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



I can comment on most of these questions. Some might seem underspecified,
but I listed them in general terms without all the specifics. Didn't mean
to confuse anyone. I wonder what questions teachers on this list ask their
students.

#1: Might have been better to ask what is the acceleration at any time (10
m/s2 downward as gravity is constant).

#2: Acceleration on incline depends on angle, so concave hill wins since
ball has highest acceleration at start.

#3: Car acceleration is constant. Balloon moves forward as it has less
inertia (like bubble in level with cart/pulley). These are similar.

#5: Both teams pull with same force (related to #4 -- like a two-person
game). Winner determined by friction on ground. Can show this with
two-person game with different shoes, or one person on skateboard, etc.

#8: Many think that a ball that sticks "carries" momentum to knock
something over, or they forget the vector notation of momentum with
rebounding ball.

#9: Application of Archimedes Principle. Maybe students confuse it with
density since ice floats?

#10: Students are just surprised with the answer.

#12: Kids think the ring expands inward. I ask them to think about
expanding a photograph of the ring or a donut, etc.

#13 "Three bulbs in series" is not vague, even without a diagram. Not sure
what the confusion is here. Kids just think electrons leave the negative
battery terminal, so the bulb closest to this should receive current
first. They forget what is happening at the other terminal and where the
electrons are in the circuit.

#14: This is asked after I teach about reflection, refraction,
diffraction, and interference.

#15: Mirror is fixed (can't be wiggled).

#16: Kids don't draw ray diagram. They see (2-D) ray diagrams in books and
inverted images with lenses. So they think if you cover the top half of a
lens, the bottom half of the image will disappear.

Kids just find these and other questions difficult. I wonder what others
on this list think about all of this.



Phys-L@Phys-L.org writes:
On 07/16/2013 02:53 PM, Anthony Lapinski sent us some thought-provoking
questions.

they stump most of my kids, even my "honors" ones.

We reeeeally need to understand why so many students consider these
questions "hard" and/or "counterintuitive".

I will say a few words about each of the questions, but first I have
a question of my own:

Have you taught your students how to handle ill-posed questions?

In particular, the first rule is this: Whenever you see a question
for the first time, ask yourself how badly ill-posed it is.

I suspect there are a lot of people on this list (and in the larger
community) who have not taught their students the first thing about
this. I did some googling. I got approximately

26,000 hits from: physics site:uchicago.edu
69 hits from: "ill-posed problem" site:uchicago.edu
16 hits from: physics "ill-posed problem" site:uchicago.edu
25 hits from: physics "regularizer" site:uchicago.edu

11,000 hits from: physics site:dartmouth.edu
30 hits from: "ill-posed problem" site:dartmouth.edu
15 hits from: physics "ill-posed problem" site:dartmouth.edu
2 hits from: physics "regularizer" site:dartmouth.edu

I surmise that it is possible -- indeed common -- for people to get
a PhD from a reputable institution without having any systematic
training in recognizing (let alone handling) ill-posed problems.

MOTION:

[1] Throw a ball straight upward. What is its acceleration at the peak?

As I have said many times before, ideas are primary and fundamental.
Terminology is tertiary. Terminology is important only insofar as it
helps us formulate and communicate the ideas.

I am not at all convinced that question [1] is a valid test of the
student's knowledge of physics principles, or thinking ability. It
could well be nothing more than an ESP exam and a vocabulary exam,
requiring the student to read the teacher's mind to figure out
whether the vector acceleration or the scalar acceleration was
intended.
http://www.av8n.com/physics/acceleration.htm

[2] The ball and three hill problem (constant angle, concave, and
convex) -
which hits the bottom first?

This is a simplified version of a famous problem, namely the world's
first "calculus of variations" problem. Is this really a test of
reasoning? Asking a high-school student can invent calculus and
then invent calculus of variations is asking a lot. More likely,
this is a test of whether the student remembers seeing the question
before.

FORCES:
[3] Helium balloon in car. When the car accelerates, which way does
the balloon move?

The question is grossly underspecified. The physics permits a wide
range of answers, depending on timescales and other details.

You could improve the question as follows:
There are two identical cars. Each has a helium balloon inside,
floating, tied to a string. The string is anchored at a fixed
point in the car. Both cars are closed and air-tight. Both
setups are identical, except that one car is at rest in the
conventional terrestrial lab frame, while the other is undergoing
a strong, steady, horizontal acceleration. Describe how the
acceleration affects this balloon. Compare it to the other balloon.

[4] Two equal masses attached to the ends of a string which passes over
a
pulley. What is the string tension?

Trivial if you understand force in terms of momentum flow.
http://www.av8n.com/physics/force-intro.htm

[5a] Tug-of-war -- which team pulls with more force?

Huh? You stumped me. See also item [5b].

[5b] What determines the winner?

Huh? Tug of war is complex. Victory depends on many factors, including
strategy, size, strength, endurance, and number of players on each side,
et cetera.

GRAVITATION:
[6] Orbiting astronauts in the ISS. They float, but is gravity
acting on them?

Gaack. This is the poster-child for ill-posed problems.
http://www.av8n.com/physics/ill-posed.htm
I have to wonder whether the person who cooked up this question
understands what "gravity" means.
http://www.av8n.com/physics/weight.htm#sec-various-notions

SPRINGS:
]7] Cut a spring in half, what happens to its stiffness?

