Misconceptions in Mechanics in First Year Engineering Students
CELEMIN, Miguel 1 & COVIAN, Enrique
1Avda. de Portugal,41, 24071-Leon (SPAIN),
Universidad de Leon,
dfqmcm@isidoro.unileon.es
Abstract: In March, 1992, the paper: The Force
Concept Inventory (Hestenes, Wells and Swackhamer), was
published in the March issue of The Physics Teacher. The FCI
is a 29 multiple choice questions test concerning the
Newtonian concept of force. The FCI can be used for
evaluating instruction - by means of the analysis of the
correct choices - and also, as a diagnostic tool, for
identifying and classifying misconceptions. As it is
generally known, misconceptions are common-sense beliefs
about motion and force that are incompatible with Newtonian
mechanics.
The FCI was translated into the Spanish language by the
first author of this paper. When the FCI was given to the
first year engineering students of different Spanish
universities, not only the correct choice to each of the 29
questions was asked for, justification to each choice was
also required and then examined. It has been observed that a
lot of students did not know to justify an important
percentage of their correct choices. Influence of
justification has already been reported in a previous paper.
Incorrect choices inform about the existence of
misconceptions these ones classified according
Hestenes's taxonomy. The FCI was first given, in Spain,
in 1992, to the first year agricultural engineering students
of engineering at the University of Leon; after that, it has
been applied to other first year students at different
Spanish universities. In this paper, the results got in Spain
by means of the FCI will be presented and compared with those
corresponding to the American universities where FCI was also
given.
Keywords: misconceptions, force, test,
mechanics
1 Introduction
In the past very few years, different authors have treated
the problem of misconceptions in physics. As it is generally
known, misconceptions are erroneous common-sense beliefs that
when referred to physics; particularly, when referred to the
Newtonian thinking, lead to a distorted perception of the
physical world. Additionally, conventional instruction
produces little change in these beliefs and this result is
independent of the instructor and the mode of instruction
[HESTENES et al, 1992]. In this paper, it will be shown the
situation concerning the type - according Hestenes's
taxonomy- and frequency of misconceptions in different first
year Spanish students of engineering. These results will be
compared with those obtained by Hestenes et al. in the
Arizona State University.
2 The FCI test
The Force Concept Inventory (FCI) by David Hestenes,
Malcolm Wells and Gregg Swackhamer, was published on volume
30 of The Physics Teacher magazine on March, 1992. It
consists of 29 multiple option questions which require a
choice between a group of alternatives of Newtonian concepts
and common-sense about the six dimensions of the concept of
"force" according with the Hestenes's taxonomy of
misconceptions (Annex 1). Each question has only one correct
option that is the Newtonian concept and all the questions
have the same importance. The global result of the FCI
informs about the correct understanding of the concept of
"force" and also, let know about the Newtonian thinking and
presence of misconceptions.
The FCI was applied by their authors to different populations
formed by high school and university students at Arizona
(USA). The FCI has also been applied to four different
populations belonging to three Spanish universities. To
evaluate the evolution of teaching-learning process, the FCI
has to be given two times to each population; the first one,
before the instruction period and the second one, after it.
Conclusions to be drawn in this paper are based on five
populations of university students (one of the USA and the
others of Spain) selected among those students that take the
two applications of the FCI in each population.
3 Application of the FCI
Table 1 provides information about each centre and its
university where the two applications of FCI were done as
well as the number of students that took part in them.
The FCI was firstly applied in Spain in 1992-1993 course, at
the ESyTIA of the University of Leon, under the 1971
curriculum. It was applied two times: the first one before
the instruction period, October 1992, and the second one
after it, that was in April 1993; 90 students took the two
applications of the FCI.
Table 1. Educational Centre and University, their acronyms,
and dates in which the FCI has been applied and students who
took it in each Centre.
EDUCATIONAL CENTRE
UNIVERSITY (COUNTRY)
|
1st FCI APPLICATION
|
2nd FCI APPLICATION
|
|
CENTRE AND UNIVERSITY ACRONYMS
|
Students
|
Month
Year
|
Students
|
Month
Year
|
Escuela Superior y Tecnica de Ingenieria Agraria
Universidad de Leon, (Spain)
ESyTIA, ULE
|
90
|
October
1992
|
90
|
April
1993
|
Escuela Superior y Tecnica de Ingenieria Agraria
Universidad de Leon, (Spain)
ESyTIA, ULE
|
83
|
October
1996
|
83
|
February
1997
|
Escuela Tecnica Superior de Ingenieros Agronomos
Universidad Politecnica de Madrid, (Spain)
ETSIA, UPM
|
43
|
October
1997
|
43
|
March
1998
|
Escuela Tecnica Superior de Ingenieros de Caminos
Canales y Puertos
Universidad de Cantabria, (Spain)
ETSICCP, UC
|
86
|
October
1997
|
86
|
March
1998
|
Arizona State University (EE.UU.)
