Re: Spring Problem

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Wed, 29 Oct 1997 SSMOTHERMAN@MSCC.CC.TN.US wrote:

> 	We have a horizontal, unstretched spring connected at one end by a
> rigid support.  I want to apply a force at the other end to stretch the spring. 
> By the 3rd law, the force I exert to the right (F=kx) will always be equal in
> magnitude to the force that the spring exerts back to the left (F=-kx).  In
> this case, how can there ever be an acceleration of the end of the spring?

Footnote to my previous post:

Rereading the problem I note that you put emphasis on "the end of the
spring", and raise the question of how *it* (that end) can accelerate.
It's our old bugaboo of zeros and infinities we were talking about a
couple of days ago. A force to the right is exerted upon the end of the
spring by an external agent. The spring exerts and equal and opposite
force to the left on that end of the spring. If you consider "the end of
the spring" as a body, it has equal and opposite forces on it, so how can
it accelerate. Simple. The "end of the spring" has mass of zero, hence F =
ma becomes 0 = 0a, and any value of acceleration will satisfy the
equation. Now if you consider forces on any piece of the spring at the
end, even if only very small, then the two forces on it will not be equal,
but then, they aren't an action-reaction pair, either, since they both act
on *one* body.

	-- Donald

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Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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