him standing
on the scale during the ballistic cardio demo)...

Paul Nord wrote:
> Um... now I'm full of doubts.
> You're adding energy to the system. Imagine a constant stream of
> balls going up and coming down... or a stream of water.
> The mass of water in-flight is going to lower the mass in the tank and
> also the force the tank exerts on the ground. But the force of water
> going up and coming back down is going to increase the force on the
> ground. You're saying they're the same. If I spray higher, or with
> more force, it will increase the hang time and the mass of water in
> flight.
> Ok, now I'm confused. Someone help me out here.
> Paul
> On Dec 20, 2007, at 12:22 PM, J. Terrence Klopcic wrote:
>> A comment on the Juggling counter-example. It is true that the
>> juggler exerts an extra force on the floor both when he/she throws
>> and catches the ball. However, the statement that there is a net
>> increase in the time-averaged force needs a footnote. The increase
>> in the time averaged force is, I believe, the same as if he/she had
>> just stood there holding the ball. (If I haven't erred in my quick
>> algebra, that is a cute result, isn't it?)