ASU
|
116
Approx.
|
Unknown
|
116
Approx.
|
Unknown
|
Then, in 1996-1997 course, under the 1995 curriculum, the FCI
was newly applied at the ESyTIA; in this occasion 83 students
took the first and the second application of the FCI; first
time before, second time after the instruction period, that
was: October 1996 and February 1997 respectively.
The same process was repeated at the ETSIA of the Universidad
Politecnica de Madrid and at the ETSICCP of the Universidad
de Cantabria, both in 1997-1998 course. A total of 43
students took the two applications of the FCI at the ETSIA
and 86 students at the ETSICCP; in both cases, the first
application was taken in October 1997 and the second one in
March 1998.
It has also been considered the results of the two
applications of the FCI at the Arizona State University, the
first one previous than the instruction period and the second
one after it. The total number of students that took the test
was, approximately, 116.
It has to be taken into account that, after secondary
instruction, no selection is required to become a first year
student at the ESyTIA (ULE). Certain selection is asked for
the first year students at ETSIA (UPM); finally, it is
necessary to have a good qualification to begin studying at
the ETSICCP (UC). It is also worthy to know that, at the
ESyTIA, a new curriculum was approved in 1995; therefore,
when the FCI was applied in the course 1996-1997, the new
curriculum had been first implemented in the preceding
course.
4 Results
First column in table 2 lists the misconceptions that reached
or overtook the 50% of presence, at least in one of the five
populations, in the first application of the FCI. The rest of
the columns show the percentages reached in each population.
Table 2. List of misconceptions that have reached or
overtaken 50% presence in the 1st application of the FCI in
any of the five analysed populations.
|
MISCONCEPTION
|
ESyTIA, ULE
OCTOBER 1992
|
ESyTIA, ULE
OCTOBER 1996
|
ETSIA, UPM
OCTOBER 1997
|
ETSICCP, UC
OCTOBER 1997
|
ASU
Pretest
|
|
[I.1] (9b)
|
19%
|
12%
|
23%
|
15%
|
52%
|
|
[I.1] (22c)
|
53%
|
60%
|
23%
|
24%
|
87%
|
|
[I.3] (5c)
|
57%
|
57%
|
44%
|
40%
|
62%
|
|
[I.3] (16c)
|
30%
|
39%
|
28%
|
14%
|
52%
|
|
[AF.1] (12b)
|
74%
|
69%
|
77%
|
80%
|
29%
|
|
[AR.1] (2a)
|
34%
|
57%
|
74%
|
50%
|
72%
|
|
[AR.1] (11d)
|
31%
|
40%
|
33%
|
24%
|
51%
|
|
[AR.1] (13b)
|
68%
|
66%
|
58%
|
52%
|
13%
|
|
[AR.2] (11d)
|
31%
|
40%
|
33%
|
24%
|
51%
|
|
[AR.2] (13c)
|
3%
|
11%
|
12%
|
9%
|
74%
|
|
[CI.1] (18a)
|
60%
|
52%
|
40%
|
35%
|
63%
|
|
[Ob] (9b)
|
19%
|
12%
|
23%
|
15%
|
52%
|
|
[R.2] (28d)
|
50%
|
55%
|
26%
|
24%
|
45%
|
|
[G.3] (3d)
|
32%
|
43%
|
19%
|
17%
|
54%
|
[Code of misconception after Hestenes's taxonomy, see
Annex no. 1] (Number of question and choice, see Annex no.
2).
There was not any misconception presented in a percentage
equal or superior to 50 in all the five populations analysed.
Misconceptions [AF.1] (12b) and [AR.1] (13b) were found in
the four Spanish populations with more than 50% percentage of
presence. The misconception [AR.1] (2a) was chosen by 34% of
the students that took the FCI in the course 1992-1993 at
ESyTIA; nevertheless, four years later, that percentage rose
till 57%. Percentages equal or superior to 50% were also
found, in the aforementioned misconception, in the UPM, UC
and ASU populations.
