Re: Work/Energy Theorem

["Eugene P. Mosca" <mosca@nadn.navy.mil>]

Hi Jim, you wrote:

> Is the so called work-energy theorem absolute?
 
 
The work-energy theorem is gotten by integrating F = ma.  For a particle
this gives the work done by the net force equals the change in the
particle's kinetic energy.  This, however, is only valid for a particle.  

Newton's second law for systems is F_ext_ = m*A_cm_.  Integrating it give
the so called pseudowork-energy theorem--that the net pseudowork, the sum
of the external forces times the displacement of the center of mass (for
non-constant forces this is an integral), equals the change in that part
of the kinetic energy associated with the speed of the center of mass
0.5*M*(V_cm_)^2.

> Can the kinetic energy of an object/system change if no work is done
> to/by the object/system? 

It sure can.  Imagine standing still on a frictionless surface and then
pushing off a wall to get yourself moving.  Since the points of
application of either the force on you or the force on the wall do not
move, no work is done either on or by you.  However, you do gain kinetic
energy as you slide away from the wall. 

By the way, it is interesting--at least to me--that while the work done by
a force is frame dependent, the work done by an action/reaction force pair
is frame independent.  That is, the work done by an action-reaction pair
is an Galillean invariant. 

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Eugene (Gene) P. Mosca           Phone 410-293-6659 (Fax 3729)
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