On 11/09/2003 05:39 AM, Robert J. Beichner wrote:
> ... Bruce Sherwood... His favorite example: you apply a force F and
> slide a block a distance d across a rough surface. The work you've
> done is just Fd. Meanwhile, a frictional force, f, is opposing the
> block's motion. If there is no acceleration, F and f have the same
> magnitude. Since the change in KE is zero, the net work done is zero.
> Most people indicate this as Fd - fd = 0.
Then most people need to be more careful.
> All the energy is accounted for
No, it is not.
> ... but the block gets warmer! Where does that energy come from?
It "comes from" a proper accounting of the force, distance,
work, and energy.
In particular you must distinguish
-- the microscopic force versus the average force.
-- the microscopic displacement versus the average displacement
-- etc. etc. etc.
Once you make these distinctions, you can see that
taking averages does not commute with taking dot
products. That is, (the average of F dot dx) is not
(the average of F) dot (the average of dx).