Regarding question number 12 (Annex no. 2), it has to be said
that Hestenes et al considered option "b" as the
correct one, because "buoyancy gets little attention in
physics curriculum today" (Hestenes et al. 1992).
Buoyancy effect is usually explained to the first year
Spanish students of engineering; nevertheless, according to
the results got in question 12, it seems that its
understanding is still incomplete.
Seven misconceptions: [I.1] (9b), [I.3] (16c), [AR.1] (11d),
[AR2] (11d), [AR.2] (13c), [0b] (9b), [G.3] (3d), having been
selected by more of 50% of the students that took the FCI in
the ASU, reached percentages under 50% in the four Spanish
populations analysed.
Table 3 presents the evolution of the percentage found in the
misconceptions listed in the first column of table 2; that
is, table 3 adds to the information included in table 2 the
percentage found in the second application of the FCI.
Table 3. Evolution of the percentages included in table 2
obtained after the 2nd application of the FCI.
|
|
ESyTIA, ULE
|
ESyTIA, ULE
|
ETSIA, UPM
|
ETSICCP, UC
|
ASU
|
|
MISCONCEPTION
|
OCT
92
|
APR
93
|
OCT
96
|
MAR
97
|
OCT
97
|
FEB
98
|
OCT
97
|
FEB
98
|
Pretest
|
Post-test
|
|
[I.1] (9b)
|
19%
|
18%
|
12%
|
12%
|
23%
|
7%
|
15%
|
7%
|
52%
|
6%
|
|
[I.1] (22c)
|
53%
|
22%
|
60%
|
40%
|
23%
|
26%
|
24%
|
16%
|
87%
|
13%
|
|
[I.3] (5c)
|
57%
|
30%
|
57%
|
40%
|
44%
|
56%
|
40%
|
22%
|
62%
|
13%
|
|
[I.3] (16c)
|
30%
|
23%
|
39%
|
51%
|
28%
|
9%
|
14%
|
5%
|
52%
|
21%
|
|
[AF.1] (12b)
|
74%
|
72%
|
69%
|
71%
|
77%
|
86%
|
80%
|
74%
|
29%
|
92%
|
|
[AR.1] (2a)
|
34%
|
36%
|
57%
|
54%
|
74%
|
35%
|
50%
|
19%
|
72%
|
23%
|
|
[AR.1] (11d)
|
31%
|
29%
|
40%
|
33%
|
33%
|
30%
|
24%
|
5%
|
51%
|
21%
|
|
[AR.1] (13b)
|
68%
|
74%
|
66%
|
72%
|
58%
|
47%
|
52%
|
42%
|
13%
|
2%
|
|
[AR.2] (11d)
|
31%
|
29%
|
40%
|
33%
|
33%
|
30%
|
24%
|
5%
|
51%
|
21%
|
|
[AR.2] (13c)
|
3%
|
0%
|
11%
|
8%
|
12%
|
7%
|
9%
|
2%
|
74%
|
51%
|
|
[CI.1] (18a)
|
60%
|
54%
|
52%
|
51%
|
40%
|
40%
|
35%
|
19%
|
63%
|
21%
|
|
[Ob] (9b)
|
19%
|
18%
|
12%
|
12%
|
23%
|
7%
|
15%
|
7%
|
52%
|
6%
|
|
[R.2] (28d)
|
50%
|
54%
|
55%
|
52%
|
26%
|
37%
|
24%
|
10%
|
45%
|
23%
|
|
[G.3] (3d)
|
32%
|
28%
|
43%
|
40%
|
19%
|
0%
|
17%
|
2%
|
54%
|
20%
|
[Code of misconception after Hestenes's taxonomy, see
Annex no. 1] (Number of question and choice, see Annex no.
2).
First of all, it has to be said that, regarding
misconceptions listed in table 3, there are some that, after
instruction, show a percentage higher than that presented in
the first application of the FCI. Three of them: [I3], [AF.1]
and [AR.1] even exhibited percentages in different
populations that were higher than 50%. Among these persistent
misconceptions it has to be highlighted the one defined as:
"only active agents exert forces", the concept
involved being the buoyancy effect as well as that other one
stated as "greater mass implies greater force".
When comparing decreasing percentages from first to second
application of FCI, there are seven occasions in which the
percentage after instruction still remains over 50 %. This
situation has been observed in the same population in five
among the seven occasions. The concepts or principles
involved and misconception detected being, respectively:
buoyancy effect [AF.1] (12b); 3rd Newton's Law [AR.1]
(2a); 2nd Newton's Law [CI.1] (18a) in two occasions
and, finally, 2nd Newton's Law [R.2] (28d). The
concepts involved in the two other occasions were known:
buoyancy effect [AF.1] (12b), and 3rd Newton's Law
[AR.2] (13c).
