IB Physics 2015 Higher level Paper 2 Question 3

Question: Students are expected to provide a definition of an electromotive force.

Mark scheme: 
The work done per unit charge in moving a quantity of charge completely around a circuit.
OR the power delivered per unit current.
OR work done per unit charge made available by a source.

Comments: 

As an example, the question could be phrased as “define the electromotive force (emf) of an ideal battery” instead of simply “define electromotive force.” The electromotive force of a real battery is different from an ideal battery that has no internal resistance. On the other hand, it is possible to have an induced electromotive force in the electrical circuit due to a metal wire moving perpendicularly across the Earth’s magnetic field. Thus, the question should be more precise.

This mark scheme is slightly different from Tsokos’ (2008) definition of electromotive force: “In the case of the battery, the ratio of work done by non-electrical forces, W, to a quantity of charge q that moves from one terminal of the battery to the other is called the emf of the battery (p. 319).” That is, the mark scheme does not include the nature of forces (non-electrical) involved in the work done. For example, Lerner (1996) writes that “the external work per unit charge that must be expended to produce an increase ∆V in the electric potential of the charge is called the electromotive force (Lerner, 1996, p. 727).” He also explains that the external force that acts on the unit charge in producing an electromotive force can be a non-conservative force, whereas the electric force that opposes the external force is a conservative force. (Similarly, the force in which your arm raises an object is non-conservative, but the gravitational force that opposes this external force is conservative.)

In addition, the mark scheme does not specify the condition “open circuit” or “no current is being drawn” that can be found in the mark schemes of other examination boards. Importantly, in an article titled Electromotive force, potential difference, and voltage, Page (1977) writes that “[i]n an open circuit, the electromotive force is measured by the potential difference that it maintains. In a closed circuit, it is equal to the instantaneous power developed, divided by the value of the current in the circuit (p. 979).” Mathematically, the effective electromotive force (V) of a real battery can be calculated by the equation V = E – Ir; E is the maximum voltage across the output terminals when no electric current flows through the real battery, I is the electric current that flows through the battery, and r is the internal resistance of the battery. Therefore, the effective electromotive force of an electrical source is dependent on whether the electrical circuit is open or closed.

Feynman Insights?:

Currently, there is no agreement on the definition of electromotive force. In The Feynman Lectures on Physics, it is stated that “the emf is defined as the tangential force per unit charge in the wire integrated over length, once around the complete circuit (Feynman et al., 1964, section 16–1 Motors and generators).” In short, the electromotive force (Emf) around a closed circuit is the line integral of the electric field (E) in the wire, and it can be mathematically expressed as  Emf = ∫ E · ds. However, Feynman’s definition can be misleading because it has a connotation that the electromotive force is a kind of force. Thus, one may prefer the term electromotive potential or electromotive voltage (Legault & Peschard, 2001). 

Furthermore, Feynman adds that “[w]e have already defined the emf in a conducting circuit as the total accumulated force on the charges throughout the length of the loop. More specifically, it is the tangential component of the force per unit charge, integrated along the wire once around the circuit. This quantity is equal, therefore, to the total work done on a single charge that travels once around the circuit (Feynman et al., 1964, section 17–1 The physics of induction).” Importantly, Feynman clarifies that the electromotive force is the total work done on a unit charge in the electrical circuit. Historically speaking, Volta defines the electromotive force as a nonelectrostatic action on charge-carriers in the electrical circuit, that causes unlike charges to remain separated. However, current physicists redefine the term electromotive force as the total work done (measured in joules) instead of a force (measured in newtons).

Note: 

Page also mentions that “[i]n the case of a battery, its electromotive force can be determined by an open-circuit measurement of the potential difference between its terminals; in the case of a series-wound generator (converting mechanical energy to electric energy), the emf is a function of the load current, and is ideally zero under open-circuit conditions (Page, 1977, p. 979).” 

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.
2. Legault, N., & Peschard, D. (2001). Concerning the electromotive force (or emf). The Physics Teacher, 39(2), 69. 
3. Lerner, L. S. (1996). Physics for scientists and engineers. Boston, MA: Jone and Barlett. 
4. Page, C. H. (1977). Electromotive force, potential difference, and voltage. American Journal of Physics, 45(10), 978-80. 
5. Tsokos, K. A. (2008). Physics for the IB Diploma (5th ed.). Cambridge: Cambridge University Press.

