Re: plug and chug

[John Clement <clement@HAL-PC.ORG>]

> There has been some discussion of problems that are not "plug-and-chug",
> but if there were any examples, I missed them.  So here are two from my
> weekly 15 minute quizzes.  The text was "The Mechanical Universe", the
> course was calculus based, notes and calculators were not permitted.

Here is a problem designed for cooperative group problem solving from the
Hellers' book available at:
http://www.physics.umn.edu/groups/physed/Research/CGPS/GreenBook.html

===================================
Because of your knowledge of physics, you have been assigned to investigate
a train wreck between a
fast moving passenger train and a slower moving freight train both going in
the same direction. You
have statements from the engineer of each train and the stationmaster as
well as some measurements
which you make. To check the consistency of each person's description of the
events leading up to the
collision, you decide to calculate the distance from the station that the
collision should have occurred if
everyone were telling what really happened and compare that with the actual
position of the wreck
which is 0.5 miles from the station. In this calculation you decide that you
can ignore all reaction times.
Here is what you know:
• The stationmaster claims that she noted that the freight train was behind
schedule. As regulations
require, she switched on a warning light just as the last car of the freight
train passed her.
• The freight train engineer says he was going at a constant speed of 10
miles per hour.
• The passenger train engineer says she was going at the speed limit of 40
miles per hour when she
approached the warning light. Just as she reached the warning light she saw
it go on and
immediately hit the brakes.
• The warning light is located so that a train gets to it 2.0 miles before
it gets to the station.
• The passenger train slows down at a constant rate of 1.0 mile per hour for
each minute as soon as
you hit the brakes.
DO ONLY THE PROBLEM SOLVING STEPS NECESSARY TO FOCUS THE PROBLEM
AND DESCRIBE THE PHYSICS OF THE PROBLEM. DO NOT SOLVE THIS PROBLEM.
===================================
This type of problem is not used on the individual portion of their exams,
only on the group portion of exams.

Here is one of my favorite problems from Minds on Physics.  It is available
at
http://umperg.physics.umass.edu/projects/MindsOnPhysics/MOPSamples/
Click on activity 16.
===================================
Merinda and her little bother Joey are having a foot race from the edge of a
road to a street lamp and back.  At t=0 sec, Merinda starts.  She runs at
2.5 m/s all the way to the street lamp and back to the starting point.  Joey
is not yet ready at t=0s, and doesn't start running until t=2 s; then he
runs at 1.5 m/s to the street lamp and back. (The drawing shows the lamp is
15 m from the curb)

When and where do they meet?  Where is Joey when Merinda reaches the street
lamp?  How far apart are Joey and Merinda when Merinda gets back to the
starting point?
===================================
HS students successfully solve this problem using a strobe diagram, and also
using a graph.  However only 1-2% are able to solve it using equations.
They first do a strobe diagram, then try equations.  After about 10 min they
are encouraged to switch to the graphical method.  Students who actually
successfully use equations often take hours to figure out the answer.  I
always suggest that sketching the graph first makes it possible to easily
figure the equations.  Each class finishes the problem in under 45 min, and
even finishes the accompanying reflections.

I think it is fair to say these are both NOT plug and chug problems.

John M. clement
Houston, TX