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Re: [Phys-L] [SPAM] Re: The Make-Believe World of Real World Physics

I'm going to come out of left field with this, if you know what I mean. I think there are at least two good reasons for starting with average velocity problems.

The first is that is all we really can experience in our lives. Instantaneous quantities are mathematical idealizations, and not directly in our experience. So if we want to begin concretely with our own experiences, there we are. Thinking it this why leads to a natural set of developmental questions when we know the velocity is indeed changing. Working with students to figure out how to do that gives a rationale for the development of kinematics.

Second, problem solving is the 800 lb gorilla in the room. Students have great difficulty at all levels transforming real situations into mathematically tractable solutions. By using constant speed and then average speed, we can reduce the cognitive load so they can work on problem solving skills. As the physics concepts grow you can transform similar problems so that the cognitive load now shifts to the physical side.

For example, I like one of the Heller rich context problems that goes something like this. One day I was walking around the lake and I saw my friend pass me by walking the other way at a constant speed. I said hey and kept going at a constant speed. A bit later I remembered that I had a message for my friend, but didn't have my cell with me. So I wondered when I would meet my friend again as we walk around the lake.

This problem is beyond just the d=vt because it involves two motions and setting some things equal, so it is a good next step for developing problem solving skills. Once the student figure out how to solve this, you can change it to add more physics. You could have one person stop for while, or move faster or slower, lots of wrinkles that add new physics ideas about motion, but the overall solution strategy of multiple equations and setting some thing equal remains.

So I think constant speed and average velocity questions have real place because they connect with our experience and the allow the reduction of cognitive load when developing problem solving skills.

Others have talked about the acceleration at the top of a vertical motion. I would use this as a tool to engage students. Let them say that the acceleration at the top is zero. Then ask what is the velocity at the top, and they will likely say zero. Then I ask, doesn't the acceleration tell us about how the velocity is changing. We can work on that for a while to get to yes it does and the velocity is therefore not changing. So if the object has a zero velocity and its velocity is not changing what would we predict it would do, and does it do that? So we have some rethinking to do. There are lots of pitfalls in this business and this questions embodies many of them, so I try to tread lightly and lead them rather than try to tell them something they do not believe.

joe

On Jul 30, 2013, at 5:41 AM, Anthony Lapinski wrote:

I've always done these types of problems. Basic d = vt with applications,
like most other equations in physics. We do sample problems in class, and
they try similar ones for homework. I give them the tools. No tricks. I am
surprised about some teacher reactions to doing these kids of problems,
the most basic ones in physics.

Curious what others think about this.


Phys-L@Phys-L.org writes:
On 07/29/2013 06:40 PM, Paul Lulai wrote:
I think this question (how fast / far to have a certain avg speed) is
a lot of work that isnt worth the payoff and is also a bit of a
trap. It feels like we are baiting them into trying to do it
incorrectly. I am sure there are science & technical folks that do a
lot with average speed, but we do next to nothing with it in high
school, except ask trick questions like this one. I suppose it is a
way to check the difference btn speed and the vector nature of
velocity. It just seems like there would be other ways that could
check the same conceptual point and be less misleading. I don't do
much at all w avg speed. While I am sure it can be helpful in some
situations, this isnt an area I am going to go crazy preparing for.

Several follow-up points:

1) This is a moving target:

1a) In the early part of the introductory high-school
course, there are lots of good reasons to stay away
from these "inverse speed" problems.

1b) OTOH suppose it's a college course. The students are
seeing all this stuff for the second time, and they know
a little bit of calculus. Then you could make a pretty
good case for including such problems. These have some
direct real-world applications.

Example: Suppose you are riding your bike on a hilly
course. It's half uphill and half downhill.
Strategy A: With ordinary effort, you can go 12 mph
on the uphills and 24 mph on the downhills.
Strategy B: You realize that with extra effort, you
can go 1 mph faster (13 mph) on the uphills. However,
at this point you are limited by your cardiopulmonary
capacity, so the only way you can sustain this is to
take it easy on the downhills, so you go 3 mph slower
(21 mph).

So, the question arises, is strategy B faster than
strategy A? Is it even remotely possible that gaining
1 mph uphill is worth losing 3 mph downhill?

The further question arises: How do we understand this?

============================

2) This is a fine illustration of the point I have been
making: if you don't have the tools to answer this question,
it is indeed hard and scary and counterintuitive. On the
other hand, if you do have the tools, it's no big deal.

Furthermore, the tools that you need to deal with this
question are tools that you want to learn anyway, because
they have many other applications.

We agree that leading students into a trap is a monumentally
bad idea. It is better to teach them how to swim /before/
throwing them into deep water.

Hint: I like to think in terms of /weighted averaging/.
*) If you are averaging over time, you want the average
of the velocity.
*) If you are averaging over distance, you want the
average over the _inverse velocity_.
-- Note that taking the inverse is a nonlinear operation,
and it does _not_ commute with taking the average.

Further hint: You can understand the effect of small
/changes/ in speed by expanding things to first order.

The students grew up on a steady diet of simple linear
problems. This is fine as a starting point, but not as
an ending point. Real life is highly nonlinear. At
some point they need to learn how to deal with this.
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l


_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l

Joseph J. Bellina, Jr. Ph.D.
Emeritus Professor of Physics
Co-Director
Northern Indiana Science, Mathematics, and Engineering Collaborative
574-276-8294
inquirybellina@comcast.net