Take a spring, stretch it an inch or two, and imagine the force exerted by it. You will have no difficulty with this problem, and a layman or child will have no difficulty either, especially if you use the term “pull” instead of “force” in your question. Now take a second similar spring, hook it to the first one, and stretch the combination until each spring is extended to the same distance as the single spring before. When you then ask about the pull, most nonphysicists will state that it is obviously twice what it was before, because there are two springs instead of one. Try to convince them that the force has the same magnitude as before, because each spring is stretched by the same amount! How would you proceed?
REFERENCES
1.
J. Piaget, The Child's Conception of Physical Causality, Littlefield Adams, Paterson N.J. (1960);
B. Inhelder, J. Piaget, The Growth of Logical Thinking from Childhood to Adolescence, Basic Books, New York (1958).
2.
M. Almy, E. Chittenden, P. Miller, Young Children's Thinking, Teacher's College Press, New York (1966).
3.
J. Bruner, The Process of Education, Harvard U.P., Cambridge (1960).
4.
J. McV. Hunt, Intelligence and Experience, Ronald, New York (1961).
5.
6.
R. Karplus, C. S. Lavatelli, “Conservation” and “Classification,” Davidson Films, San Francisco (1967).
7.
R. Karplus, R. W. Peterson, “Intellectual Development Beyond Elementary School II. Ratio, A Survey,” in School Science and Mathematics, December 1970, page 813, and “Formal Thought,” Davidson Films, San Francisco (1967).
8.
See reference 4, pages 362–363.
9.
C. E. Silberman, Crisis in the Classroom, Random House, New York (1970).
10.
The “Science Curriculum Improvement Study” curriculum materials are published by Rand McNally and Company, Chicago.
11.
and J. Langer, University of California, Berkeley, private communication.
12.
PSNS Project Staff, An Approach to Physical Science, Wiley, New York (1969).
13.
IPS Group, College Introductory Physical Science, Prentice Hall, New York (1969).
14.
R. Karplus, Introductory Physics, A Model Approach, Benjamin, New York (1969).
15.
Brunschwig, “Waves and Sound—an Mperiment that Walks,” in AAPT Announcer vol. 1, no. 2, December 1971
16.
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© 1972 American Institute of Physics.
1972
American Institute of Physics
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