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

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

Why do you say "the average...does not work well for anything but a
linear graph"?  In what way does the average force not work as well as
the area under the curve?

I am also intrigued by your statement that the area-under-a-curve method
"[brings] in calculus ideas without the formalism."  Doesn't the
average-force method also bring in the same calculus ideas?

I must be missing something because the two ways seem equivalent (except
that, pedagogically, as JC points out, the average-force method may
better address the tendency of students to take either the initial or
final force values).


----------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@po-box.esu.edu    http://www.esu.edu/~bbq 

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu 
> [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf 
> Of John Clement
> Sent: Tuesday, June 13, 2006 12:35 PM
> To: 'Forum for Physics Educators'
> Subject: Re: [Phys-l] Work and Energy: which first?
>
> 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