Lillian C. McDermott
43
History
3/15/10
First mark
Second mark
Top view
Frictionless table
m
B
> m
A
F
o
A
F
o
B
Momentum and energy comparison experiment.
During the interview, students are asked to compare the final kinetic energies and
momenta of two dry-ice pucks (one brass and one plastic) that move on a glass table, as
shown in the accompanying figure.
A constant force
(F)
is applied by a steady stream of
compressed air in a direction perpendicular to two parallel lines.
The pucks start from rest
at line A and move in a straight line, not rotating and essentially without friction, to line B.
A correct explanation was necessary for a correct response.
The comparisons can
be made by direct application of the work-energy and impulse-momentum theorems.
Since the force is constant and parallel to the displacement
(
Δ
x)
, the theorems reduce to
F
Δ
x
=
Δ
K
and
F
Δ
t
=
Δ
p
.
The change in kinetic energy of the blocks (considered as point
particles) equals the work done by the external force and is the same for both pucks.
Since the same force is applied to both, the brass puck acquires a smaller acceleration
(F =
ma)
.
During the longer time the brass puck spends between the lines, it receives a greater
impulse and hence experiences a greater change in momentum than the plastic puck.
(A
correct comparison of the final momenta of the pucks also follows from the equality of the
kinetic energies and the algebraic relationship between kinetic energy and momentum.)
The 28 students who participated in the interviews were volunteers from two
introductory physics courses at UW.
There were 16 from the algebra-based course and 12
from the honors section of the calculus-based course.
The average of their final grades
was higher than the average for the classes in which they were enrolled.
Only about half
the students in the honors section gave correct responses with correct explanations.
None
from the other course did.
Following is an example from one of the interviews.
I:
What ideas do you have about the term work?
Lillian C. McDermott
44
History
3/15/10
S:
Well, the definition that they give you is that it is the amount of force applied
times the distance.
I: Okay.
Is that related at all to what we’ve seen here?
S:
Well, you do a certain amount of work on it for the distance between the two
green lines.
You are applying a force for that distance, and after that point it’s
going at a constant velocity with no forces acting on it.
I:
Okay, so we do the same amount of work on the two pucks or different?
S: We do the same amount.
I:
Does that help us decide about the kinetic energy or momentum?
S: Well, work equals the change in kinetic energy, so you are going from zero
kinetic energy to a certain amount afterwards…so work is done on each
one…but the velocities and masses are different so they [the kinetic energies]
are not necessarily the same.
The interview excerpt above demonstrates that, even if correct, the responses on
multiple-choice tests do not necessarily indicate understanding.
Probing in depth is
necessary for an accurate assessment.
Had the questioning been terminated earlier, it
would have seemed as if the student understood the relationship between the work done
and the change in kinetic energy.
It was only by continuing to probe that the investigator
was able to determine by his last question that the student did not really connect the actual
motion of the pucks with the work-energy theorem.
The tutorial (
Changes in Energy and Momentum
) that we developed on this
material has two parts.
The first guides students through the reasoning needed to compare
the momenta and energies of the two pucks in the demonstration used in the interviews.
The second part extends the application of the theorems to motion in more than one
dimension and is more difficult.
We use it only in the honors section of the introductory
calculus-based course and in some of the workshops that we conduct for faculty.
In 1992
The Physics Teacher
published results from the administration of the
Mechanics Baseline Test
(
MBT
) at eight universities and high schools.
88
Two questions on
the
MBT
were based on the impulse-momentum and work-energy comparison tasks
developed by Ron Lawson.
We gave the
MBT
version of these tasks as a post-test to
about 400 students in the calculus-based course after they had worked through the tutorial
on the two theorems.
To our dismay, we noted that the nationally reported
MBT
results
were significantly better than those of the UW students.
When we re-analyzed the UW
88
D. Hestenes and M. Wells, “A mechanics baseline test,”
Phys. Teach.
30
(3), 159-166 (1992).
