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Dimensional Analysis

Dimensional Analysis. Dimensional Analysis. The systematic method of converting from one unit to another. Why is dimensional analysis important?. How Does Dimensional Analysis Work?. A conversion factor is used, along with what you’ re given, to determine what the new unit will be.

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Dimensional Analysis

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  1. Dimensional Analysis

  2. Dimensional Analysis • The systematic method of converting from one unit to another. • Why is dimensional analysis important?

  3. How Does Dimensional Analysis Work? • A conversion factor is used, along with what you’re given, to determine what the new unit will be.

  4. How Does Dimensional Analysis Work? • If we write these expressions mathematically, they would look like 3 cm = 50 km

  5. Examples of Conversion Factors • 60 s = 1 min • 60 min = 1 h • 24 h = 1 day

  6. Examples of Conversions • You can write any conversion factors as fractions. For example, you can write: 60 s = 1 min as 60s or 1 min 1 min 60 s

  7. Examples of Conversions • Again, just be careful how you write the fraction. • The fraction must be written so that like units cancel.

  8. Steps • Start with the given value. • Write the multiplication symbol. • Choose the appropriate conversion factor. • The problem is solved by multiplying the given data & their units by the appropriate unit factors so that the desired units remain. • Remember, cancel like units.

  9. Learning Check #1 2. How old are you in days? Given: 17 years Want: # of days Conversion: 365 days = one year

  10. Solution • Check your work… 6.205 x 103days 17 years 1 365 days 1 year X =

  11. Learning Check #2 3. There are 2.54 cm in one inch. How many inches are in 17.3 cm? Given: 17.3 cm Want: # of inches Conversion: 2.54 cm = one inch

  12. Solution • Check your work… 6.81 inches 17.3 cm 1 1 inch 2.54 cm X = Be careful!!! The fraction bar means divide.

  13. Multiple-Step Problems • Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions. • Example: How old are you in hours? Given: 17 years Want: # of hours Conversion #1: 365 days = one year Conversion #2: 24 hours = one day

  14. Solution • Check your work… 17 years 1 365 days 1 year 24 hours 1 day X X = 148,920 hours

  15. Combination Units • Dimensional Analysis can also be used for combination units. • Like converting km/h into m/s. • Write the fraction in a “clean” manner: km/h becomes km h

  16. Combination Units • Example: Convert 0.083 km/h into cm/s. Given: 0.083 km/h Want: # m/s Conversion #1: 1000 m = 1 km Conversion #3: 1 hour = 60 minutes Conversion #4: 1 minute = 60 seconds

  17. Solution • Check your work… 83 m 1 hour 0.083 km 1 hour 1000 m 1 km X = 83 m 1 hour 1 hour 60 min 1 min 60 sec = X X 0.023 m sec

  18. Jabberwocky • Work on this problem individually. • Show all of your work. • Turn in your answer to me

  19. Crash of Flight 143 • Watch this video and answer the following questions. • 1. What was the cause of the Crash of Flight 143? • 2. How does this relate to the importance of using dimensional analysis?

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