Student ability to apply the concepts of work and energy to extended systems

American Journal of Physics

Volumn 77, Issue 11, 2009, Pages 999-1009

  Lindsey, Beth A ^a,b   Heron, Paula R L ^a   Shaffer, Peter S ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

^b GEORGETOWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350014980     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3183889     Document Type: Article

References (33)

1. See, for example, T. A. Moore, Six Ideas That Shaped Physics, Unit C: Conservation Laws Constrain Motion, 2nd ed. (McGraw-Hill, New York, 2003); R. W. Chabay and B. A. Sherwood, Matter and Interactions I: Modern Mechanics (Wiley, New York, 2002).
2. B. A. Sherwood, " Pseudowork and real work.," Am. J. Phys. 0002-9505 51 (7), 597-602 (1983) 10.1119/1.13173; A. B. Arons, " Development of energy concepts in introductory physics courses.," Am. J. Phys. 0002-9505 67 (12), 1063-1067 (1999). 10.1119/1.19182
3. J. W. Jewett, Jr., " Energy and the confused student I: Work.," Phys. Teach. 0031-921X 46 (1) 38-43 (2008) 10.1119/1.2823999; J. W. Jewett, Jr., " Energy and the confused student II: Systems.," Phys. Teach. 0031-921X 46 (2), 81-86 (2008) 10.1119/1.2834527; P. W. Bridgman, The Nature of Thermodynamics (Harvard U. P., Cambridge, 1941).
4. M. E. Loverude, C. H. Kautz, and P. R. L. Heron, " Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas.," Am. J. Phys. 0002-9505 70 (2), 137-148 (2002). 10.1119/1.1417532
5. R. A. Lawson and L. C. McDermott, " Student understanding of the work-energy and impulse-momentum theorems.," Am. J. Phys. 0002-9505 55 (9), 811-817 (1987). 10.1119/1.14994
6. A. Van Heuvelen and X. Zou, " Multiple representations of work-energy processes.," Am. J. Phys. 0002-9505 69 (2), 184-194 (2001). 10.1119/1.1286662
7. U. Ganiel, " Elastic and inelastic collions: A model.," Phys. Teach. 0031-921X 30 (1), 18-19 (1992). 10.1119/1.2343453
8. X. Zou, " Making internal thermal energy' visible.," Phys. Teach. 0031-921X 42 (6), 343-345 (2004). 10.1119/1.1790340 (Pubitemid 39174362)
9. C. Singh and D. Rosengrant, " Multiple-choice test of energy and momentum concepts.," Am. J. Phys. 0002-9505 71 (6), 607-617 (2003). 10.1119/1.1571832 (Pubitemid 36743007)
10. In addition to Refs., see R. Driver and L. Warrington, " Students' use of the principle of energy conservation in problem situations.," Phys. Educ. 0031-9120 20 (4), 171-176 (1985) 10.1088/0031-9120/20/4/308; A more complete listing of articles relating to work and energy in a thermodynamical sense, particularly to student understanding of heat and temperature, can be found in L. C. McDermott and E. F. Redish, " Resource Letter: PER-1: Physics education research.," Am. J. Phys. 0002-9505 67 (9), 755-767 (1999). 10.1119/1.19122
11. B. A. Lindsey, P. R. L. Heron, and P. S. Shaffer, " Student understanding of energy: Difficulties related to systems. " (in preparation).
12. Several pilot sites have used versions of the instruction materials we have developed on energy. They have also administered pretests and post-tests. The results obtained are consistent with those presented in this paper.
13. See, for example, P. S. Shaffer and L. C. McDermott, " Research as a guide for curriculum development: An example from introductory electricity. Part II: Design of an instructional strategy.," Am. J. Phys. 0002-9505 60 (11), 1003-1013 (1992). 10.1119/1.16979
14. L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice-Hall, Upper Saddle River, NJ, 2002).
15. References provide examples of studies in mechanics that involve systems undergoing changes in both kinetic and potential energy, but neither of these studies probed these concepts or the relation between them in detail.
16. The work-energy theorem, Wnet =Δ K, is derived from Newton's laws and therefore cannot fail. The relation holds unambiguously for individual particles, but there are many situations in which the application may not be obvious, especially for extended systems. The treatment of the relation Wnet =Δ K in textbooks is particularly problematic when it is derived by relating the net force on a system to the net work done on that system. As described in Sec., these quantities are not necessarily related for extended systems. For a complete discussion of the work-energy theorem, see A. J. Mallinckrodt and H. S. Leff, " All about work.," Am. J. Phys. 0002-9505 60 (4), 356-365 (1992). 10.1119/1.16878
17. The second article in the sequence of articles by Jewett in Ref. provides a particularly accessible summary of this issue.
