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

[bblais at BRYANT.EDU (Brian Blais)]

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



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