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5.6 problem solving and dimensional analysis

Learn converting units, temperature scales, and density calculations with practical examples. Enhance your problem-solving skills effortlessly with conversion factors and mathematical formulas.

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5.6 problem solving and dimensional analysis

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  1. 5.6 problem solving and dimensional analysis • I have to buy 72 CostCo muffins, but they only sell them by the dozen. Do I just give up? May it never be! • I convert into dozens! • but I have to know the relationship b/t individuals and dozens! • called a conversion factor! • here 1 dozen = 12

  2. unit1x conversion factor = unit2 • we’ll…1) make astarting point,2) determinewhere we’re going,then…3) build a bridgeto it with theconversion factor

  3. 1) write down what you know (given),2) where you’re going, then3) build a “bridge” (your book calls the bridge an equivalence statement) between them… • Change 100 mm into m. bridge where you’re going given 100mm x 1 m 0.1 = m  1000 mm

  4. Change 546 cm into mm. bridge where you’re going given 546cm x 10 mm 5460 = mm  1 cm

  5. Convert 7.75g to µg. bridge where you’re going given µg 7.75g x 106 7.75x106 or 7,750,000 = µg  g 1

  6. Change 45mm into km. • (Hint: you might make this a 2-stepper.) 1 km 45mm 1 m = 1000 m 1000 mm 4.5x10-5 or .000045 km

  7. 5.7 temperature conversions:an approach to problem solving • here we learn both the different temp scales and how to convert between them

  8. the Big Three Temp Scales are Fahrenheit, Celsius, and Kelvin • in science we use almost exclusively C and K

  9. converting between K and C • a degree C and K are the same amount; they just differ by their starting points • they only differ by 273 • thus, and simply • TC + 273 = TK

  10. examples • What is 70˚C in kelvins? • TC + 273 = TK • 70 + 273 = 343 K • Nitrogen boils at 77 K. What is that in C? • TC + 273 = TK • TC = TK - 273 • TC = 77 - 273 • TC = -196 ˚C

  11. converting between F and C • here we have different size units and different starting points! yikes! • short story:TF = 1.80TC + 32

  12. examples • It’s 28˚C outside. What is that in F? • TF = 1.8TC + 32 • TF = 1.8(28) + 32 • TF = 50. + 32 • TF = 82 ˚F • It’s -40˚C in that lab freezer. What’s that in F? • TF = 1.8TC + 32 • TF = 1.8(-40) + 32 • TF = -72 + 32 • TF = -40˚F (!)

  13. examples • You have a 101˚F fever. What is that in C? • TF = 1.8TC + 32 • 101 = 1.8TC + 32 • 69 = 1.8TC • 38 = TC • Page 142 has a bunch of cutesy conversion equations

  14. 5.8 density • density is just how much matter is crammed in a certain space • in science speak it’s mass/volume: D = mass/Volume • finding mass is no problem; how do you find volume?

  15. one can either use dimensions (V = l x w x h) orvolume displacementfor irregular objects (Vtot = Vfinal – Vinitial) • take volume before, volume after - tada!the difference is the volume of your object

  16. d.m.v helper m D V

  17. d.m.v helper m D V

  18. d.m.v helper m D V

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