Re: [Phys-L] overdamping

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

Thanks!
In terms of energy:
The faster the object is moving through the fluid, the faster the kinetic energy of the object is being transformed into thermal energy.  If two objects of different masses but of the same size and shape are released from rest from the same stretched-spring position, at any same-for-each-object position on the way back to equilibrium, the spring will have given the same amount of energy to each of the objects, but because the lower mass object will have been moving faster on its way to that position, more of the energy it got from the spring will have been transformed into thermal energy.  So the total mechanical energy of the spring plus object (the energy stored in the spring plus the kinetic energy of the object associated with the movement of its center of mass through space) as a function of total distance traveled, decreases with increasing total distance traveled, more rapidly in the case of the lower mass object, meaning that the dampening is greater in the case of the lower mass object.

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Carl
> Mungan
> Sent: Wednesday, October 21, 2015 4:57 PM
> To: PHYS-L
> Subject: Re: [Phys-L] overdamping
>
> Most excellent. There’s one good answer to my second query: There’s an
> extra effect due to mass in the drag case, in addition to the regular F=ma
> effect of mass in both the spring and drag cases. Great. -Carl
>
> > On Oct 21, 2015, at 4:49 PM, Jeffrey Schnick <JSchnick@Anselm.Edu
> <mailto:JSchnick@anselm.edu>> wrote:
> > I think the idea is that with increasing mass the contribution to the
> acceleration made by the spring decreases in magnitude for one reason and
> the contribution to the acceleration made by the fluid decreases in
> magnitude for that same reason and another reason.  The first reason is that
> from F=ma, the greater the mass for the same force, the smaller the
> acceleration.  The additional reason for the case of the fluid is that, if we
> release the object from rest at maximum stretch, from the same position
> with different masses, even without dampening, at every position of the
> object on its way to the equilibrium position, the greater the mass, the
> smaller the velocity at that position.  With the fluid in place, the smaller
> velocity results in a smaller retarding force.  Thus, greater mass leads to less
> dampening.
>
>
> -----
> Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F) Naval
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