Past papers

Feynman's insights, goofs or...?

In a letter to Miss Cox, Feynman (1975) admits that there is a goof in The Feynman Lectures on Physics and explains that her teacher was right in penalizing her for giving the wrong answer. However, there are both insights and goofs in Feynman’s famous lectures and students should not simply memorize his words for examinations. As another example, Feynman (1994) explains that “you can either have the idea that heat is some kind of a fluid which flows from a hot thing, and leaks into the cold thing; or you can have a deeper understanding, which is closer to the way it is – that the atoms are jiggling, and their jiggling passes their motion on to the others (p. 127).” Feynman’s explanations of heat can be considered incorrect because they are related historical conceptions of heat. Currently, in assessment criteria, physics teachers may define heat as a “process of energy transfer” or “energy in transit by virtue of a temperature difference.”

Furthermore, in Feynman’s words, “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).” Based on current assessment criteria, the electromotive force is commonly defined as an open-circuit potential difference or work done per unit charge in moving a quantity of charge completely around a circuit. Thus, students could be penalized if they quote Feynman’s definition of electromotive force during an examination. 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, the discussions below on Feynman’s lectures (insights or goofs) could be both enlightening and entertaining!

References:

1. 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.

2. Feynman, R. P. (1994). No Ordinary Genius: The Illustrated Richard Feynman. New York: W. W. Norton & Company.

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.

Past papers:

Advanced Placement (Physics 1)

Year 2016

AP Physics 1: Algebra-Based 2016 Free Response Question 1 (Rolling wheel)

AP Physics 1: Algebra-Based 2016 Free Response Question 2 (Ball’s collisions)

AP Physics 1: Algebra-Based 2016 Free Response Question 3 (Cart on tracks)
AP Physics 1: Algebra-Based 2016 Free Response Question 4 (Electrical resistance)

AP Physics 1: Algebra-Based 2016 Free Response Question 5 (Wave speed)

Year 2015

AP Physics 1: Algebra-Based 2015 Free Response Question 1 (Atwood’s machine)

AP Physics 1: Algebra-Based 2015 Free Response Question 2 (Electric current)

AP Physics 1: Algebra-Based 2015 Free Response Question 3 (Horizontal block-spring)

AP Physics 1: Algebra-Based 2015 Free Response Question 4 (Projectile)

AP Physics 1: Algebra-Based 2015 Free Response Question 5 (String: standing waves)

International Baccalaureate (Higher level)

Year 2015

IB Physics Paper 2 Time Zone 1 2015 Question 1 (Fluid)

IB Physics Paper 2 Time Zone 1 2015 Question 2 (Newton’s First Law)

IB Physics Paper 2 Time Zone 1 2015 Question 3 (Electromotive force)

IB Physics Paper 2 Time Zone 1 2015 Question 4 (Entropy)

IB Physics Paper 2 Time Zone 1 2015 Question 5 (Quantum efficiency)

IB Physics Paper 2 Time Zone 1 2015 Question 6 (Greenhouse effect)

IB Physics Paper 2 Time Zone 1 2015 Question 7 (Wave-like electrons)

Board of Studies Teaching and Educational Standards (HSC)

Year 2015

BOSTES HSC Physics 2015 Question 26 (Earth’s gravitational field)

BOSTES HSC Physics 2015 Question 27 (Hertz’s experiments)

BOSTES HSC Physics 2015 Question 28 (Faraday’s law)

BOSTES HSC Physics 2015 Question 29 (LHC’s superconductor/mass dilation)

BOSTES HSC Physics 2015 Question 30 (Cassini mission)

BOSTES HSC Physics 2015 Question 31 (Geophysics: remote sensing)

BOSTES HSC Physics 2015 Question 32 (Medical physics: imaging)

BOSTES HSC Physics 2015 Question 33 (Astrophysics: space-based telescopes)

BOSTES HSC Physics 2015 Question 34 (Modern physics: nucleus)

BOSTES HSC Physics 2015 Question 35 (Device physics: transducer)

Selected Publications

1. Wong, C. L., Chu, H. E., & Yap, K. C. (2016). Are Alternative Conceptions dependent on Researchers’ Methodology and Definition? : A Review of Empirical Studies related to Concepts of Heat. International Journal of Science and Mathematics Education. 14(3), 499-526.

