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Solving problems. Define the problem in words, stating what is known and unknown When possible, draw a picture, labeling physical properties Determine what needs to be found, cataloging known and unknown properties Relate unknowns to the known properties through formulae

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solving problems
Solving problems
  • Define the problem in words, stating what is known and unknown
  • When possible, draw a picture, labeling physical properties
  • Determine what needs to be found, cataloging known and unknown properties
  • Relate unknowns to the known properties through formulae
  • Solve the formulae symbolically for the unknowns in terms of the known properties
slide2
Estimate order of magnitude of answer and check units
  • Substitute values for known properties to get best estimate of numerical value
  • Interpret numerical results in terms of physical world
1 state problem
1. State problem
  • Most real world problems are not well stated!

Example: Problems registering for a class

What you say: “I can’t get registered for a class!”

What the problem is: Need to override flags that requires previous physics class, and concurrent enrollment in lab and Trig

What you don’t say: “Need to do an override in either Banner or Blue & Gold to remove flags”

2 draw picture
2. Draw picture
  • “Picture is worth a thousand words”
  • Keep it simple
  • Label everything relevant to problem, but no more
    • Err on side of too much if not sure
  • Draw arrows for items with directions
  • Drawing often provides insight into physical relationships
  • Not all problems can be expressed as a drawing!
3 determine what needs to be found
3. Determine what needs to be found
  • Creates a catalog:
  • Usually have more Knowns than Unknowns
4 write down formulae
4. Write down formulae
  • Number of unique formulae should equal number of unknowns
    • Too few means problem can’t be solved uniquely
    • Too many means problem is overly constrained
  • No particular “right” formula
    • Must containing at least one unknown
    • Pick one with least number of unknowns
  • Interpret symbols appropriately
    • More physical quantities than symbols, so same letter can have multiple meanings
    • Can use different symbols, but be sure to define them!
5 solve equations symbolically
5. Solve equations symbolically
  • Shows relationships between physical parameters
  • Often need to substitute results of one equation into another
    • Beware circular substitutions!
    • “Stair step” solutions together
  • Only way to get full credit on tests!
6 estimate answer
6. Estimate answer
  • Check units
    • Must have same units on both sides of equation!
    • Simple way of estimating types of needed parameters
  • Order of Magnitude check
    • Is answer physically possible?
    • Does answer “make sense”?
7 substitute values
7. Substitute Values
  • Watch for conversions between units
  • Double check that units match across equals sign
  • Realize that answer is only valid for specifics of this problem.
  • Is the answer reasonable and what you expected?
  • Does the precision of the answer reflect the precision of the known parameters?
8 interpret results
8. Interpret Results
  • This is where units become important
  • What does the number mean?
  • Remember to take precision into account
standard units
Standard Units
  • All other units built from combinations of these
metric prefixes
Metric Prefixes
  • Play an important role in making numbers more meaningful
  • Upper case letters usually indicate large scale, lower case usually indicates small scale
  • Life sciences runs full range of scales
    • MCD Biology tends to small scale
    • EPO Biology tends to large scale
order of magnitude estimates
Order of Magnitude Estimates
  • Keep one, or at best two, significant figures
  • Is result reasonable?
  • Do units match on both sides of equations?