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Dimensional Analysis

Dimensional Analysis. In dimensional analysis always ask three questions: What data are we given? What quantity do we need? What conversion factors are available to take us from what we are given to what we need?. Dimensional Analysis. Method of calculation using a conversion factor .

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Dimensional Analysis

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  1. Dimensional Analysis • In dimensional analysis always ask three questions: • What data are we given? • What quantity do we need? • What conversion factors are available to take us from what we are given to what we need? Chapter 1

  2. Dimensional Analysis Method of calculation using a conversion factor. * ALWAYS place the #1 in front of the largest unit.! Chapter 1

  3. Dimensional Analysis Example: We want to convert the distance 8 in. to feet. (12in = 1 ft) Chapter 1

  4. Dimensional Analysis Example: We want to convert the distance 8 in. to feet. (12in = 1 ft) Chapter 1

  5. Dimensional Analysis Convert the quantity from 2.3 x 10-8 cm to nanometers (nm) First we will need to determine the conversion factors Centimeter (cm)  Meter (m) Meter (m)  Nanometer (nm) Or 100 cm = 1 m 109 nm = 1 m Chapter 1

  6. Dimensional Analysis Convert the quantity from 2.3 x 10-8 cm to nanometers (nm) 100 cm =1 m 1 x 109 nm = 1 m Now, we need to setup the equation where the cm cancels and nm is left. Chapter 1

  7. Dimensional Analysis Convert the quantity from 2.3 x 10-8 cm to nanometers (nm) 1 cm = 0.01 m 1 x 10-9 m = 1 nm Now, fill-in the value that corresponds with the unit and solve the equation. Chapter 1

  8. Dimensional Analysis Convert the quantity from 2.3 x 10-8 cm to nanometers (nm) Chapter 1

  9. Dimensional Analysis Convert the quantity from 31,820 mi2 cm to square meters (m2) First we will need to determine the conversion factors Mile (mi)  Meter (m) Meter (m)  kilometer (km) Or 1 mile = 1.6 km 1000m = 1 km Chapter 1

  10. Dimensional Analysis Convert the quantity from 31,820 mi2 cm to square meters (m2) Now, we need to setup the equation where the cm cancels and nm is left. 1 mile = 1.6 km 1000m = 1 km Chapter 1

  11. Dimensional Analysis Convert the quantity from 31,820 mi2 cm to square meters (m2) Now, we need to setup the equation where the cm cancels and nm is left. 1 mile = 1.6 km 1000m = 1 km Notice, that the units do not cancel, each conversion factor must be “squared”. Chapter 1

  12. Dimensional Analysis Convert the quantity from 31,820 mi2 cm to square meters (m2) Chapter 1

  13. Dimensional Analysis Convert the quantity from 31,820 mi2 cm to square meters (m2) Chapter 1

  14. Dimensional Analysis Convert the quantity from 31,820 mi2 cm to square meters (m2) Chapter 1

  15. Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). Determine the conversion factors Meter (m)  Kilometer (km) Kilometer(km)  Mile(mi) Seconds (s)  Minutes (min) Minutes(min)  Hours (hr) Or 1 mile = 1.6 km 1000m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1

  16. Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). 1 mile = 1.6093 km 1000m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1

  17. Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). 1 mile = 1.6 km 1000m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1

  18. Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). 1 mile = 1.6093 km 1000m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1

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