Home area for Cheng Chin's SMART program.
This space is for the one day version of the Cratering lab which is used for Cheng's summer SMART outreach program.
Outline
Motivation : Describe cratering and pose question of how would you estimate the yield of a nuclear bomb, or the energy of an asteroid that made a crater on earth or the moon?
Scientific Process :
Develop a specific and testable question to explore.
Use theory or build a model to describe how you expect the system to behave. Understand your underlying assumptions.
Design an experiment to test the model.
Conduct your experiment.
Evaluate how well your data do, or do not, match your model.
Use your model to predict something beyond the range you tested.
Test your prediction.
Use your model to estimate energies for the Sedan crater and the one that killed the dinosaurs.
Examples of Scaling Laws
Metabolic Rate as a function of Body Weight. From the mass of a mouse to the mass of an elephant span 6 orders of magnitude. Corresponding metabolic rates cover about 4 orders of magnitude.
Average Life Span vs Mass.
Brain Mass vs Body Mass.
Aerodynamics. Wind tunnel tests.
Financial Markets.
Instructor Preparation Notes
Instructors should be prepared talk about the following:
Scaling Laws and their significance. Some examples are given above.
What is a power law.
Importance of thinking about what you are doing as you are doing the experiment.
What data to take?
How well do you know what you have measured. What is limiting your ability to know your measured quantities better?
Is your data “good enough”. When do you have enough data?
What are your measured quantities.
How useful it is to plot and visualize the data as you take it.
How physicists think about scientific investigation.
Curve Fitting this has to be very qualitative.
Things to be prepared for while the lab is running.
Look for opportunities to get all the students together for group discussions, or to demonstrate something. I gave the example of doing this when the students are all at the point of needing to think about the range of energies they should cover. Another possibility is illustrating how to plot the data in log-log space to evaluate their progress.
How to motivate students to improve their setups and techniques. There is a balance between just taking some quick and probably crappy data, and tediously refining your process. Students will get frustrated if you wait too long to suggest changes, but you also don't want to just tell them the “right” way to do everything. An important lesson in all this is the thinking that goes into doing the experiment.
How will you guide students in deciding how much data to take and over what range of values. Some important considerations for this experiment are:
Since this is a powerlaw, and a shallow one at that, you want to cover as many orders of magnitude in energy as you can. You really cannot answer this question without looking at the data as you collect it.
When do they have enough data?
How many times should they repeat measurements? Why repeat measurements?
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