The misconception AF.1 (12b) is still chosen by more than 50%
of the students that took the second application of the FCI;
in three of the five populations examined, the percentage in
the second application was even higher than it was in the
first one. Misconception AR.1 (13b) only diminishes in two of
the four populations that registered percentages over 50% in
the first application, but percentages in the second
application are near (in two populations) or clearly over
50%. The percentage of occurrence of misconception AR.1 (2a)
in the second application was lower than in the first one in
all of the populations where that percentage had been higher
than 50%. Nevertheless, the percentage of occurrence was
still superior to 50% in one of those populations. In table 3
it have been highlighted in bold italic characters all
occasions in which the percentage reached in the second
application of the FCI became over 50%.
Finally, it has to be noted that the biggest decreasing of
misconception percentage were obtained in the ASU population.
In the ASU, just the misconception AF.1 (12b) increases its
presence from first to second application, though the latter
one was over 90%; the percentage of occurrence of
misconception AR.2 in the second application was still over
50%.
4 Summary and conclusions
The FCI (Hestenes et al, 1992) has been applied to four
Spanish university populations in three universities:
Universidad de Leon, Universidad Politecnica de Madrid and
Universidad de Cantabria and the results got compared with
those obtained by Hestenes et al at the University of Arizona
(USA). In this paper, the FCI has been used to know the reach
of the problem posed by the misconceptions.
In Spain, the FCI has been applied before and after the
teaching-learning process corresponding to the Newton's
Mechanics in first year students of engineering. This means
that the number of students participating in the first
application was normally bigger than it was in the second
one. Selecting those students that had taken the first and
the second application of the FCI formed the Spanish
populations considered in this paper.
In examining the percentages of choice of each misconception,
attention has been paid to those equal or superior to 50%. In
the first application of the FCI there was not any
misconception with a percentage equal or greater than 50% in
all of the populations analysed. There was two misconceptions
that reached or overtook 50% in four populations, they were
those defined by Hestenes et al as "only active agents
exert forces" and "greater mass implies greater
force". The latter misconception was found in choice
"a" of the question no 2 and in the choice
"d" of the question no13. The concepts or
principles involved in the aforementioned misconceptions were
the buoyancy effect and the third Newton's Law. Taking
into consideration the previous results it can be said that
it has been found an incomplete comprehension of the third
Newton's Law among the populations analysed.
Among the considered misconceptions listed in table 3, there
are some that increase their percentage in the second
application of the FCI; four of them, in eight occasions,
even reached a percentage higher than 50%. One of the most
persistent misconception was that defined as "only
active agents exert forces" when checked by means of
the concept of the buoyancy effect. The percentage of
occurrence of the previous misconception was over 50%, in the
second application in all the five populations. It has to be
said that misconception "greater mass implies greater
force", when checked by means of the third
Newton's Law, has also shown a notable persistence
because the percentage found in the second application has
been nearly and in some cases clearly over 50%.
In addition to the misconceptions listed in tables 2 and 3,
there was not any misconception showing percentages over 50%
in the second application. Nevertheless, it would have to be
studied the admissible percentage of a misconception in a
second application of the FCI; the 50% used in this study
seems to be a superior limit, being desirable to diminish
this percentage. In any case, it seems necessary to develop
teaching-learning techniques oriented to reduce the problem
posed by the misconceptions.
It would be, therefore, necessary to design strategies to
reduce these percentages.
Annex 1 : Misconceptions cited in tables 2 and 3, after
Hestenes's taxonomy
1. Impetus
I.1. Impetus supplied by "hit", its presence is associated
with question 9, option "b" and question 22,
option "c".
I.3. Impetus dissipation, its presence is associated with
question 5 option "c" and question 16, option
"c".
2. Active Force
AF.1. Only active agents exert forces; its presence is
associated with question 12, option "b".
3. Action/Reaction Pairs
AR.1. Greater mass implies greater force, its presence is
associated with question 2, option "a", question
11, option "d" and question 13, option
"b".
AR.2. Most active agent produces greatest force; its presence
is associated with question 11, option "d" and
question 13 option "c".
4. Concatenation of Influences
CI.1. Largest force determines motion; its presence is
associated with question 18 option "a".
5. Other Influences of Motion
Ob. Obstacles exert no force; its presence is associated with
question 9 option "b".