IB Physics 2015 Higher level Paper 2 Question 2

Question: Students have to explain why the resultant force acting on a skier moving at constant velocity must be zero. The purpose of this question is to assess students’ knowledge of Newton’s first law of motion. 

Mark Scheme: 
(1) Newton’s first law states that a body remains at rest or moves with) constant velocity / steady speed / uniform motion unless external / net / resultant / unbalanced force acts on it. (2) A clear link between constant velocity and no resultant force.

Comments: 

This question is about using Newton’s first law of motion to explain why the resultant force acting on an object that is moving at constant velocity must be zero. Students are expected to state Newton’s first law and to relate “constant velocity” to “no resultant force.” However, in Physics for the IB diploma, Newton’s first law of motion is stated as “[w]hen no forces act on a body, that body will either remain at rest or continue to move along a straight line with constant speed (Tsokos, 2008, p. 69).” This version of Newton’s first law does not use the term such as “external force,” “net force,” “unbalanced force,” and “resultant force” that are specified in the mark scheme.

On the other hand, another version of Newton’s first law is “a free particle always moves with constant momentum relative to an inertial frame of reference: p = constant (Alonso & Finn, p. 100).” However, the mark scheme does not state Newton’s first law in terms of linear momentum. Currently, very few textbook authors state Newton’s first law in this form. In addition, this version of Newton’s first law adopts the term “free particle” instead of “resultant force.” Thus, it is unclear how the mark scheme could be interpreted by physics teachers. Importantly, the three Newton’s laws of motion can be consistently related to the linear momentum as summarized below: 

1. Newton’s first law: A free particle always moves with constant linear momentum. 

2. Newton’s second law: Force is defined as the rate of change of linear momentum. 

3. Newton’s third law: The principle of conservation of linear momentum.

In schools, physics teachers may use an air-track experiment to show that an object can be moving at a constant velocity for a short period of time. Strictly speaking, Newton’s first law cannot be exactly demonstrated by this experiment. That is, we cannot completely eliminate frictional forces or gravitational forces on an object experimentally. In The Nature of the Physical World, Eddington (1928) criticizes Newton’s first law, and rephrases it as “[e]very body continues in its state of rest or uniform motion in a straight line, except in so far as it doesn’t (p. 124).”

Feynman insights?: 

Newton’s first law of motion is also known as the principle of inertia. Historically speaking, Newton (1687) states that “[e]very body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon (p. 19).” The term resultant force is not used in the original formulation of Newton’s first law as well as many later versions of the principle of inertia. For example, in Volume I of The Feynman Lectures on Physics, Feynman states that “if an object is left alone, is not disturbed, it continues to move with a constant velocity in a straight line if it was originally moving, or it continues to stand still if it was just standing still (Feynman et al., 1963, section 9–1 Momentum and force).” Essentially, Feynman is conceptualizing an isolated body that is left alone and it is not disturbed by external forces.

In Volume II of The Feynman Lectures on Physics, Feynman proposes a broader definition of straight line: “ ‘Straight-line’ motion — the analog of ‘uniform velocity along a straight line’ — is then that motion which takes a watch from one place at one time to another place at another time in the way that gives the longest time reading for the watch. This will be our definition for the analog of a straight line in space-time (Feynman et al., 1964, section 42-4 Geometry in space-time).” In a similar sense, modern formulation of the principle of inertia may be stated as: “[t]here is a special class of observers, relative to whom all free objects appear to either be at rest or to move along geodesics in spacetime. These are observers who are in free fall in a gravitational field (Smolin, 2013, p. 341).” However, in this version, the term “free objects” does not necessarily mean that the objects are not acted upon by a resultant (gravitational) force.

Note: 
1. In Newtonian Mechanics, French (1971) writes that “Moreover, there is the far from trivial question of defining a straight line in a real physical sense: it is certainly not intuitively obvious, nor is it an abstract mathematical question. (How would you define a straight line for this purpose?) (p. 164).”

2. About 2000 years before Newton has formulated his three laws of motion, Mozi (墨子) writes that, “止，以久也。止，無久之不止”; it means that “if there is no such force, the motion will never stop (Needham, 1962, p. 58).”

