[Phys-L] Re: Energy is primary and fundamental?

[rlamont at POSTOFFICE.PROVIDENCE.EDU (rlamont)]

In order to use the equation

v_avg=(vf+vo)/2 = vf/2

one first needs to demonstrate that v is a linear function of
time, or equivalently, the acceleration is constant. That
linearity does not come from energy concepts, so energy is not
"fundamental" in this case. The kinematics of free fall is the
"fundamental" entity here and "energy" can be shown to be
consistent with it.

Likewise, a previous poster used y = 4.9 t^2. This also made the
kinematics of free fall the "fundamental" assumption in order to
solve the problem.

I would like to see a solution that does not appeal to the
solution itself in such a circular manner.

Bob at PC

> -----Original Message-----
> From: Forum for Physics Educators [mailto:PHYS-
> L@list1.ucc.nau.edu] On Behalf Of Brian Blais
> Sent: Wednesday, August 17, 2005 5:27 PM
> To: PHYS-L@LISTS.NAU.EDU
> Subject: Re: Energy is primary and fundamental?
>
> rlamont wrote:
> > What is your approach to the following simple problem? A ball
is
> > dropped from rest and falls for 5 seconds. Without using
> > acceleration, just energy, calculate its speed at the end of
the
> > 5 seconds?
>
> Since I put forward the proposal that one can cover just
conservation
> laws, and avoid acceleration and force, I will tell you how I
cover such
> problems.  Perhaps you don't like it, but I have found it
effective.
> Note that I said earlier that one cannot cover *all* topics in
this way:
> force is necessary sometimes.  I have felt, however, that in
the context
> of an intro physics for non-majors, conservation laws are more
flexible
> and powerful, and easier to cover than the notions of force.
>
> Now, on to the problem you proposed.
>
> I recognize that the energy approach for these types of
problems
> works
> best starting from distances and working to times, but it can
be done
> the other way (although it's a bit messy).  By the time I
introduce
> energy, we have already talked about instantaneous velocity and
> average
> velocity (using examples like commuting to Boston, where one's
> velocity
> changes all over yet it makes sense to the students to talk
about an
> average).
>
> To do the problem above (which I wouldn't just jump into) I
would do
> the
> following:
>
> v_avg=(vf+vo)/2 = vf/2  (in this case)
>
> mgh + 0 = 0 + 1/2 m vf^2    (eq 1)
>
> v_avg*t = h = vf *t/2
>
> solve for vf, plug into (eq 1) and solve for h.  I would plug
in the
> value of "t" early, to reduce the number of symbols.
Preferably we
> would have done enough problems before so that there is a
starting
> intuition.  I don't like to do a lot of albebraic
manipulations, because
> one loses sight of the big picture, but it is necessary
sometimes.
> also, the value of "g" I use is  10 J/kg m.  I think the units
are more
> intuitive this way (it takes 10 J to lift 1 kg by 1 m).
>
>
> does this help?
>
>                                 bb
>
>
>
> --
> -----------------
>
>              bblais@bryant.edu
>              http://web.bryant.edu/~bblais