Transcript Addressing Student Misconceptions of Atwood’s Machine

Addressing Student Misconceptions of
Atwood’s Machine: Review of a Research
Based Method
Beth Dietz, Madison Park TVHS
Christina Yee, Charlestown HS
June 1, 2004
Journal Article:

“Research as a guide for teaching introductory mechanics: An illustration in the
context of Atwood’s machine” McDermott, L. Department of Physics, University
of Washington, Seattle, Washington. Am. J. Phys 62 (1) Jan. 1994
modified
Main Ideas:
1) Teachers must know misconceptions in order to
target learning experiences to have students gain
more understanding. Misconceptions can be identified
through research.
2) Research can be used to create changes in intro
physics curriculum to enhance effectiveness of
instruction.
3) Research must guide the design of curriculum to
be effective.
Example: Atwood’s Machine
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used in typical introductory physics course.
used to learn about Newton’s Laws for a system with
two objects, where the motion of one affects the
motion of the other.
Often find the acceleration of the blocks and tension
in the string (which is massless and inextensible).
Isolate bodies, draw FBDs,apply 2nd Law and derive
equations for unknown variables.
Research Study: Test Group
Written test to 3 different classes of
calculus-based physics students.
 Students had studied Newton’s Laws,
analyzed textbook problems,
experienced an experiment in class and
homework questions.

Question Asked?
(a)
(b)
Students were asked to compare the tension in the
string at position (a) vs. the tension of the string at
position (b).
Typical Student Responses
Typical Student Responses

50% identified the force at (a) and (b) to be the same.
 Misconceptions:
 1. Tension in string with 2 weights, 2x greater.
 2. Tension pulls in two directions with 2 weights, only
one with wall.
 3. Tension force was sum of forces at end of string.
 4. The wall did not exert a force
 Also some thought tension in string was 0 N because
it was canceled out by vector addition.
Main Concept: Tension in a String
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“There was widespread inability to distinguish tension
from weight. So led to misunderstanding that it is not
the weight of the one block that acts directly on the
other—but rather the force exerted by the string.”
p.47
Most students did not infer the relative magnitudes of
weights and tension from direction of acceleration.
Students also did not recognize that force on the
sliding block does not affect hanging block in
modified case.
modified
Misconception Break-Down:
Linguistic
The term “Tension” creates student
confusion.
 Why?
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Daily use= tautness
 Confusion between scalar and vector
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–
–
Force exerted on object by string
Magnitude of this force
Misconception Break-Down:
General
1.
2.
3.
4.
Isolation of systems
Identification of forces
3rd law force pairing
Recognizing that Fnet determines
acceleration
Conclusion of Research:
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Teaching Atwood’s machine is pointless if students
believe there are 2 acceleration and 2 tensions!
Students have difficulty with concepts of tension and
acceleration that need to be addressed prior to
“practice problems” done on their own.
Group work, interaction and analysis during the
tutorial sessions provided more conceptual insight
than lecture (regardless of the quality of the lecturer).
Answer new methods
New Way to Teach Atwood’s Machine

