"Bob Engelhardt" wrote in message
...
Let's say there's a lever with 3 forces acting on it:

1 2 3
V_________________________V____________V
/\

let F1, F2, & F3 be the forces and L1, L2, & L3 be the distances of those
forces from the fulcrum.

Then
F1*L1 = F2*L2 + F3*L3

Simple enough. Now, let's say that F1 is a fixed force (e.g., a weight
sitting on the lever). Then F2 & F3 could be any combination of forces,
as long as it balances.

Now say that points 2 & 3 are fixed. I.e., the lever is "tied down" at
those points. What are the forces acting on those tie downs? Is the
torque (moment of inertia, if you will) attributable to each equal, so
that the forces are inversely proportional to the distances? I.e.:
F2*L2 = F3*L3 (= 1/2 F1*L1)

It seems intuitively so, but if it is, how do you show that it is?

This has been bugging me for days, so any resolution that you can offer
will be greatly appreciated.

Bob

The answer is that there is nothing that fundamentally sets the ratio of
tensions at the two tie-downs. By lengthing one tie-down a smidgen, you
reduce the tension at that point and increase it at the other.

So then you will ask, "what if the lever is infinitely stiff as are both
tie-downs, and both tie downs have exactly equal length?" This is the same
class of question as "what happens when an infinite force meets an infinite
mass?" When you talk about a non-real world, you have to make up your own
rules. Depending on the rules of physics you create for infinite stiffness,
you might say there is no tension at 3 since it has all been relieved at
point 2.