3. You may want to take a look at this website:
http://feynman-answer.blogspot.sg/2016/04/newtons-first-law-of-motion.html

References:
1. Alonso, M., & Finn, E. J. (1992). Physics. Wokingham: Addison-Wesley.
2. Eddington, A. (1928). The Nature of the Physical World. New York: Cambridge University Press. 
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley. 
4. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley. 
5. French, A. (1971). Newtonian Mechanics. New York: W. W. Norton. 
6. Needham, J. (1962). Science and Civilisation in China: Volume 4, Physics and Physical Technology, Part 1, Physics. Cambridge: Cambridge University Press.
7. Newton, I. (1687/1995). The Principia. (A. Motte, Trans.). New York: Prometheus.
8. Smolin, L. (2003). The Principle of Inertia. In J. Brockman (ed.), This explains everything. New York: Harper Perennial.
9. Tsokos, K. A. (2008). Physics for the IB Diploma (5th ed.). Cambridge: Cambridge University Press.

IB Physics 2015 Higher level Paper 2 Question 1

Question: This question is about the rate of flow of water through a narrow tube that varies with the pressure difference above the tube. The pressure difference is proportional to the height (h) of water as shown in the diagram below. A student measures the height h in cm with a meter ruler. The flow rate of water (R) is obtained by measuring the volume of water collected in a measuring cylinder within a time of 100 sec. Students are expected to deduce the flow rate of water R for h = 0, which is about -1.6 cm³/s^-1. Moreover, they have to explain why this value of R is not physically possible. 

Mark scheme: (1) The flow rate is negative.
(2) This means that water is running uphill (or gaining potential energy) or words to that effect.

Comments:
In this question, physics teachers could let students try to make sense of negative flow rate of water. Currently, the mark scheme of this question does not accept negative flow rate because it implies water running uphill or gaining potential energy. However, students sometimes need to make sense of complex numbers or negative mathematical values. For example, it is possible to have negative acceleration, negative work, negative refractive index, negative energy levels, negative magnetic susceptibility, and even negative latent heat of solidification. Furthermore, in Feynman’s Tips on Physics, Feynman (2005) mentions that “the particles lose energy when they come together, so that means when r is smaller, the potential energy should be less, so it’s negative – I hope that's right! I have a great deal of difficulty with signs (p. 48). Interestingly, David Gross and Frank Wilczek had made mistakes with regard to signs before completing their work that earns them a Nobel Prize.

In general, physics teachers and students should not simply dismiss answers that are negative in value. For instance, we could interpret that water does evaporate (at h = 0), and as a result, water molecules can move upward and gain gravitational potential energy. In fact, this happens daily and eventually results as rainfalls. Alternatively, the value of R may be explained to be negative because of experimental errors. In other words, the incorrect (extrapolated) flow rate could be due to the experimental setup or errors in measurement. Thus, it is possible that a physical quantity is negative because of theoretical and empirical reasons. However, one may still argue whether it is possible to have a flow rate of water as -1.6 cm³/s^-1. Perhaps, students can design another experiment by using a larger apparatus in a higher humidity condition?

Feynman’s insights?:

There are several opportunities to highlight Feynman’s insights pertaining to negative values in this question. Firstly, in an article titled The theory of positrons, Feynman (1949) suggests that “the ‘negative energy states’ appear in a form which may be pictured in space-time as waves traveling away from the external potential backward in time (p. 749).” For example, a positron could be visualized as an electron that is moving backward in time. Similarly, Dirac was awarded Nobel Prize (1933) because he established a connection between electrons in negative-energy states and positrons. In Dirac’s (1942) words, “[n]egative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative sum of money, since the equations which express the important properties of energies and probabilities can still be used when they are negative (p. 8).”

Furthermore, in an article titled Negative probability, Feynman (1987) writes that “[i]t is usual to suppose that, since the probabilities of events must be positive, a theory which gives negative numbers for such quantities must be absurd. I should show here how negative probabilities might be interpreted (p. 235).” That is, we need not simply reject the concept of negative probability and teach students that most negative physical quantities must be absurd. On the contrary, we should explain that an ability to interpret negative physical quantity may reflect a breakthrough in thinking.