18. Questions as posed always referred to the changes in "total energy" of a system. In practice, they could also have asked about the changes in "total mechanical energy" of the system, where "total mechanical energy" refers to the sum of the kinetic energy, gravitational potential energy, and elastic potential energy. In each of these problems, the change in total mechanical energy of each system is equivalent to the change in total energy of the system, as we did not ask students to consider systems in which nonmechanical forms of energy (such as thermal energy) were changing.
19. Reference presents results from our investigation into student ability to apply the concepts of work, potential energy, and changes in energy when students are asked to consider two or more different choices for the objects included in the system under consideration.
20. Because the online pretests were administered unsupervised, students could consult textbooks, the web, etc. during that time. There is no evidence that students used these resources.
21. Due to rounding, the percentages shown do not always sum to the totals that are given in the tables. In particular, percentages do not always sum to 100%.
22. It might be argued that the part of the wall in contact with the spring undergoes an infinitesimal displacement. If students were to make reference to this fact, their response would be considered correct. In practice, student responses generally referred to the motion of the spring or the block. No students made reference to any displacement of the wall.
23. The data shown in Table are from a section in which the question was asked before instruction on work and energy had been completed. The term "work" had not yet been introduced in lecture, but the students had completed a laboratory experiment on work and energy that included the definition of work. Findings from related questions posed in sections after all lecture instruction on work and energy indicate that the results are similar even with lecture instruction.
24. This question also gave some evidence for difficulties identified in other studies. For instance, about 5% gave responses such as "The wall is not the cause of the movement of the block, so it does no work on the system." This argument is consistent with the previously reported tendency of students to associate work only with "active" forces (Ref.).
25. This problem provides a striking example of a case in which the net force on the system cannot be used to calculate the net work on the system. The net force on this system is zero, but the net work is nonzero. The net force can only be associated with the net work for cases in which the displacement of the point where each force is applied is the same (as is true for a particlelike system).
26. On the version of the two-block problem that had no preliminary questions, 45% of the students answered the question about the net work done on the system correctly (30% with correct reasoning). About 50% gave the incorrect answer that the net work done is zero (N=203). Both versions (with and without the preliminary questions) were administered under the same circumstances.
27. The reflexive use of the phrase "energy is conserved" by students is documented in Ref., as well as in T. O'Brien Pride, S. Vokos, and L. C. McDermott, " The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems.," Am. J. Phys. 0002-9505 66 (2), 147-157 (1998). 10.1119/1.18836 (Pubitemid 128449859)
28. The student difficulties with conservation of energy documented in this paper are consistent with observations of students by Eric Mazur. He suggested using the term "conserved" to apply only to the total energy of the universe and "constant" for cases in which the energy of a particular system is not changing. Thus, energy is always conserved because the total energy of the universe never changes, but the energy of any individual system may or may not be constant. E. Mazur (private communication). This issue was also discussed by E. Mazur in his Millikan Award lecture at the 2008 Summer Meeting of the AAPT in Edmonton, Alberta, " Physics reality distortion: Why the world of physics and the real world are different in students' minds.. "
29. L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics, 2nd ed. (Prentice-Hall, Upper Saddle River, NJ, in preparation).
30. The first law of thermodynamics states that Wnet,ext +Q=Δ Etotal, where Q represents the heat transferred to the system. We neglect the heat term in this equation because we are focusing on the context of introductory mechanics.
31. This task also appears in the tutorial Changes in Energy and Momentum in Ref..
32. The treatment of energy described in this section is modeled after that described in Ref
33. The exercises on systems that we had incorporated into the tutorials were motivated, in part, by the reflections of experienced instructors who have argued that the choice of system is critical to coherent instruction on energy conservation. See, for example, Refs..