2. Wong, C. L., Chu, H. E., & Yap, K. C. (2014). Developing a Framework for analyzing definitions: A Study of The Feynman Lectures. International Journal of Science Education. 36(15), 2481-2513.

3. Wong, C. L. (2013). Is there a best definition of weight? The Physics Teacher, 51(9), 516-7.

4. Lim, K. M., Lee, G. C. F., Sheppard, C. J. R., Phang, J. C. H., Wong, C. L., & Chen, X. (2011). Effect of polarization on a solid immersion lens of arbitrary thickness. Journal of the Optical Society of America A, 28(5), 903-911.

5. Yap, K. C., & Wong, C. L. (2007). Assessing conceptual learning from quantitative problem solving of a plane mirror problem. Physics Education, 42(1), 50-55.

BOSTES HSC Physics 2015 Question 35

Question: 
Students are expected to assess the impact on society in the use of transducers. The answer should include one input transducer and one output transducer (excluding thermistors).

Marking Guidelines:

Criteria	Marks
Provide applications of transducers (excluding thermistors). Assess the impact on society in the use of these transducers. The answer includes the application of an input transducer and an output transducer.	6

(Source: https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/guides/2015-hsc-mg-physics.pdf)

Comments:

According to Usher (1985), the term ‘sensor’ is widely used in the United States, whereas ‘transducer’ is more commonly used in Europe. Furthermore, sensor is derived from the Greek word sentire which means “to perceive” and transducer is originated from the Greek word trans-ducere which means “to lead across.” Currently, a transducer is sometimes defined as a device that transforms electrical energy into non-electrical energy, or vice versa. Alternatively, the American National Standards Institute (ANSI) standard MC6.1 defines a transducer as “a device which provides a usable output in response to a specific measurand (Instrument Society of America, 1975).” In this definition, an output is an electrical quantity, and a measurand is a physical quantity which is measured. However, ANSI’s definition of transducer is not widely adopted. Essentially, the transducer may be considered to be a sensor that converts energy from one form to another.

In this question, students are expected to discuss the impacts of an input transducer and an output transducer on society. However, the types of transducers can be classified as active and passive. Furthermore, we can distinguish the types of transducers according to the quantity that is measured: temperature transducers (e.g. a thermocouple), pressure transducers (e.g. a diaphragm), displacement transducers (e.g. linear variable differential transformer), and flow transducers. More importantly, with the use of a control system, the input transducer can convert a measurable quantity (temperature, pressure, displacement, flow rate) into an electrical quantity (voltage, current, resistance, capacitance) that can be processed by an electronic instrument.

In the marking guidelines, possible answers include solar cells (input transducer) and current meters (output transducer). For solar cells, one may state that there is a conversion of light energy to electrical energy. The impacts of solar cells to society include the reduction of global warming and the improvement in the quality of life by gaining access to communications technologies. For current meters, we can use them to detect electrical energy in a circuit and it can be viewed by connecting to a control system. The impacts of current meters to society include an increase in safety and efficient control of systems. However, students should understand and explain the principles of operations in the use of these transducers.

Feynman’s insights or goofs?:

Feynman has a good explanation on the operation of photoconductive cells (input transducer). He explains that “photons of light (or x-rays) can be absorbed and create a pair if the photon energy is above the energy of the gap. The rate at which pairs are produced is proportional to the light intensity. If two electrodes are plated on a wafer of the crystal and a ‘bias’ voltage is applied, the electrons and holes will be drawn to the electrodes. The circuit current will be proportional to the intensity of the light. This mechanism is responsible for the phenomenon of photoconductivity and the operation of photoconductive cells (Feynman et al., 1966, section 14–1 Electrons and holes in semiconductors).” In short, the operation of solar cells is based on the photoelectric effect. Nevertheless, photoelectric devices can be classified as photo-emissive cells, photovoltaic cells, and photoconductive cells, which may be confusing to introductory students.

