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# Confering its nature (was "are normal ...?")

John Mallinckrodt wrote (in part):

First of all, it is misleading to suggest that gravity might
"cause" a tension or normal force and, somehow, confer its
conservative nature to the tension or normal force.

True for gravitational but not for electrostatic interactions.
Consider two positively charged objects which attract each
other gravitationally. An equilibrium will be established
when attractive and repulsive forces are equal. In this case
we can say that one mass rests on another and that the
reaction force (really an electric force) is conservative. Is
the conservative nature of the electric force "conferred to"
the normal force? I would think so.

The same is true for a common case in which normal
forces are identified with perfectly elastic forces. JohnM
made this clear by writing that

to be a *candidate* for being "conservative," a force
must be directly calculable from a "configuration."
For instance, ... the spring force is determined from
the extension of the spring.

Once the common assumption of rigidity is removed
the normal forces can be said to be conservative, to the
first approximation, as explained by by JohnM:

On the other hand it's easy to relax the "inextensible" and
"perfectly rigid" assumptions. After all, an extensible rope is a
"spring" and a nonperfectly rigid surface is a "trampoline"--a
more complicated "spring." Then, one may be able to calculate the
force from the strain and consider the force to be conservative.
Note carefully, however, that the conservative nature is connected
with an ability of the spring or the trampoline *itself* to store
potential energy; that energy should not be considered to be
stored in the supported body or even in the interaction of the
supported body with the spring or trampoline.

Finally, note that real ropes and real surfaces are generally at
least somewhat "dissipative." They exert forces that are not
completely calculable from their configurations and may exhibit
hysteresis and/or velocity-dependence. For instance, a rope may
(and usually does) exert a stronger pull at each specific length
while being extended than when it is subsequently allowed to
relax. As a result, the work done *by* an external agent to
extend the rope is smaller than the work done *on* the external
agent as it is allowed to relax.

I was very surprised to find out that the author of the original
question is a seven-years-old child. This reminded me about
another exceptional student described on our list about 10 years
ago. His name was Christopher (?) and he was able to solve
complicated physics and mathematics problems in very creative
ways. Where is he now? Is he still as creative as he was nearly