Resistance
R.2. Motion when force overcomes resistance, its presence is
associated with question 28 option "d".
Gravity
G.3. Heavier objects fall faster; its presence is associated
with question 3, option "d".
Annex no 2: Text of the questions associated to the
misconceptions listed in tables 2 and 3
The questions involved in misconceptions listed in tables 2
and 3 are, in order of appearance, the following:
|
2.
|
Imagine a head-on collision between a large truck and a
small car. During the collision,
|
|
|
a)
|
The truck exerts a greater amount of force on the car
than the car exerts on the truck.
|
|
|
b)
|
The car exerts a greater amount of force on the truck
than the truck exerts on the car.
|
|
|
c)
|
Neither exerts a force on the other, the car gets smashed
simply because it gets in the way of the truck.
|
|
|
d)
|
The truck exerts a force on the car but the car doesn't
exert a force on the truck.
|
|
|
e)
|
The truck exerts the same amount of force on the car as
the car exerts on the truck.
|
|
|
|
3.
|
Two steel balls, one of which weighs twice as much as the
other, roll off of a horizontal table with the same
speeds. In this situation:
|
|
|
a)
|
Both balls impact the floor at approximately the same
horizontal distance from the base of the table.
|
|
|
b)
|
The heavier ball impacts on the floor at about half the
horizontal distance from the base of the table than does
the lighter
|
|
|
c)
|
The lighter ball impacts on the floor at about half the
horizontal distance from the base of the table than does
the heavier.
|
|
|
d)
|
The heavier ball hits considerably closer to the base of
the table than the lighter, but not necessarily half the
horizontal distance.
|
|
|
e)
|
The lighter ball hits considerably closer to the base of
the table than the heavier, but not necessarily half the
horizontal distance.
|
|
|
|
5.
|
A boy throws a steel ball straight up. Disregarding
any effects of air resistance, the force(s) acting on
the ball until it returns to the ground is (are):
|
|
|
a)
|
Its weight vertically downward along with a steadily
decreasing upward force.
|
|
|
b)
|
A steadily decreasing upward force from the moment it
leaves the hand until it reaches its highest point beyond
which there is a steadily increasing downward force of
gravity as the object gets closer to the earth.
|
|
|
c)
|
A constant downward force of gravity along with an upward
force that steadily decreases until the ball reaches its
highest point, after which there is only the constant
downward force of gravity.
|
|
|
d)
|
A constant downward force of gravity only.
|
|
|
e)
|
None of the above, the ball falls back down to the earth
because that is its natural action.
|
|
|
|
* Use the statement and diagram below to answer the next
question.
|
|
The diagram depicts a hockey puck sliding, with a
constant velocity, from point "A" to point "B" along
a frictionless horizontal surface. When the puck
reaches point "B", it receives an instantaneous
horizontal "kick" in the direction of the heavy print
arrow.
The diagram depicts a hockey puck sliding, with a
constant velocity, from point "A" to point "B"
along a frictionless horizontal surface. When
the puck reaches point "B", it receives an
instantaneous horizontal "kick" in the direction of the
heavy print arrow.
|
|
|
|
9.
|
The main forces acting, after the "kick", on the
puck along the path you have chosen are:
|
|
|
a)
|
The downward force due to gravity and the effect of air
pressure.
|
|
|
b)
|
The downward force of gravity and the horizontal force of
momentum in the direction of motion.
|
|
|
c)
|
The downward force of gravity, the upward force exerted
by the table, and a horizontal force acting on the puck
in the direction of motion.
|
|
|
d)
|
The downward force of gravity and an upward force exerted
on the puck by the table.
|
|
|
e)
|
Gravity does not exert a force on the puck; it falls
because of the intrinsic tendency of the object to fall
to its natural place.
|
|
|
|
Two students, student "A" who has a mass of 95 Kg and
student "B" who has a mass of 77 Kg, sit in identical
office chairs facing each other. Student "A" places his
bare feet on student "B's" knees, as shown below. Student
"A" then suddenly pushes outward with his feet, causing
both chairs to move.
|
|
11.
|
In this situation,
|
|
|
a)
|
Neither student exerts a force on the other.
|
|
|
b)
|
Student "A" exerts a force on "B", but "B" doesn't exert
any force on "A".
|
|
|
c)
|
Each student exerts a force on the other but "B" exerts
the larger force.
|
|
|
d)
|
Each student exerts a force on the other but "A" exerts
the larger force.
|
|
|
e)
|
Each student exerts the same amount of force on the
other.
|
|
|
|
12.
|
A book is at rest on a tabletop. Which of the following
force(s) is(are) acting on the book?
