1.05 Dimensional Analysis or Unit Factor Method 12in = 1 ft 1 dime= 10 pennies 1 in = 2.54 cm Dr. Fred Garces Chemistry 100 Miramar College 100 yd = 300 ft *If you plan to be in the nursing field please go to the following urlhttp://www.alysion.org/dimensional/analysis.htm Read the context in this website to appreciate the importance in dimensional analysis in all type of calculation applications. 1 1.05 Dimensional Analysis and Calculations
Dimensional Analysis Dimensional Analysis Unit Conversion-Factor Factor Label method Ratios which are equivalent to the number 1 such as 12in/1ft or 60 min/1 hr or 5280 ft/1 mi. are called unit factors, or conversion factors. They are the key to most of the calculations in this course. What you need to remember is that the numerator and denominator of conversion factors must always represent equivalent quantities. <iframe title="youtube video player" class="youtube-player" type="text/ html" width="480" height="390" src=" http://www.youtube.com/embed/az3j60gyo6u" frameborder="0" allowfullscreen></iframe> 2 1.05 Dimensional Analysis and Calculations
Communicating in a foreign land Guadeloupe 0.05%, China 0.83% and Italy 29% speak English Consider traveling abroad Travel to Italy; How do you communicate? Cab fare is 17.25!to the hotel, how much is it in $? Suppose you are abroad and you want to communicate to the locals but you do not speak their language. How can you make your intentions known? One way is to use a translator. Another type of translator is the currency exchange. 3 1.05 Dimensional Analysis and Calculations
Basic Idea The Basic idea of conversion factors is to change the units that are given in a problem to units that is being sought. Desired Goal Unit Accomplished goal Given Unit Translator Speak English 4 1.05 Dimensional Analysis and Calculations
Liras to dollars How much is 17.25 in dollars? Need to know currency exchange: 0.69 = $ 1.00 (Translator) Given information Translator Goal 17.25 * $ 1. 00 0.69 = $ Work it out Currency Exchange rate 5 1.05 Dimensional Analysis and Calculations
Misc Conversion factors. Banker has $100 to purchase a wedding cake but the baker doesn t want his money instead, the baker needs 1 day tutoring for his son to pass the SAT. In this town the banker found the following tradesman, how can the banker secure a wedding cake? Occupation Skill Need. 1. Baker 1 wedding cake 1 day tutoring 2. Plumber 1 hr labor 25lb stag 3. Carpenter Roofing labor 3 hr computer help 4. Farmer1 50 bushel corn $100 5. Farmer2 1 25 lb hog 50lb fish 6. Brew master 2 kegs beer Fix car radiator 7. Jewel smith Labor to craft necklace 4 hr house keeping 8. Auto mechanic car repair 1 25lb hog 9. Teacher 1 day tutoring fix broken necklace 10. Computer tech 3 hr computer setup 50 bushels corn 11. Fisherman 50lb fish Fix roof 12. Hunter 25lb stag 2 keg beer 13. Housekeeper 4 hrs house keeping 1 hr plumber 14. Banker $100 wedding cake 1 9 7 13 2 12 6 8 5 11 3 10 4-14 6 1.05 Dimensional Analysis and Calculations
Misc Conversion factors. Banker has $100 to purchase a wedding cake but the baker doesn t want his money instead, the baker needs 1 day tutoring for his son to pass the SAT. In this town the banker found the following tradesman, how can the banker secure a wedding cake? Occupation Skill Need. 1. Baker 1 wedding cake 1 day tutoring 2. Plumber 1 hr labor 25lb stag 3. Carpenter Roofing labor 3 hr computer help 4. Farmer1 50 bushel corn $100 5. Farmer2 1 25 lb hog 50lb fish 6. Brew master 2 kegs beer Fix car radiator 7. Jewel smith Labor to craft necklace 4 hr house keeping 8. Auto mechanic car repair 1 25lb hog 9. Teacher 1 day tutoring fix broken necklace 10. Computer tech 3 hr computer setup 50 bushels corn 11. Fisherman 50lb fish Fix roof 12. Hunter 25lb stag 2 keg beer 13. Housekeeper 4 hrs house keeping 1 hr plumber 14. Banker $100 wedding cake 1 9 7 13 2 12 6 8 5 11 3 10 4-14 7 1.05 Dimensional Analysis and Calculations
