The problem description below pertains to the CTL proposal,
"Preparing Students for STEM Majors: A Thinking Skills Approach",
submitted by J. Deming and N. Moore.
Global Overview
A typical week in the course might look like the following. The science topic
for the week is the study of equilibrium and oscillations. The mathematics
emphasized in this unit would be periodic functions like sine and cosine,
frequency, angular frequency, and oscillation period.
Before the Week Starts:
On the Friday preceding the week, the students would be assigned a series of
thinking questions to answer in their lab journals before coming to monday's class.
Typical preparation questions for a week on oscillations might look like:
Over the summer, you found a job at Rapala. Your specific internship involves making
bobbers that are heavy enough to cast well, but still oscillate wildly when a fish
is nibbling on the bait. To get familiarized with the project, your boss suggests
you figure our what parameters are important in making a good bobber.
Please answer the following questions in your lab journal before coming to class on monday.
- Think about a child, swinging on a swingset. If the kid doesn't pump their legs, and their parent stops pushing them, what will their motion look like over time? Draw a picture, and then draw a graph.
- Find a swingset at one of the parks in Winona and try the swings out. Think about what you're doing quantitatively and record what you notice. For example, how much time elapses between successive visits to the top of the swing's arc? When are you pushed down into the seat of the swing the most, etc.
- While you're out at the park, try and find a swingset that's full of kids. Do all of the kids swing at the same rate? Are there any relationships you can identify?
On Monday: Problem and equipment are introduced
On Monday the students would gather in their groups and discuss their answers to
their preparation questions. After sharing observations, the students would be given
two systems, the first being a film canister, pennies, and a beaker of water, to
model a fishing bobber of varying density. The second system would be a wire spring,
a stand to hang the spring from, and a set of weights. In addition to the equipment described
above, the students would also be given a list of study questions which would help
structure their study of the mechanical system.
System 1: Fishing Bobbers
To investigate the fishing bobber, take an empty film cannister and add enough pennies for the cannister to just barely float.
Look at the cannister. Make it bounce in the water for a while. After playing with the system, please write down answers to the following questions. (not to be handed in, just to organize your thoughts)
- Draw a graph that describes the bobber's motion over time.
- Take half of the pennies out and play with the cannister some more. Describe what has changed about the motion.
- Is a "good" bobber long and thin or wide and fat?
- How would you describe the cannister's equilibrium position? From previous investigations, do you have a graph
(or can you make one?) that gives this equilibrium position as a function of the number of pennies you've added?
- If you move the cannister away from equilibrium, what makes the cannister move back to equilibrium? Draw two pictures to explain your answer.
System 2: Mechanical Springs
For the second system, the mechanical spring, the questions would be similar:
The bouncing motion you saw with the bobbers reminded you of the motion of your old
car (that had broken shock absorber). Whenever you drove over a bump, the back end
of the car would bounce and then oscillate for a few seconds. Hang a spring from the
lab stand and then add some mass with the mass-hanger.
- What does it take for the spring not to jiggle or bounce around?
- Describe the spring's motion after mass is added. (a graph might be useful here)
- Find the spring's equilibrium position, and then track how that equilibrium position changes with the addition of mass (weight) to the mass hanger. (a graph might be useful here)
- How much time does the spring take to oscillate once?
- How does this time depend on the mass you've added to the spring? (a graph might be useful here)
- How does this time depend on how far the spring is from equilibrium initially? (a graph might be useful here)
- If you move the spring/mass-hanger away from equilibrium, what makes the system move back to equilibrium? Draw two pictures to explain your answer.
Wendesday: Continued Investigation and Free-form Exploration
Wednesday's work would be similar, albeit less structured with physical systems
of rubber bands and clock pendulums. Students would again need to design their own
investigations into the systems and create their own description of the physics they're seeing.
Note that in these questions, the students are asked to think about questions that are more
complicated than simple experiment design.
System 3: Rubber Bands
Rubber bands are similar to springs, plus, in a water environment they won't rust, so they
might be better to use in a fishing lure. We've got some sections of bicycle tire and rubber
bands in class. Please investigate the rubber bands like you did springs.
- Do rubber bands behave basically the same as springs? Are there relevant differences in their behavior?
- What the difference is there between a thin strip of rubber (1cm in width) and a thick strip of rubber
(2cm in width). What about the difference between a strip of 10cm in length compared to 20cm in length.
- The flexibility of an uncooked linguine noodle is different depending how the noodle is bent.
Why is a lasagna noodle much stiffer than a fettuccine noodle?
System 4: Clock Bobs
The bob on a grandfather clock (a pendulum) has some of the same back and forth behavior that the other
systems presented exhibit. As you did before, please try to identify equilibrium, the nature of the
motion a pendulum exhibits, and how that motion changes as the pendulum's construction changes.
While you're making this investigation, please try to figure out the answer to the following questions:
- Why do long-legged people walk faster than short legged people?
- Is there a physiological reason why people swing their arms while walking?
Friday: Summarizing Knowledge and Making Connections to New Systems
On Friday, the students would be asked to summarize and extend their knowledge by working
in groups on a few short answer problems of the following sort. Rather than reproducing the questions on this web page,
please follow the following links to the pdf questions that the students answered in an exercise like this.
- The Friday quiz given to students in WSU SCIE 201, Spring 2008, Spring Questions
- The solution we provided after the students finished is also available, Solution