1. A downward force due to gravity.
2. The upward force by the table.
3. A net downward force due to air pressure.
4. A net upward force due to air pressure.
|
|
|
a)
|
1 only
|
|
|
b)
|
1 and 2
|
|
|
c)
|
1, 2 and 3
|
|
|
d)
|
1, 2 and 4
|
|
|
e)
|
none of these, since the book is at rest there are any
forces acting on it.
|
|
|
|
* Refer to the following statement and diagram while
answering the next question.
|
|
A large truck breaks down out on the road and receives a
push back into town by a small compact car.
|
|
13.
|
While the car, still pushing the truck, is speeding
up to get up to cruising speed;
|
|
|
a)
|
The amount of force of the car pushing against the truck
is equal to that of the truck pushing back against the
car.
|
|
|
b)
|
The amount of force of the car pushing against the truck
is less than that of the truck pushing back against the
car.
|
|
|
c)
|
The amount of force of the car pushing against the truck
is greater than that of the truck pushing against the
car.
|
|
|
d)
|
The car's engine is running so it applies a force as it
pushes against the truck but the truck's engine is not
running so it can't push back against the car, the truck
is pushed forward simply because it is in the way of the
car.
|
|
|
e)
|
Neither the car nor the truck exert any force on the
other, the truck is pushed forward simply because it is
in the way of the car.
|
|
|
|
16.
|
Which of the paths in the diagram to the right best
represents the path of the cannon ball?
|
|
|
|
18.
|
An elevator, as illustrated, is being lifted up an
elevator shaft by a steel cable. When the elevator is
moving up the shaft at a constant velocity;
|
|
|
a)
|
The upward force on the elevator by the cable is greater
than the downward force of gravity.
|
|
|
b)
|
The amount of upward force on the elevator by the cables
equals to that of the downward force of gravity.
|
|
|
c)
|
The upward force on the elevator by the cable is less
than the downward force of gravity
|
|
|
d)
|
It goes up because the cable is being shortened, not
because of the force being exerted on the elevator by the
cable.
|
|
|
e)
|
The upward force on the elevator by the cable is greater
than the downward force due to the combined effects of
air pressure and the force of gravity.
|
|
|
|
22.
|
A golf ball driven down a fairway is observed to travel
through the air with a trajectory (flight path) similar
to that in the depiction below.
Which of the following force(s) is(are) acting on the
golf ball during its entire flight?
1. The force of gravity
2. The force of the "hit"
3. The force of air resistance
|
|
|
a)
|
1 only.
|
|
|
b)
|
1 and 2.
|
|
|
c)
|
1, 2 and 3.
|
|
|
d)
|
1 and 3.
|
|
|
e)
|
2 and 3.
|
|
|
|
28.
|
A large box is being pushed across the floor at a
constant speed of 4,0 m/s. What can you conclude
about the forces acting on the box?
|
|
|
a)
|
If the force applied to the box is doubled, the constant
speed of the box will increase to 8 m/s.
|
|
|
b)
|
The amount of force applied to move the box at a constant
speed must be more than its weight.
|
|
|
c)
|
The amount of force applied to move the box at a constant
speed must be equal to the amount of the frictional
forces that resist its motion.
|
|
|
d)
|
The amount of force applied to move the box at a constant
speed must be more than the amount of the frictional
forces that resist its motion.
|
|
|
e)
|
There is a force being applied to the box to make it move
but the external forces such as friction are not "real"
forces they just resist motion.
|
References
CELEMIN, M. & PALENCIA, C. Evaluating the effectiveness
of teaching learning process. Copenhagen. PTEE'97.
Available from
http://www.pwg.vslib.cz/Recent/PTEE%201997/proceed.htm.
CELEMIN, M. & COVIAN, E. El FCI como instrumento de
evaluacion del proceso ensenanza aprendizaje de la mecanica
en ensenanzas tecnicas. Las Palmas de Gran Canaria
:Universidad de lasPalmas de Gran Canaria,1998, 19 s. ISBN
84-89728-69-O.
HESTENES, D.; WELLS, M. & SWACKHAMER, G. Force Concept
Inventory. Stony Brook: The Physics Teacher (number 30),
March, 1992, 141-158.
Acknowledgements
The present study has been financed by means of a grant of
The Department of Education (Consejeria de Educacion) of the
Autonomous Government (Junta de Castilla y Leon).