Re: Spring potential energy without Work (sort of)

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

On Monday, October 15, 2001 2:59 PM, RAUBER, JOEL wrote:
> [snip]
> 3) The spring requires some calculus, which shouldn't
> surprise us since it
> is an example of a force that produces a non-constant
> acceleration when it
> is the only force acting on an object.  And algebra based
> courses tend to
> require some handwaving when treating such forces (or at least their
> kinematics when working with instantaneous quantities).
> [snip]

It seems to me that it involves as much calculus as deriving (1/2 mv^2).
This is usually done (in an algebra course) by stating that if v
increases linearly with time then v_avg = (v_i + v_f)/2.  If this hand-
waving works, then we might as well say that if F increases linearly
with distance then F_avg = (F_i + F_f)/2, no?*

Is this hand-waving somehow worse than the hand-waving performed to get
v_f^2 = v_i^2 + 2 a Delta x?

*[since F = kx, then
F_avg*Delta x = k (x_i + x_f)*(x_f - x_i)/2 = 1/2 k Delta (x^2).]

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| rcohen@po-box.esu.edu      East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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