Note:
1. During Feynman’s Nobel Lecture titled The development of the space-time view of quantum electrodynamics, he explains that “one step of importance that was physically new was involved with the negative energy sea of Dirac, which caused me so much logical difficulty. I got so confused that I remembered Wheeler's old idea about the positron being, maybe, the electron going backward in time. Therefore, in the time-dependent perturbation theory that was usual for getting self-energy, I simply supposed that for a while we could go backward in the time, and looked at what terms I got by running the time variables backward. They were the same as the terms that other people got when they did the problem a more complicated way, using holes in the sea, except, possibly, for some signs (p. 26).”

2. In an article titled Simulating physics with computers, Feynman (1982) writes that “[t]he only difference between a probabilistic classical world and the equations of the quantum world is that somehow or other it appears as if the probabilities would have to go negative, and that we do not know, as far as I know, how to simulate. Okay, that’s the fundamental problem (p. 480).”

3. In Feynman’s Tips on Physics, Feynman explains that “another question is, what happens if v_a exceeds the velocity of escape? Then v_escape/v_a is less than 1, and b turns out negative - and that doesn’t mean anything; there is no real b (Feynman et al., 2006, p. 75).”

References:

1. Dirac, P. A. (1942). Bakerian lecture: The physical interpretation of quantum mechanics. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 180(980), 1-40.

2. Feynman, R. P. (1949). The theory of positrons. Physical Review, 76(6), 749-759.

3. Feynman, R. P. (1965). The development of the space-time view of quantum electrodynamics. In L. M. Brown (ed.), Selected papers of Richard Feynman. Singapore: World Scientific.

4. Feynman, R. P. (1982). Simulating physics with computers. International journal of theoretical physics, 21(6/7), 467-488.

5. Feynman, R. P. (1987). Negative probability. In B. J. Hiley & F. D. Peat (eds.), Quantum implications: essays in honor of David Bohm (pp. 235-248). London: Routledge & Kegan Paul.

6. Feynman, R. P., Gottlieb, M. A., Leighton, R. (2006). Feynman’s tips on physics: reflections, advice, insights, practice: a problem-solving supplement to the Feynman lectures on physics. San Francisco: Pearson Addison-Wesley.

Introduction

This blog discusses problems of assessment that are related to physics examination questions, textbook definitions, and assessment criteria (sometimes known as criteria sheets, grading criteria, grading schemes, mark schemes, marking instructions, scoring rubrics, or scoring guidelines). Essentially, you may find critical analyses of physics examination questions as well as textbooks’ presentations of a concept that are incorrect or inconsistent with respect to the assessment criteria. Importantly, physics teachers should not simply teach students how to answer examination questions by following assessment criteria. It is possible that assessment criteria may continue to evolve or at least appear to be inconsistent over the years. Therefore, examiners should continually improve assessment questions in order that they are free of errors and have minimal ambiguities. Better still, there could be deeper discourses among physics teachers and students on problems of physics assessment.

Nevertheless, a major role of assessment is for teachers to get to know their students and determine the students’ approaches to learning (Hazel, Logan, & Gallagher, 1997). It is possible that the types of assessment affect students’ understanding of the course objectives, motivation, interest, quality of their learning, as well as their ability on future pursuits. The categories in assessment questions may include the following: (1) Type: The question may be quantitative or qualitative. (2) Structure: The question can be assigned as multiple choice, short definite, and short flexible. (3) Context: For instance, the context of the question can be masculine, feminine or neutral (Hazel et al., 1977). This blog focuses on short definite questions that are qualitative. Although multiple choice questions are commonly found in examinations, the grading criteria and examiners’ reports tend to have fewer details. Thus, they are usually excluded in this blog.

Importantly, we should be cognizant of physics questions, that require complex marking strategies, may be marked less accurately (Sütő & Nádas, 2008). However, as many examination boards have provided similar assessment questions over the years, we could compare the consistency of assessment criteria within the same examination board as well as among different examination boards. In addition, textbook authors may have different opinions in the presentations of a concept or definition. Similarly, examiners have their own views on how physical concepts should be defined or presented.

