Re: Elastic potential energy

[Sandin <sandint@NCAT.EDU>]

In the 10th edition of Sears and Zemansky's University Physics, on pages
175 and 176 we derive the expression for the work done in stretching a
spring from its unstretched length to a length X via calculus and
graphically, then follow up with the work to stretch it from xsub1 to
xsub2.
Then on page 205, we relate the work done to the elastic potential energy,
emphasizing the U = 1/2 kx^2 equation. However, we also show expressions
for the change in U when x changes from xsub1 to xsub2. Also, at the
bottom of the page in a caution, we state that "x = 0 must be the position
at which the spring is neither stretched or compressed" in order to state
that U = 1/2 kx^2.
                                                Tom Sandin

On Fri, 16 Nov 2001, Justin Parke wrote:

> I agree.  I see my mistake (feeling rather silly) in not recognizing that 1/2 kx^2 comes from an integral where (typically) the force is zero at the origin.  I think it would be a useful discussion in a calculus-based introductory text.  (Any textbook writers out there?)
>
> Thanks for the comments
>
> Justin Parke