The use of tutorial sessions, which are:
Student-centered with emphasis on
concepts
 Pre-tests and highly structured worksheets
guide students through reasoning tasks
 Instructor’s role is to conduct q&a with
students
 Students find their own answers and build
their own knowledge.
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Research on tutorial
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Pretest given to 100 students about role
of string with the following set up:
B
2
A
1
Assume string is massless. B is greater
mass than A.
Pre-Test Question #1
B
2
A
1
Compare the acceleration of B with A.
 Results (out of 100 students)
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– 85 stated accelerations were equal.
– 15 used dynamical arguments that the Forces exerted
by the two strings were equal and so the accelerations
be different because of the different masses.
 Pre-test
question given to 450 students
and still 15% incorrect reasoning.
Pre-Test Question #2
B
2
A
1
Compare the force exerted by string 1
on A with the force exerted by string 2
on B.
 Results (out of 100 students)
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– 40% stated Force of string 1 was greater.
– 40% used 2nd Law, since a1=a2, then due to mass
difference, string 2 would have greater force.
– 20% Force exerted by 1&2 were equal. Students did
not take into account external vs. internal forces.
Looking at friction and way strings
transmit force.
Belief that a string transmitted force
applied to one object unchanged to the
other object.
 50% of students claimed that force of 2
on A was equal to frictional force
exerted on B.
 Students believed frictional force on B
acted directly on A.
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Feel Good About Physics ‘cause even
physicists mess up!
Pretest was given to 20 graduate
physics students.
 100% agreed accelerations were same.
 60% argued correctly that force of 1 on
A was greatest
 Many FBDs were incorrect.
 Same general problems as UG class.
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There must be a better way!
In use of tutorial class, develop
questions from simple to complex
systems.
 Use methodology of elicit, confront and
reassure.
 Make explicit the steps to understanding
that students fail to do on their own.
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Steps to understanding
Atwood’s Machine
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Start with pre-test on simple system:
A
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B
No friction present. Students asked to
compare the magnitude of all forces.
St
1
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pretest was difficult. Why?
Incorrect use of Newton’s 3rd Law (FAB>FBA)
Assumption that FAB=Fhand
Next step: use question with friction present and blocks moving
at constant velocity.
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Students asked to draw separate FBDs
Focus on agent that exerts force, body it acts on
Then they are asked to rank magnitude of horizontal forces
Students realize Fhand must overcome frictional forces of both
blocks so it must be greatest in magnitude.
Looking at the situation with clear steps helps build acceptance of
Newtonian view of external forces on object affecting its motion.
Building Understanding Step #2
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Pre-test question #2: Two bodies connected by
inextensible string.
Compare Pre-test #1 with #2 set up:
B
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A
Compare a in #1 with #2. Students come up with
aA=aB.
How do you know if a and v of two objects are equal?
– The separation between the objects must remain the same.
Building Understanding re: Tension Scenario
Mass ≠ 0
B
A
Building Understanding re: Tension Scenario
•Students are asked to isolate A, B and Rope from
each other to help students recognize force of rope.
•Students guided through some problems:
•Asked for horizontal comp. Of forces on A,R and B:
B
FRBx
R
FRBx
A
FARx
FARx
Fhand
Rank Magnitude of Forces
To rank forces must use 2nd Law
 FAR – FBR= MRa if MR ≈ 0 then:
 FAR = FBR
 Newton’s 3rd Law: FAR = FRA
 FBR=FRB and so
 FRA=FRB
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Rank Magnitude of Forces
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Students see more than 1 force on A.
Those who did not include Fhand earlier are forced to do so.
Students realize that Fhand must overcome FRA so it must be
greater.
Fhand>FRA = FAR > FBR=FRB
*****************************************
Why use of massless strings? What are the consequences of
massless string?
FAR-FBR = 0 then FAR= FBR
No net force is needed to accelerate a massless string.
A taut, massless string exerts equal and opposite forces at both
ends.
Tension and force exerted on objects
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Picture block & rope cut
Cutting strings
 Tension in a taut, massless string is
equal to force it exerts on objects it
connects.
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Atwood’s Vertical Machine
Students now understand:
 (1) for an inextensible string the
acceleration will be the same for the two
objects it connects.
 (2) Massless string the tension is the
same at both ends.
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Ignore pulley issues.
Atwood’s Vertical Machine
Pre-test
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Predict the motion if system released.
– Most students correctly guessed that heavier weight
would move down and lighter weight up.
– http://www.msu.edu/user/brechtjo/physics/atwood/at
wood.html
– They showed different magnitudes for the forces
exerted by the strings. Typical incorrect FBD shown
below:
Draw Correct FBD for Vertical Atwood
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Values are given for weights of 4N and 6N. Students
asked to find Fnet and a for each weight.
Still problem with 2 masses, 2 accelerations--students needed to be reminded of effect of string on
motion.
Students used past info to remember that
accelerations must be equal. Recheck FBD’s and
correct themselves in practice.
Can infer that a must be in between weight of both
blocks and less than free fall.
Effectiveness of Tutorial
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Compared 3 UG physics classes
All classes used same text, lecturers,
content in the same order
 2 classes had 4 lectures/week, 1 had 3
lectures + 1 tutorial session/week
 Assessment of all groups via 3
examination questions.
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Assessment: Exam Question #1
A
C
B
C
Sliding Block has m=100g and hanging block B has a mass of 200g. An object of
200g is held at the same height as Block B. Compare the accelerations of B and
C when they are released. Consider with friction and without friction.
Assessment: Exam Question #1 Results
For Friction situation: 100% of 3 classes were correct in C
reaching bottom first.
No Friction situation:
Tutorial: 70% predict C hit first
Previous Tutorials (not this one): 55% predict C first
No tutorial: 45% predicted C first
Tutorial students could express the constraint of the T up on Block
B, which led them to the correct answer.
Non-tutorial students “seemed unaware of the upward force
exerted by string on B”
Assessment: Exam Question #2
A
C
B
C
In this case, how does the tension in the string change when the block A is
released?
Assessment: Exam Question #2 Results
Common incorrect answer was tension would not change because
only change taking place was with Block A. Failure to recognize
that within system, one change can affect all parts.
Class with tutorial:
50% recognized that T becomes less than
weight of B.
Class without tutorial: 25% when B accelerates down, T becomes
less than its weight.
There was less tendency to treat blocks and string independently.
Assessment Exam Question #3
D
A
B
C
A
C
1. Draw FBDs for each of the three blocks, indicate any
third law force pairs and rank from (largest  smallest)
the magnitude of the net force on each block.
2. Describe any changes in motion of blocks and on the net
force on Blocks A and C.
Assessment Exam Question #3: Results Part 1
Tutorial Class:
90% drew correct FBD; 70% idenified correct 3rd Law pairs
98% recognized B and C exert forces opposite to direction of motion
60% had Fc>Fb>Fa
Non-Tutorial Class:
30% drew correct FBD; 15% idenified correct 3rd Law pairs
60% had Fc>Fb>Fa
Assessment Exam Question #3: Results Part 2
Tutorial Class:
80% predicted that since overall system mass went down, that
acceleration went up. Since A & C remain same mass, their net force
has to increase.
Non-Tutorial Class:
35% were correct.
Conclusions from Research Project:
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Much better performance with tutorial on FBDs, identifying 3rd Law
Pairs, and qualitative analysis
More time spent on concepts without initial math the better the
results on exams.
**Numerous encounters with material fights deeply held
uncertainties.
Teachers role is to move students from passive recipients to active
learners (tell them that from the beginning).
Intro Physics should help students identify what they do and do not
know and what is a scientific explanation.