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DIMENSIONAL ANALYSIS

DIMENSIONAL ANALYSIS . - Convert a given result from one system of units to another - Unit factor method . Ex 1) A pin measuring 2.85 cm in length. What is its length in inches?. Need an equivalence statement 2.54cm = 1in Divide both sides by 2.54cm Unit Factor

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DIMENSIONAL ANALYSIS

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  1. DIMENSIONAL ANALYSIS - Convert a given result from one system of units to another - Unit factor method

  2. Ex 1) A pin measuring 2.85 cm in length. What is its length in inches? • Need an equivalence statement 2.54cm = 1in • Divide both sides by 2.54cm • Unit Factor • Multiply any expression by this unit factor and it will not change its value

  3. Ex 1) A pin measuring 2.85 cm in length. What is its length in inches? • Pin is 2.85cm need to multiply by the unit factor

  4. Ex 2) A pencil is 7.00 in long. What is the length in cm? • Convert in  cm • Need equivalence statement 2.54cm = 1in • Unit Factor

  5. DIMENSIONAL ANALYSIS • Unit factors can be derived from each equivalence statement 2.54cm = 1in • 2 unit factors and

  6. DIMENSIONAL ANALYSIS and • How to choose – look at direction of required change • in  cm (need to cancel in – goes in denominator) • cm  in (need to cancel cm – goes in denominator)

  7. Ex 3) You want to order a bicycle with a 25.5in frame, but the sizes in the catalog are given only in cm. What size should you order?

  8. Ex 3) A student entered a 10.0-km run. How long is the run in miles? • km  mi • Equivalence statement 1m = 1.094yd • Strategy first km  m  yards  mi • Equivalence statements: 1km = 1000m 1m = 1.094 yd 1760yd = 1 mi

  9. Ex 3) A student entered a 10.0-km run. How long is the run in miles? • km  m

  10. Ex 3) A student entered a 10.0-km run. How long is the run in miles? • m  yd

  11. Ex 3) A student entered a 10.0-km run. How long is the run in miles? • yd  mi • Original 10.0 which has 3 sig figs so you want 3 sig figs in your answer

  12. Ex 3) A student entered a 10.0-km run. How long is the run in miles? • Can combine all conversions into one step

  13. DO NOWEx 4) If a woman has a mass 115lb, what is her mass in grams? • lb  g • Equivalence Statement 1lb = 453.6g Ex 5) If a woman has a mass 115lb, what is her mass in grams? • dollar  cents • Equivalence Statement 1 dollar = 100 cents

  14. Ex 6) Determine the length of a 500.0 mi automobile race in km • mi  yd  m  km • Equivalence statements – 1mi = 1760yd 1m = 1.094yd 1km = 1000m

  15. Ex 7) The average speed of a nitrogen molecule in air at 25C is 515m/s. Convert this speed to miles per hour • m/s  km/s  mi/s  mi/min  mi/hr • Equivalence statements – 1km = 103 1mi = 1.6093km 60s = 1min 60min = 1hr

  16. Ex 8) If you are going 50 mi/hr, how many feet/sec are your going? • mi  ft ; hr  min  sec • Equivalence statement 5280 ft=1mi

  17. Ex 9) Convert 22.50 gal/min to L/s • gal  L; min  sec • Equivalence statement 1 gal = 3.7854L

  18. Ex 10)Bamboo can grow up to 60.0 cm/day. Calculate this growth rate in inches per hour • cm in; day hr • Equivalence statement 1 in = 2.54 cm

  19. Ex 11)How much bleach (bl) would you need to make a quart of 5% bleach solution (bls)? – (refer to brightstormyoutube video for this question if you get confused) • qt  oz; need 5% bls • Equivalence statement 1 qt = 32 oz 5oz bs = 5% Bleach 100 ozbls = 100 % bleach solution

  20. Ex 12) A bumblebee flies with a ground speed of 15.2 m/s. Calculate its speed in km/hr • m  km ; s min  hr • Equivalence statement

  21. Ex 13) Convert 0.510 in/ms to km/hr • in cm  m  km; ms s  min  hr • Equivalence statement 1 in = 2.54cm

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