Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 6.6
In the design of a roller coaster, is it possible for any hill of the ride to be higher than the first one? If so, discuss how. If not, then discuss why this would be impossible. Explain your reasoning using the properties of energy conservation.
Solution and grading rubric:
- p:
Correct. Either of two answers suffices using properties of energy conservation: (a) if the roller coaster car starts at rest from the first hill, and no additional energy is put into the system after it is released, then the second hill can at most be as high as the first (under ideal conditions only), or lower; or (b) if the car has been given sufficient kinetic energy at the top of the first hill, then it may make it over a second hill that is higher. - r:
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. - t:
Nearly correct, but argument has conceptual errors, or is incomplete. Argument somehow based on momentum conservation; but at least recognizes that the second hill must be at most as high as the first hill unless something is done. - v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Typically states that the second hill can be higher, but does not clearly explain how this would be possible. - x:
Implementation/application of ideas, but credit given for effort rather than merit. - y:
Irrelevant discussion/effectively blank. - z:
Blank.
Grading distribution:
p: 27 students
r: 0 students
t: 7 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students
A sample of a "p" response (from student 2607) is shown below:
Another "p" response (from student 5711):
A sample of a "v" response (from student 7937), where it is argued that each subsequent hill can be higher than the first:
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