In a review article (Wong, Chu, & Yap, 2016), students’ alternative conceptions of heat were analyzed based on five categories: “residing in an object,” “ontological category,” “movement,” “cause and effect,” and “condition.” The findings suggest that there could be some misunderstanding of students’ alternative conceptions due to different opinions on the definition of heat as well as textbooks’ descriptions of heat. For example, Baierlein (1994) proposes that heat is an adjective, Zemansky (1970) disagrees that heat is a verb, and Romer (2001) prefers to define heat as a process rather than a noun. Moreover, the so-called alternative conceptions could be traceable to textbook definitions or linguistic usage in textbooks. Similarly, academic performances of students are dependent on the assessment criteria which could be subjective or inadequate.

On the other hand, Feynman (1975) admits that there is a mistake in The Feynman Lectures on Physics and cautions Miss Cox to examine logic and argument carefully rather than to simply believe in authorities (See the letter below). Furthermore, there are possibly much more mistakes or inadequacies in many physics textbooks and assessment criteria. However, Feynman’s lectures and his other works are often insightful. It is worthwhile to analyze Feynman’s discussions of physical concepts that are related to examination questions and assessment criteria. More importantly, classroom discourses based on Feynman’s lectures can be both enlightening and entertaining!

RICHARD P. FEYNMAN* TO BEULAH E. COX, SEPTEMBER 12, 1975 Miss Beulah E. Cox Williamsburg, Virginia Dear Miss Cox: Your instructor was right not to give you any points for your answer was wrong, as he demonstrated using Gauss’ law.  You should, in science, believe logic and arguments, carefully drawn, and not authorities.  You also read the book correctly and understood it. I made a mistake, so the book is wrong.  I probably was thinking of a grounded conducting sphere, or else of the fact that moving the charges around in different places inside does not affect things outside. I am not sure how I did it, but I goofed. And you goofed too, for believing me. We both had bad luck. For the future, I wish you good luck in your physics studies. Sincerely, Richard P. Feynman

Currently, assessment criteria provided by examination boards in the websites could be the finalized versions instead of the proposed initial versions. These assessment criteria serve essentially as a guide to the markers or teachers on how marks should be awarded, based on the considerations of the question requirements and the range of students’ responses. In other words, the sample answers in the assessment criteria could be modified during the moderations such that the marks could be increased or decreased depending on the students’ answer scripts. That is, examiners’ initial proposed assessment criteria might be different from the finalized versions for other various reasons that teachers may not be aware of. However, we will discuss assessment criteria of examination boards such as Advanced Placement (AP), Board of Studies, Teaching and Educational Standards (BOSTES), and International Baccalaureate (IB).

In essence, this blog provides my reflections on selected examination questions and assessment criteria based on Feynman’s insights. Please feel free to give any comments or suggestions. Perhaps an appropriate ending to this introductory post is the following quote from Feynman: “[p]erhaps my lectures can make some contribution. Perhaps in some small place where there are individual teachers and students, they may get some inspiration or some ideas from the lectures. Perhaps they will have fun thinking them through – or going on to develop some of the ideas further (Feynman et al., 1963, preface).”

References:
1. Baierlein, R. (1994). Entropy and the second law: A pedagogical alternative. American Journal of Physics, 62(1), 15-26.
2. Feynman R. P. (1975). Letter to Beulah E. Cox. In Feynman, R. P. (2005). Perfectly reasonable deviations from the Beaten track: The letters of Richard P. Feynman (M. Feynman, ed.). New York: Basic Books.
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
4. Hazel, E., Logan, P., & Gallagher, P. (1997). Equitable assessment of students in physics: importance of gender and language background. International Journal of Science Education, 19(4), 381-392.
5. Sütő, W. M. I., & Nádas, R. (2008). What determines GCSE marking accuracy? An exploration of expertise among maths and physics markers, Research Papers in Education, 23(4), 477-497.
6. Romer, R. H. (2001). Heat is not a noun. American Journal of Physics, 69(2), 107-9.
7. Wong, C. L., Chu, H. E., & Yap. K. C. (2016). Are Alternative Conceptions dependent on Researcher’s Methodology and Definition?: A Review of Empirical Studies related to Concepts of Heat. International Journal of Science and Mathematics Education. 14(3), 499-526.
8. Zemansky, M. W. (1970). The use and misuse of the word “heat” in physics teaching. The Physics Teacher, 8(6), 295-300.