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From: tmb@talcott.UUCP (Thomas M. Breuel)
Newsgroups: net.physics
Subject: Re: cancelling forces
Message-ID: <511@talcott.UUCP>
Date: Fri, 20-Sep-85 11:04:18 EDT
Article-I.D.: talcott.511
Posted: Fri Sep 20 11:04:18 1985
Date-Received: Sun, 22-Sep-85 16:32:23 EDT
References: <546@sri-arpa.ARPA>
Organization: Harvard University
Lines: 59

In article <546@sri-arpa.ARPA>, sloan@uw-tanga.arpa writes:
> From:  Kenneth Sloan 
> 
> 
> Here's a new subject to think about, start aguments, etc.
> 
> Let's say I have a robot that pushes a box.  I put a certain amount of
> energy into it, and get most of that energy out as work performed on
> the box (the rest being lost to maintain the robot's life support systems).
> 
> Now I set up another one of these, and place it alongside the first
> robot.  I have them push in the same direction so that the forces add.
> Now the output of this system is a moving box with the same direction
> and twice the speed.  I'm putting twice as much energy in and getting
> twice as much energy out.
> 
> Here's the question...  If I place them on opposite sides of the box,
> the pushes will cancel.  Now I appear to be getting no energy out of
> this system, at least not in the form of a moving box.  I am still
> putting as much energy into the system.  All I did was move one of the
> devices.  What is happening to the energy?  Is there an output in
> another form of energy?  Is it building up in one of the devices
> somewhere?
> 
> -Ken Sloan


There are several types of energy in the system:

-- internal energy (the robot's internal battery)
-- kinetic energy (the energy stored in the motion of the boxes and the robots)
-- thermal energy (energy that is essentially lost)
-- stress energy (stored in the 'shape' of materials)

If one robot pushes one box, it converts internal energy into
kinetic energy. During the motion, part of that kinetic energy
is converted into thermal energy by friction. At the end of
the motion, the robot can recover what is left of the kinetic
energy and convert it back into internal energy, or can
just convert it into thermal energy with a simple mechanical brake.
(Note that by conservation of momentum, the kinetic energy is
stored in the relative motion of robot-box to the planet that
they are on). If there is no friction and no internal losses,
the whole process does not require any net energy.

If two robots push two boxes into one another, they convert
internal energy into stress energy. As in the case of kinetic
energy, in the real world, some of that stress energy is
necessarily lost and converted into heat, both during the
deformation (friction) and while the force on the bodies is
maintained (deformation). When the robots stop pushing,
they again have the choice of converting the stress energy
back into internal energy or of converting the stress energy
into heat.

Altogether, the 'paradox' exists only because many people still
have pre-Newtonian ideas about 'energy', 'momentum', 'force' &c.

					Thomas.