I have been asked to comment on a question on an exam at some other
university that I will not mention.
On an exam, the professor intended to write a center-of-mass problem
similar to what we often see...
A 20-kg dog is in a 50-kg boat on a calm lake. The boat is
free-floating without any anchor or attachment to the dock. The dog 20
m from the dock.
Here is the ambiguous statement followed by the question...
The dog walks 3 meters toward the dock. After this walk, how far is the
dog from the dock?
Here's why it is ambiguous... The professor did not say with relation to
what the dog moved. Did he travel 3 meters relative to the dock, or
three meters relative to the boat.
Since the dock was mentioned in the statement about the 3-m walk, but
the boat was not, and since the initial position of the dog was given
with respect to the dock, many students thought the dock was obviously
the reference point, and so the dog clearly walked three meters relative
to the dock. Some of these students even thought it might be a trick
question, but they answered it literally... "the dog ends up 17 meters
from the dock.
The professor says that since they were studying center of mass, it
should have been obvious that the boat goes away from the dock while the
dog walks toward the dock, and it should have been obvious that the
professor meant the 3-meter walk was relative to the boat.
However, some students have found example problems in textbooks in which
the moving dog or person moves a distance relative to the dock (or
shore) and the question is how far does the boat move away from the
dock/shore. That is, when a problem is given in which a person in a
boat walks a certain distance, it is not always assumed the distance
walked is with respect to the boat. The wording "walks 3 meters toward
the dock" could easily be construed to mean 3 meters with respect to the
dock. (I myself assumed this when I first read the problem. Then I
realized the prof really meant relative to the boat, otherwise the
problem is trivial. Then I thought uh-oh... He wasn't clear.)
At least one student even wrote down the CM analysis and stated that the
center of mass of the dog/boat system does not move. The student
indicated the boat would move away from the dock. But the student
finally wrote the answer as, "But hey, if the dog starts 20 meters from
the dock and walks 3 meters toward the dock, he ends up 17 meters from
the dock."
I would be inclined to give this student full credit (as well as all the
others who answered 17 m even if they didn't give the CM information).
Comments?
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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