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Re: [Phys-l] FCI answer?



I would say that physics books that talk about an impulse perpendicular to
an initial trajectory doesn't change the energy is nonsense. If you are not
going to change the energy and only the direction with a single impulse it
must be angled opposite to the initial direction. It makes no difference
whether it is instantaneous or over a period of time.

Now if you talk about a series of instantaneous impulses each perpendicular
at each time, over a period of time, you get no change in energy only in the
limit as you go to an infinite number of such impulses. But the net impulse
averaged over the time will be angled back in the opposite direction of the
initial velocity. However, if you cut the trajectory into a finite number
of segments and do the calculation you will get a slight increase in energy,
which decreases as you go to the limit. But if you consider the "net force"
or "net impulse" over each segment, that is not perpendicular to the
original trajectory at the beginning of each segment. This net impulse will
produce no change in energy. This can be subtle!!!!

It is quite possible that they are interpreting the question as work energy.
But to have zero work energy the net impulse must be angled and not
perpendicular. I would say that if this is going on, then this question
should be classified as a fairly hard one because students must select the
appropriate model. Model selection is one the primary skills needed for
problem solving. A good test has both easy and hard questions to be able to
discriminate between students.

As to their being motion, a net impulse that produces V_k in the Y direction
will do so no matter what the horizontal velocity happens to be. The reason
for swift kick is so the student will not be as tempted to visualize a
curved trajectory. Then #8 explicitly asks which will be the trajectory
"after" the kick. This keys in the clue that the final trajectory must be a
straight line. Which further gives the clue to #9 that the velocities add
vectorially.

Perpendicular forces can produce no change in energy because they are
cancelled by other forces, or there is not motion in that direction, such as
the normal and gravitational forces for objects on inclined planes. They
can also produce no change in energy if they change direction as to always
be perpendicular. This is the case for circular motion. This problem is
carefully set up so that there should be no ambiguity about the fact that
the force always is only in one direction. Again students will often
confuse these cases because they have not separated the circular motion
model from the constant force model.

Minds on Physics actually has students consider the case of net forces which
will not produce changes in energy or speed. I don't know if Young does
that as I do not have a copy.

John M. Clement
Houston, TX


Thanks for all the interesting discussion. I agree that kinetic energy,
work, momentum and impulse are probably not in the view of what the
developers wanted to test. However, the published research shows that on
#9, the normalized gain is negative for the test groups. I would be
interested to see what the "incorrect" answers were on the post-test; I
speculate that many students interpreted the question in a work-energy
viewpoint. (It is still possible to get the correct answer to #8 with that
perspective since the arrows shown aren't drawn to scale. There need not
be a change in speed to have a change in direction.)

In addition, whether the writers intended to test only for vector
addition, the reality is that "good physics" must consider the work-energy
implications of the drawing and description. I take this position in light
of many problems in college texts (Young, for example) who describe
impulsive forces that don't change the KE, only the direction of the
velocity.

The fact of the kick on a stationary puck causing a speed of V_k
notwithstanding, the kick is NOT on a stationary puck, but a moving one.
And "swift kick" is physics problem talk for "instantaneous," isn't it?
Kind of like saying "a light string" in describing Atwood machines.

I think I understand the intent of the question, but I think it is poorly
described. Maybe it should be reworded as a "horizontal kick of short, but
finite, duration and constant direction." Then I would agree that it's
unambiguous.

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