Re: [Phys-L] ?conservation of _internal_ energy

[Herbert Schulz <herbs@wideopenwest.com>]

> On Jan 14, 2016, at 1:48 PM, John Denker <jsd@av8n.com> wrote:
>
> On 01/14/2016 12:26 PM, Herbert Schulz wrote:
>
> > Why certainly work is being done by the `blue' box on the `red' box
> > and the `red' box on the `blue' box via the interactive forces (which
> > must be equal and opposite in direction of course).
>
> You keep saying that, without proof ... indeed without evidence.
>
> Here's my evidence.  
>
> 1) The only "interactive force" is the contact force at the 
>  point of contact.  By symmetry, there is no displacement at
>  this point.  By definition, work is F·dx.  Here dx is zero.
>  Therefore no work.  For details see
>     https://www.av8n.com/physics/thermo/state-func.html#sec-internal-energy

Howdy,

Work isn't being done on the CM of the System (both boxes together) but certainly the spring is pushing against the spring in the red box and that box DOES move so the work done on it by the red box is non-zero. And visa versa.

How about grabbing the two ends of a spring and stretching it. The center point of the Spring doesn't move but you certainly are doing work on the spring which is going into Potential Energy.

> 2) You could equally well replace the red system by a rigid
>  infinitely-massive wall.  Again the displacement of the point
>  of contact is zero and therefore the work is zero.
>
>  As another way of obtaining the same result, the energy 
>  transferred to the wall is p^2/(2M) where M goes to infinity,
>  so the mechanical energy transfer (aka work) is zero.
>
>  Are you claiming you can do work against the proverbial
>  brick wall?  Really?

Howdy,

When the mass goes to infinity strange things can happen! M may go to infinity but what about p? As M gets larger v gets smaller and it can go to anything. Also remember that perfectly rigid walls are, in reality, impossible; even a real brick wall can have energy transferred to it (via microscopic flexing). So a totally rigid, infinitely massive wall is a fiction but a useful concept.


> If you think my analysis is wrong, please explain where it
> goes wrong and/or provide a comparably-specific argument that
> produces a different answer.

Let's see... the Spring/box pushes against the wall with some force. Therefore the wall pushes back against the Spring/box with an equal but opposite force. That causes the box/Spring to accelerate and move (i.e., it has finite mass) so work is being done by that force on the Spring/box.

Good Luck,

Herb Schulz
(herbs at wideopenwest dot com)