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

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

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