Almost trivial if you understand force in terms of momentum flow,
http://www.av8n.com/physics/force-intro.htm
and if you have memorized the /terminology/ surrounding "stiffness".

MOMENTUM:
[8] To best knock something over, would you throw a ball that sticks
or one that rebounds?

Is this really a stumper? If so, I have to suspect that way
too much time was spent on forces, and not enough on momentum.

FLUIDS:
[9] When an ice cube melts in a glass of water, what happens to the
water level?

OK, that is a legitimately tricky question for non-experts.
There are a lot of ways to get it wrong. There are a lot
of things happening, many of which cancel to first order.
There is a "right" way of looking at it, but sophomoric
overconfidence could easily lead to settling on the wrong
answer before seeing the right answer.

[10] Stick your finger in a beaker of water on the scale (but don't
touch the
bottom). What happens to the scale reading?

That seems a lot less tricky. Maybe I'm missing something,
but I see several ways of getting this one right, and I don't
immediately see how to get it wrong.

HEAT:
[11] Why do some pots have copper bases and steel sides?

OK, that seems like an interesting real-world reasoning problem.
It requires knowing a significant amount about the real world,
starting with knowing the properties of materials (steel versus
copper) and also knowing how pots are used, and what makes a
"good" pot better than a "bad" pot.

[12] Ball and ring demo. Heat it -- what happens to the hole?

Trivial if you know the first thing about scaling laws.
http://www.av8n.com/physics/scaling.htm

ELECTRICITY:
[13] Three bulbs connected in series to a battery. Which bulb
receives current first?

This is another poster-child for ill-posed problems.
http://www.av8n.com/physics/ill-posed.htm
It is so amazingly underspecified that it makes my head spin.
If you show me an actual circuit, I can answer the question ...
but if you just paint a vague word-picture ("three bulbs")
it is so obviously unanswerable that I cannot imagine why
anybody would ask the question.

SOUND:
[14] What wave property is primarily responsibility for your voice
sounding louder through a (non-electric) cheerleader horn?

I can understand why this would be a stumper, for multiple reasons.
The typical HS physics book says a little about waves and a little
about geometrical optics, but says very little about the connection
between the two (physical optics). Asking students to invent this
branch of physics on the spot is asking a lot. Also, the book
typically talks mostly about one-dimensional waves, and maybe a
tiny tiny bit about two-dimensional wave. Asking students to leap
from there to three-dimensional waves is asking a lot.

On top of all that, this is a vocabulary exam. Even if the student
is able to picture the correct physics, it's not obvious what piece
of the physics should be considered "primarily" responsible, and
then hard to find just the right word to name this piece. (Multiple-
guess format would make the vocabulary problem much less acute.)

OPTICS:
[15] To see more of yourself in a plane mirror, should you hold the
mirror closer, farther, or do you need a larger mirror?

Several responses:

#1: This is the kind of question that Mazur was talking about, the
kind that makes people think physicists are crazy. Why not just
wiggle the mirror, the way people have been doing with real mirrors
for the last 6000 years or so? Or if the mirror is fixed, move
your head (aka motion parallax).

If that sort of thing was supposed to be forbidden, then the
question is wildly underspecified.

#2: Did you teach your students to _draw the diagram_ ???
Suppose you make enough assumptions and approximations to make
the question answerable, i.e. you assume the spherical cow in
the ivory tower. Then it's hard to get this question wrong if
you draw the diagram.

#3: The question as stated is not just underspecified; it is
actively misleading, because it seems to suggest that the answer
should be a function of the distance to the mirror. Anybody
who tries to figure this out using dimensional analysis is going
to crash and burn, because there are /two/ lengthscales in the
problem: the size of the person and the distance to the mirror.
Figuring out how the size of the mirror should scale as a function
of these two lengths is going to require /nondimensional/ scaling.
http://www.av8n.com/physics/scaling.htm#sec-non-dimensional

There's more to physics than dimensional analysis. Draw the diagram.

[16] If you cover the top half of a lens, what happens to the real
images
formed?

Draw the diagram already.

These are some of the many peer instruction questions I ask my (high
school) students for the topics I teach. Very practical and
counterintuitive as they stump most of my kids, even my "honors" ones.
Would your students find these counterintuitive? These questions are
intended to make students think in ways they never have before. And
thinking (and, thus, physics) is difficult.

I mostly disagree with the conclusion.

I see it as more like riding a bicycle. If you don't know how to do
it, it's scary and ultra-difficult. On the other hand, after you
learn how to do it, under ordinary conditions the basic task is not
at all tricky. On the third hand, no matter what you are doing, if
you push it to extremes, it becomes difficult, such as racing up the
Pike's Peak road in a blizzard.

Education is the process of cultivating the intuition. Our goal as
teachers should be to make the basic physics principles /become/
completely intuitive. I don't care where they start out, so long
as they /end up/ being intuitive.

Some of the questions on the foregoing list are hard for a reason,
but others such as [6] shouldn't be hard. AFAICT the only reason
[6] seems hard is because (a) the textbook gets the physics wrong,
(b) the teacher also gets the physics wrong, and (c) students have
no clue how to handle ill-posed problems.

Note that most questions graduates will encounter in the real world
will be ill-posed, unless they get a job where their primary duty
is asking "Would you like fries with that?"

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