Addressing Student Misconceptions of Atwoods Machine: Review of a Research Based Method

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Addressing Student Misconceptions of Atwoods
Machine Review of a Research Based Method

• Beth Dietz, Madison Park TVHS
• Christina Yee, Charlestown HS
• June 1, 2004

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Journal Article

• Research as a guide for teaching introductory
  mechanics An illustration in the context of
  Atwoods machine McDermott, L. Department of
  Physics, University of Washington, Seattle,
  Washington. Am. J. Phys 62 (1) Jan. 1994

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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.

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Example Atwoods Machine

• used in typical introductory physics course.
• used to learn about Newtons 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.

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Research Study Test Group

• Written test to 3 different classes of
  calculus-based physics students.
• Students had studied Newtons Laws, analyzed
  textbook problems, experienced an experiment in
  class and homework questions.

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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).
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Typical Student Responses
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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.

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Main Concept Tension in a String

• 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 otherbut 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.

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Misconception Break-DownLinguistic

• The term Tension creates student confusion.
• Why?
• Daily use tautness
• Confusion between scalar and vector
• Force exerted on object by string
• Magnitude of this force

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Misconception Break-DownGeneral

• Isolation of systems
• Identification of forces
• 3rd law force pairing
• Recognizing that Fnet determines acceleration

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Conclusion of Research

• Teaching Atwoods 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

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New Way to Teach Atwoods 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
• Instructors role is to conduct qa with students
• Students find their own answers and build their
  own knowledge.

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Research on tutorial

• Pretest given to 100 students about role of
  string with the following set up
• Assume string is massless. B is greater mass than
  A.

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Pre-Test Question 1

• Compare the acceleration of B with A.
• Results (out of 100 students)
• 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.

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Pre-Test Question 2

• Compare the force exerted by string 1 on A with
  the force exerted by string 2 on B.
• Results (out of 100 students)
• 40 stated Force of string 1 was greater.
• 40 used 2nd Law, since a1a2, then due to mass
  difference, string 2 would have greater force.
• 20 Force exerted by 12 were equal. Students did
  not take into account external vs. internal
  forces.

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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 Atwoods Machine

• Start with pre-test on simple system
• No friction present. Students asked to compare
  the magnitude of all forces.

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1St pretest was difficult. Why?

• Incorrect use of Newtons 3rd Law (FABFBA)
• Assumption that FABFhand
• Next step use question with friction present and
  blocks moving at constant velocity.
• 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.

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Building Understanding Step 2

• Pre-test question 2 Two bodies connected by
  inextensible string.
• Compare Pre-test 1 with 2 set up
• Compare a in 1 with 2. Students come up with
  aAaB.
• How do you know if a and v of two objects are
  equal?
• The separation between the objects must remain
  the same.

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Building Understanding re Tension Scenario
Mass ? 0
B
A
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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 R A

FRBx
FRBx
FARx
FARx
Fhand
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Rank Magnitude of Forces

• To rank forces must use 2nd Law
• FAR FBR MRa if MR 0 then
• FAR FBR
• Newtons 3rd Law FAR FRA
• FBRFRB and so
• FRAFRB

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Rank Magnitude of Forces

• 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.
• FhandFRA FAR FBRFRB
• 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.

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Tension and force exerted on objects

• 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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Atwoods 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.
• Ignore pulley issues.

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Atwoods Vertical Machine Pre-test

• 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

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Draw Correct FBD for Vertical Atwood

• 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---stu
  dents needed to be reminded of effect of string
  on motion.
• Students used past info to remember that
  accelerations must be equal. Recheck FBDs and
  correct themselves in practice.
• Can infer that a must be in between weight of
  both blocks and less than free fall.

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Effectiveness of Tutorial

• 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

• Sliding Block has m100g 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.

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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

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Assessment Exam Question 2

• In this case, how does the tension in the string
  change when the block A is released?

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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.

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Assessment Exam Question 3
D
B
A
A
C
C

• 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.
• Describe any changes in motion of blocks and on
  the net force on Blocks A and C.

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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 FcFbFa Non-Tutorial Class 30
drew correct FBD 15 idenified correct 3rd Law
pairs 60 had FcFbFa
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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.
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Conclusions from Research Project

• 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.