Re: [Phys-l] Work and Energy: which first?

["John Clement" <clement@hal-pc.org>]

This is not actually my way.  This type of formalism is used by Modeling and
Minds on Physics.  Taking the average has a lot of appeal, but the area is
always correct.  The average. of course, does not work well for anything but
a linear graph.  Students do have the tendency to just multiply a value of
the force x distance and ignore the fact that the force is changing.  So
they either multiply by the initial value or the final value.  I suspect
that taking the average might help a bit with this problem, but would make
things more difficult for other cases.  MOP has some examples of curves
rather than just straight line examples, so the area becomes an important
method.  It also is bringing in calculus ideas without the formalism.

Defining the energy of a spring first has the advantage of defining energy
when the student can readily identify where it is stored.

I do not know of any research which shows which sequence works better.

John M. Clement
Houston, TX

> Subject: Re: [Phys-l] Work and Energy: which first?
>
> On Monday, June 12, 2006 8:42 PM, John Clement wrote:
> > Modeling defines the energy stored in a spring as the area
> > under the force distance curve for a spring.  Once the idea
> > of a spring storing energy is defined, other places to store
> > energy are related to this by experiments.
> <snip>
>
> This is slightly off-topic but...
>
> Why would you define the energy stored in a spring as "the area under
> the force distance curve" instead of "the product of the
> position-averaged force and the distance"?  I know they are equivalent -
> I just wonder about the pedagogical advantage of stating it your way.
> Is the idea of "average" too difficult for most students?  Is it too
> hard for many students to consider what a "position-based average" is
> compared to, say, a "time-based average"?
>
> By the way, has anyone tried to introduce work-energy by comparing the
> position-averaged force vs. the time-averaged force.  I can see some
> situations where it is straightforward to calculate the
> position-averaged force (like the Hookes-ideal spring) as opposed to the
> time-averaged force.  When written in terms of the former, N2L looks
> like:
>    F_avg dot Delta x = Delta (1/2 mv^2)
> In comparison, when written in terms of the latter, N2L looks like:
>    F_avg Delta t = Delta (mv)
>
> (Which version you use depends on which is easier for the situation at
> hand)
>
>
> ----------------------------------------------------------
> Robert A. Cohen, Department of Physics, East Stroudsburg University
> 570.422.3428   rcohen@po-box.esu.edu    http://www.esu.edu/~bbq
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