Interestingly, one may quibble whether the operation of solar cells is related to photoelectric effect or photovoltaic effect. Currently, the term photoelectric effect is commonly used when the electron is ejected out of the metal into a vacuum, whereas photovoltaic effect is sometimes used when the electron is still contained within the photoelectric or photovoltaic devices. Specifically, one may define the photoelectric effect as the emission of electrons from a metal surface when light shines upon it. However, Feynman explains that photons of light can be absorbed and generate electron-hole pairs if the photon energy is greater than the “energy gap.” Furthermore, he adds that the electron-hole pairs will be drawn to the electrodes if there is a “bias” voltage. More importantly, it is possible that the operating conditions of photoelectric devices can be zero-bias, reverse bias, or high reverse bias.

Feynman also has an insightful explanation on the operation of current meters (output transducer). In his own words, “[t]he same idea can be used for making a sensitive instrument for electrical measurements. Thus the moment the force law was discovered the precision of electrical measurements was greatly increased. First, the torque of such a motor can be made much greater for a given current by making the current go around many turns instead of just one. Then the coil can be mounted so that it turns with very little torque—either by supporting its shaft on very delicate jewel bearings or by hanging the coil on a very fine wire or a quartz fiber. Then an exceedingly small current will make the coil turn, and for small angles the amount of rotation will be proportional to the current. The rotation can be measured by gluing a pointer to the coil or, for the most delicate instruments, by attaching a small mirror to the coil and looking at the shift of the image of a scale. Such instruments are called galvanometers. Voltmeters and ammeters work on the same principle. (Feynman et al., 1964, section 16–1 Motors and generators).” In this case, an important principle of operation is related to the magnetic force on current carrying wire.

To a certain extent, Feynman has sufficiently elaborated the principle of operation pertaining to current meters such as ammeters and voltmeters. Unfortunately, it could be unclear to students when he simply mentions that the discovery of the force law increases the precision of electrical measurements greatly. One may guess whether the force law refers to Lorentz’s force law (F = qE + Bqv), Coulomb’s law of magnetic force (F = kM₁M₂/r²), or Ampère’s force law (F = μ₀I₁I₂/2πr). As usual, Feynman would not care to name the force law (F = BIL or F = Bqv) involved in the magnetic force on current carrying wire as Ampère’s law or Laplace force. Similarly, he prefers to say “the law of inertia” instead of Newton’s first law of motion or Newton’s first law of dynamics. In essence, it is good to focus on the principle of operation; however, it can be confusing to students when the force law is not specified as F = BIL or F = Bqv, though it seems futile to debate whether it should be labeled as Ampère’s force law or Laplace force.

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. Feynman, R. P., Leighton, R. B., & Sands, M. (1966). The Feynman lectures on physics Vol III: Quantum Mechanics. Reading, MA: Addison-Wesley.

3. Instrument Society of America (1975). Electrical Transducer Nomenclature and Terminology. ANSI Standard MC6.1. Research Triangle Park, North Carolina: Instrument Society of America.

4. Usher, M. J. (1985). Sensors and transducers. Macmillan: London.

BOSTES HSC Physics 2015 Question 34

Question: This question is asked in the context of particle physics. Students are expected to assess the impact of three advances in knowledge relating particles and forces on an understanding of the atomic nucleus.

Marking Guidelines:

Criteria	Marks
Provide three advanced knowledge relating particles and forces. Assess their impact on the understanding of the atomic nucleus.	6

(Source: https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/guides/2015-hsc-mg-physics.pdf)

Comments:

This question is about an understanding of particles and forces that are related to the structure and behavior of the atomic nucleus. The answer may be summarized as shown below:

1. Strong interactions: The strong force is responsible for holding nuclei together and it is mediated by gluons.

2. Weak interactions: The weak force is responsible for nuclear transformation or radioactive decay processes and it is mediated by W and Z particles.

3. Electromagnetic interactions: The electromagnetic force is responsible for repulsive forces among protons in nuclei and it is mediated by photons.

4. Standard Model: A proton is composed of two up (u) quarks and one down (d) quark, whereas a neutron is composed of two down (d) quarks and one up (u) quark.

5. Asymptotic freedom: The strength of the strong interactions decreases as the quarks approach one another, and increases as they separate.

