We report results from an investigation of student ability to apply the concepts of work and energy to situations in which the internal structure of a system cannot be ignored, that is, the system cannot be treated as a particle. Students in introductory calculus-based physics courses were asked written and online questions after relevant instruction by lectures, textbook, and laboratory. Several difficulties were identified. Some related to student ability to calculate the work done on a system. Failure to associate work with the change in energy of a system was also widespread. The results have implications for instruction that aims for a rigorous treatment of energy concepts that is consistent with the first law of thermodynamics. The findings are guiding the development of two tutorials to supplement instruction.
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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.
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References 6 and 9 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, , 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 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. III C, these quantities are not necessarily related for extended systems. For a complete discussion of the work-energy theorem, see
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The second article in the sequence of articles by Jewett in Ref. 3 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 11 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 III 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. 4).
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 . 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. 5, 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.
66
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(1998
).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 , where 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. 14.
32.
The treatment of energy described in this section is modeled after that described in Ref. 6.
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. 2 and 3.
© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
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