ERTH 535: Planetary Climate Change (Spring 2017) Good Strategy for Solving Physical Problems Dr. Dave Dempsey Dept. of Earth & Climate Sci., SFSU

Educational researchers at U.C. Berkeley in the 1970's studied good physical problem-solvers to find out what strategies they used to solve physical problems and to see if those strategies could be taught to inexperienced problem solvers. The strategy they found consisted of a series of separate steps, as follows:

1. Summarize information given in the problem statement or that you otherwise know and that you need to solve the problem. In particular:

1. define each quantity in English

2. define a symbol for each quantity (preferably mnemomic in some way; to use as shorthand notation)

3. assign a value and units to each symbol

4. [optional: convert to some other units if desired]

2. State information desired (that is, what you want to know by solving the problem)

1. define each such quantity in English

2. define a symbol for each quantity

3. Identify and list relations needed to connect the information you're given (or otherwise know) to the information desired.

1. write each relation mathematically

2. identify it by name

3. define any new symbols appearing in it, in English

4. if new symbols in the relation(s) have known values (e.g., physical constants), assign values and units (though you can, and perhaps should, add these to Step I above instead of listing them here)

4. Solve the problem symbolically first, then numerically.

1. Manipulate relations listed in Step III algebraically to get a symbolic solution, narrating each step of the solution and stating any assumptions or approximations made along the way. In a symbolic solution, the info desired is on the left-hand side and only info known is on the right-hand side. There shouldn't be any actual numerical values with units in the solution—it should be symbolic and hence quite general.

2. Solve the problem numerically, in steps in the following order:

1. substitute numbers, powers of ten, and units for symbols on right-hand side of the symbolic solution

2. group separately: numbers, powers of ten, and units

3. manipulate units algebraically to simplify them (and when done, make sure that they make sense—if not, a mistake happened somewhere and there's no point in proceeding before finding the mistake)

4. combine powers of ten

5. calculate numerical solution (the very last step—no calculation should precede this!)

5. Check solution for physical reasonableness

(Is the solution physically reasonable—are units appropriate, the sign correct, the value of a reasonable order of magnitude? If not, something went wrong somewhere.)

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