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

I think it is fine to use words in ways that are new to our students. But
we should tell them clearly when we are doing this and if it is possible,
explain why. Many do arrive with clear, correct ideas about the words
"accelerate" and "decelerate". I think we have to make a clear case for
why we are going to define acceleration differently, as the slope of the
velocity graph.

I offer two reasons to do it this way:

1. When we get around to learning about forces, if we haven't already done
so, we will choose a direction to call the positive direction. The
opposite direction will be negative. If we use this new, less familiar way
of defining acceleration, one advantage is that positive forces will always
cause positive accelerations -- even though there are times when they will
cause an object to slow down. And negative forces will always cause
negative accelerations, even though they WON'T always cause the object to
slow down.

2. We are going to develop a collection of formulas that will be a
tool-kit for solving kinematics puzzles about freefall, projectiles, rocket
sleds and the like. Our unfamiliar, physics-teacher way of defining
acceleration will allow us to solve a range of puzzles with greater ease.
It's not impossible to solve them your way, but it is harder. (You will
have to break problems into multiple sections and solve each section, but
I'll be able to go in one swoop.)

I also think that some of the confusion for this particular item comes
because some students do know that velocity at the peak is zero but they
have a really fuzzy view of the difference between the words velocity and
acceleration. I find it helps if you ask them to describe the motion of an
object with zero acceleration. (I actually find that it is worth to ask
that question in class dozens of times over the course of a school year.)
If we can get them to agree that the velocity would remain constant in that
case, then they just have to ask themselves: does the ball at the peak
continue to have a constant velocity of zero? Only in cartoons...


One last question: suppose I were to ask this question of my students
(what is the acceleration of a vertically launched ball at its peak?)
having resolved to accept as correct the answer given by both groups -- the
ones who are using the "slope of velocity" definition and the ones who are
using rate of change of speed. What answer should I mark correct for that
second group? Seems like the "right" answer for them is: undefined. And
if they took my advice and drew a graph, their speed graph would have a
cusp.


On Mon, Jul 29, 2013 at 7:13 PM, John Denker <jsd@av8n.com> wrote:

You might be a redneck physicist if you always keep
a loaded trebuchet in the back of your truck.



On 07/29/2013 07:29 AM, William Maddox wrote:

If you do not like the
questions on Lapinski's list perhaps you could provide some questions
you have asked on an introductory physics test.

In some sense I do like that list of questions.
They are very thought-provoking. They are exactly the sort of
thing we should be discussing in this forum. More generally, we
should look very hard at any and all questions that consistently
stump the students. I hope other folks will post some more stumpers.

IMHO at the end of the course, physics should be intuitive, so we
really need to understand why students find some questions hard
and/or counterintuitive.

Sometimes questions are hard for a good reason ... but sometimes
they are hard for silly reasons, such as ambiguous terminology,
in which case we should rephrase the questions. I have already
suggested ways of rewriting some of them. Continuing down that
road:

On 07/29/2013 12:52 PM, Chuck Britton wrote:
Folks on the street indeed are likely to think of acceleration =
speeding up and deceleration = slowing down. therefore acc at top =
zero.

Yes! That's true and important.

My point is that the FotS (Folks on the Street) are not wrong.
1) Velocity is v; the rate-of-change of v is called acceleration.
2) Speed is |v|, the rate-of-change of |v| is called acceleration.
This definition is different, but not wrong. The concept of
scalar acceleration / deceleration is perfectly reasonable and
widely used.

The fact that we have one word with two different reasonable
meanings is not the students' fault!

On 07/29/2013 02:19 PM, Anthony Lapinski wrote:
a student in a physics class should answer it differently
(correctly). Acceleration = rate of change of velocity = gravity =
constant (in free fall).

Let's try looking at it from a slightly different angle.

On what basis "should" the student give answer (1) as opposed to (2)?

a) There's always the old "because I said so" rule. Students will
find this arbitrary and non-intuitive.

b) I find it very hard to defend the claim that the definition (2)
is wrong. Different yes; wrong no. People -- including physicists --
use the word this way every day.

c) AFAICT the best answer is that the laws of physics are *usually*
more conveniently expressed in terms of v and (d/dt)v than in terms
of |v| and (d/dt)|v|. This strikes me as an important, non-arbitrary
physics concept.

My point is, the original question did not focus on this point.
The important conceptual point was hiding behind an unimportant
terminological snafu.

What's worse, the original question asked about one-dimensional
motion, where the concepts of speed and velocity are very nearly
equally convenient, so in some sense this is the worst possible
scenario for fishing for concept (c).

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

General suggestion: If you want to get a better score, play a different
game. Ask questions that probe the concepts in a way that doesn't get
tangled up in the terminology ... and especially avoids terminology
that is known to be ambiguous.

Specific suggestion: If you are fishing for the conceptual answer (c),
ask a question that focuses much more tightly on this concept. As an
extreme example:
Question: The laws of physics are usually more conveniently formulated
in terms of
1) the position x, the velocity v, and the rate-of-change of velocity.
2) the position x, the speed |v|, and the rate-of-change of speed.

In general I cringe at multiple-guess questions, and in absolute terms
this is surely a bad question, but in relative terms it strikes me as
better than the original. In particular, if somebody gets the wrong
answer to the original question, I don't know how to interpret the
answer ... whereas with this question, if somebody it wrong, at least
we know where we stand.


Similar suggestion: If on the other hand you are fishing for the concept
that the acceleration of gravity, in the usual terrestrial reference frame,
is substantially constant over typical laboratory length scales, ask a
question that more directly probes for this concept.

For example: An object of mass m is thrown vertically upward. At times
a and b, it is on the way up. At time c, it is turning around. At times
d and e, it is on the way down. The usual spherical-cow assumptions apply:
terrestrial laboratory reference frame, laboratory length-scales,
negligible
friction, negligible buoyancy, et cetera.

c
|
|
b|
|d
|
a|
|e
|
|

Describe the force of gravity (direction and magnitude) at each of these
times (a,b,c,d, and e).

It seems to me, if a student gets the wrong answer to this one, we know
it is a conceptual problem, not a superficial terminological problem.

If this question seems too easy, there are lots of ways of making it
harder ... but I do /not/ recommend making it harder by hiding it
behind terminology that is known be both artificial and ambiguous.
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