6. Nuclear stability: Knowledge of forces and particles helps to explain how nuclei are stable despite the repulsion due to the electromagnetic interactions of protons.

Furthermore, one may prefer to include a mathematical equation to explain quarks and gluons in the nuclei. For instance, one may rewrite Einstein’s famous equation as m = E/c² and elaborate that energy is the source of mass and it is due to the energetic but massless quarks and gluons. However, much work is still needed to investigate the nature of nuclear forces.

Feynman’s insights or goofs?:

The Feynman Lectures on Physics is slightly outdated for this question. For example, in Feynman’s words, “there seem to be just four kinds of interaction between particles which, in the order of decreasing strength, are the nuclear force, electrical interactions, the beta-decay interaction, and gravity. The photon is coupled to all charged particles and the strength of the interaction is measured by some number, which is 1/137. The detailed law of this coupling is known, that is quantum electrodynamics. Gravity is coupled to all energy, but its coupling is extremely weak, much weaker than that of electricity. This law is also known. Then there are the so-called weak decays — beta decay, which causes the neutron to disintegrate into proton, electron, and neutrino, relatively slowly (Feynman et al., 1963, section 2–4 Nuclei and particles).” Currently, we use the terms strong interaction and weak interaction instead of meson-baryon interaction and beta-decay interaction. Moreover, the law involved is quantum chromodynamics rather than quantum electrodynamics.

Importantly, Feynman mentions that “There is another question: ‘What holds the nucleus together?’ In a nucleus, there are several protons, all of which are positive. Why don’t they push themselves apart? It turns out that in nuclei there are, in addition to electrical forces, nonelectrical forces, called nuclear forces, which are greater than the electrical forces and which are able to hold the protons together in spite of the electrical repulsion. The nuclear forces, however, have a short range — their force falls off much more rapidly than 1/r² (Feynman et al., 1964, section 2–4 Nuclei and particles 1–1 Electrical forces).” Note that physicists have a better understanding of the strong interaction in 1973 when Frank Wilczek, David Gross, and David Politzer propose the concept of asymptotic freedom. Furthermore, the nuclear force is sometimes explained to be a residual effect of the strong interaction.

On the other hand, Feynman adds that “[t]he origin of the forces in nuclei leads us to new particles, but unfortunately they appear in great profusion and we lack a complete understanding of their interrelationship, although we already know that there are some very surprising relationships among them. We seem gradually to be groping toward an understanding of the world of subatomic particles, but we really do not know how far we have yet to go in this task (Feynman et al., 1963, section 2–4 Nuclei and particles).” Currently, we still do not have a complete understanding of everything in particle physics. For instance, a mysterious bump in experimental data at CERN’s Large Hadron Collider in 2015 could generate over 500 theoretical papers. However, the bump could be simply explained as a noise instead.

More importantly, Wilczek (2007) explains that “[o]ur quest to understand the force that holds atomic nuclei together has turned out to be a glorious adventure. Along the way, we have found quarks, the colored gluons that mediate the strong nuclear force, and a wonderful theory — quantum chromodynamics, or QCD. This theory has guided experimental research at the high-energy frontier, inspired dreams of ‘unified field theories’ that would embrace all nature’s forces, and allowed theoretical physics to penetrate into the cosmology of the early Universe. In all this, the original problem of understanding nuclear forces has rather fallen by the wayside (p. 156).” Our understanding of nuclear forces is still incomplete. Physicists have assumed that nuclear forces are a residual effect of strong interaction without a good mathematical model.

Note: 

Wilczek (2007) explains that “[i]n principle, the equations of QCD contain all the physics of strong internucleon forces. But in practice, it is extremely difficult to solve the equations and calculate those forces. Ishii and colleagues’ breakthrough calculation required sophisticated algorithms, running on the biggest and fastest massively parallel computers currently available. Why are the calculations so difficult? The main reason is simply that nucleons are complicated objects. It is often said that protons (and neutrons) are made from three quarks. That statement contains a kernel of truth, but it is a gross oversimplification (p. 156).”

References: 

1. 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.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.

3. Wilczek, F. (2007). Particle physics: Hard-core revelations. Nature, 445(7124), 156-157.