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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

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Solving problems

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  1. 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

  2. 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

  3. 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”

  4. 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!

  5. 3. Determine what needs to be found • Creates a catalog: • Usually have more Knowns than Unknowns

  6. 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!

  7. 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!

  8. 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”?

  9. 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?

  10. 8. Interpret Results • This is where units become important • What does the number mean? • Remember to take precision into account

  11. Standard Units • All other units built from combinations of these

  12. 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

  13. Order of Magnitude Estimates • Keep one, or at best two, significant figures • Is result reasonable? • Do units match on both sides of equations?

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