Solving problems

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# Solving problems - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Solving problems' - matty

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Presentation Transcript
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
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
• 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
• “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
• Creates a catalog:
• Usually have more Knowns than Unknowns
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
• 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!
• Check units
• Must have same units on both sides of equation!
• Simple way of estimating types of needed parameters
• Order of Magnitude check
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
• This is where units become important
• What does the number mean?
• Remember to take precision into account
Standard Units
• All other units built from combinations of these
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
• Keep one, or at best two, significant figures
• Is result reasonable?
• Do units match on both sides of equations?