Very interesting. As you point out, this works because of the unique situation (object 2 was initially stationary). I never saw this in a book either.
However, if this question were a "show all work" type of problem, I would not give the student credit for this response, unless he/she can demonstrate why it works.
There are similar oddities that work for other types of problems, and the AP Physics test does not give credit for the correct answer unless the right physics is identified to show that the student understands the physics behind the solution.
Betty Jensen, Ph.D.
Michael Edmiston <edmiston@bluffton.edu> wrote: I just got done grading the final exam for a student in which the student got the correct answer to a problem by a method that did not make sense to me. I thought he got the right answer by an accidental quirk. However, it turns out the method he used is indeed a general method to get the correct answer. I am wondering if this is common knowledge. It is not in any textbook I have on my shelf, and I have never noticed this myself in 30 years of teaching. I still think the student made a lucky guess, but I want to ask list members of any of you think this method is common knowledge.
The problem is a one-dimensional perfectly-inelastic "dead-on" collision. Mass one (m1) comes in with initial velocity v1i and strikes stationary mass two (m2). The two masses stick together and the combined mass (m1+m2) goes off with final velocity vf. The data for the problem are m1, m2, and v1i and a statement that the collision is perfectly inelastic. Part-A of the problem asks them to solve for vf. Part-B of the problem asks them to solve for the percentage of KE retained.
I assumed students would get the percentage by KEf/KEi*100%. However, one student got the correct answer by vf/v1i*100%. I first marked it wrong with the comment that the answer was accidentally correct. But then I did a little algebra and discovered this method is correct in general. I doubt the student knew that. I've never seen it before. Has anybody on the list seen this? Does this appear in any textbook you are aware of?
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu
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