Friction is a complicated topic. The discussion over the last couple of
days has hardly scratched the surface, so to speak.
Consider the following setup: Two large blocks separated by something else
which (if it is macroscopic) we can call a "cart" or "bearing" or (if it is
microscopic) we can call a "lubricant".
__________________
| |
| |
| | <---- force F1
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where each O===O symbolizes a thin little cart with wheels. The carts form
a bearing between the two blocks. The lower block is constrained to not move.
1) First consider the case where there is no friction anywhere. The upper
block, with no applied force, can slide with constant velocity V, rolling
on the top of the cart-wheels. The lower block is stationary, and the
carts move with velocity V/2.
2a) Second, consider the case where the carts have little brakes on their
wheels. Now to make the upper block move with velocity V, we must apply a
steady force F1. For any given V we choose F1 so that no acceleration
occurs, because F1 is just balanced by an equal and opposite force F2
applied by the cart-wheels to the bottom of the upper block.
There is no change in the macroscopic kinetic energy of the upper block.
There is no change in its temperature, either, because I have constructed
the little carts so that whatever energy is dissipated in their brakes is
radiated into the *lower* block.
In this case, there is obviously no *net* work being done on the upper
block. Obviously the force F1 is doing work on the upper block. By any
reasonable definition, the force F2 is doing an equal and opposite amount
of work on the upper block. Since F2 is modelling friction for us, we can
see that in this case frictional forces *are* doing work on the upper block.
2b) We can also turn the little carts over so that their braking energy is
radiated into the upper block. In this case there is still no work being
done on the upper block, but heat being added.
2c) More generally, there can be an arbitrary partition of the dissipated
heat. Some can be stored in the lubricant, some can go into the upper
block, some can go into the lower block, some can be radiated directly into
outer space, or whatever. Almost anything is possible. Any claims that
friction "always" does one thing or the other are indefensible.
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Also note that simple "force dot dx" work arguments are slightly tricky in
this case, because there are several different "dx"s in very close
proximity. Is dx the distance the upper block moved, or the distance the
lower block moved, or the distance the lubricant moved, or what? The
calculations are quite doable. It's just physics. But you have to be careful.
Finally note that if we retain the friction but get rid of the driving
force F1 and allow the upper block to coast to a stop under the influence
of friction, the problem is relatively easy to analyze in the lab frame and
rather tricky to analyze in the frame attached to the upper block --
because the latter is an accelerated reference frame. Most students lack
the sophistication to correctly account for energy in such a frame.
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copyright (C) 1999 John S. Denker jsd@monmouth.com