Misc Conversion factors. Banker has $100 to purchase a wedding cake but the baker doesn t want his money instead, the baker needs 1 day tutoring for his son to pass the SAT. In this town the banker found the following tradesman, how can the banker secure a wedding cake? Occupation Skill Need. 1. Baker 1 wedding cake 1 day tutoring 2. Plumber 1 hr labor 25lb stag 3. Carpenter Roofing labor 3 hr computer help 4. Farmer1 50 bushel corn $100 5. Farmer2 1 25 lb hog 50lb fish 6. Brew master 2 kegs beer Fix car radiator 7. Jewel smith Labor to craft necklace 4 hr house keeping 8. Auto mechanic car repair 1 25lb hog 9. Teacher 1 day tutoring fix broken necklace 10. Computer tech 3 hr computer setup 50 bushels corn 11. Fisherman 50lb fish Fix roof 12. Hunter 25lb stag 2 keg beer 13. Housekeeper 4 hrs house keeping 1 hr plumber 14. Banker $100 wedding cake 1 9 7 13 2 12 6 8 5 11 3 10 4-14 8 1.05 Dimensional Analysis and Calculations
Misc Conversion factors. Banker has $100 to purchase a wedding cake but the baker doesn t want his money instead, the baker needs 1 day tutoring for his son to pass the SAT. In this town the banker found the following tradesman, how can the banker secure a wedding cake? Occupation Skill Need. 1. Baker 1 wedding cake 1 day tutoring 2. Plumber 1 hr labor 25lb stag 3. Carpenter Roofing labor 3 hr computer help 4. Farmer1 50 bushel corn $100 5. Farmer2 1 25 lb hog 50lb fish 6. Brew master 2 kegs beer Fix car radiator 7. Jewel smith Labor to craft necklace 4 hr house keeping 8. Auto mechanic car repair 1 25lb hog 9. Teacher 1 day tutoring fix broken necklace 10. Computer tech 3 hr computer setup 50 bushels corn 11. Fisherman 50lb fish Fix roof 12. Hunter 25lb stag 2 keg beer 13. Housekeeper 4 hrs house keeping 1 hr plumber 14. Banker $100 wedding cake 1 9 7 13 2 12 6 8 5 11 3 10 4-14 9 1.05 Dimensional Analysis and Calculations
Misc Conversion factors. Banker has $100 to purchase a wedding cake but the baker doesn t want his money instead, the baker needs 1 day tutoring for his son to pass the SAT. In this town the banker found the following tradesman, how can the banker secure a wedding cake? Occupation Skill Need. 1. Baker 1 wedding cake 1 day tutoring 2. Plumber 1 hr labor 25lb stag 3. Carpenter Roofing labor 3 hr computer help 4. Farmer1 50 bushel corn $100 5. Farmer2 1 25 lb hog 50lb fish 6. Brew master 2 kegs beer Fix car radiator 7. Jewel smith Labor to craft necklace 4 hr house keeping 8. Auto mechanic car repair 1 25lb hog 9. Teacher 1 day tutoring fix broken necklace 10. Computer tech 3 hr computer setup 50 bushels corn 11. Fisherman 50lb fish Fix roof 12. Hunter 25lb stag 2 keg beer 13. Housekeeper 4 hrs house keeping 1 hr plumber 14. Banker $100 wedding cake 1 9 7 13 2 12 6 8 5 11 3 10 4-14 10 1.05 Dimensional Analysis and Calculations
The Basis of Conversion Factor 1 Anything = Anything 1 1 Anything = Anything 1 doz = 12 thus Therefore 1 doz 12 12 1 doz = 1 doz 12 = 1 Anything = Anything 12in = 1 ft 1 in = 2.54 cm 1 dime= 10 pennies 100 yd = 300 ft Likewise 0.69 $1.00 = $1.00! 0.69 11 1.05 Dimensional Analysis and Calculations
Example: Distance to closes star. How many miles is the closest star, Proxima Centauri, 4.2 Light Years (LY)? 365.25 day 4.2 Light year 1yr Conversion factors: 3.0 10 10 cm / s or 186, 282 mi / hr 365 days = 1 year 24 hr = 1 day 60 min = 1 hr 24hr 1day 60min 1hr 60sec 186,282 mi = 2.5e13mi Work it out 1min 1sec 12 1.05 Dimensional Analysis and Calculations
Other Conversion factors. Length Volume 1 cm = 0.394 in 1 m = 39.4 in = 3.24 ft = 1.08 yd 1 in = 2.54 cm = 0.0833 ft 1 ft = 30.5 cm = 0.305m = 12 in 1 yd = 91.44 cm = 0.9144m = 3 ft =36 in 1 cm 3 = 1cc = 1 ml 1 L = 1000ml = 1000 cm 3 = 1.057 qt 1 qt = 0.946 L 1gal = 4 qt = 3.78 L Mass 1 g = 0.0353 oz = 0.00220 lb. 1 Kg = 1000 g = 2.20 lb. 1 mt = 1000 Kg = 2200 lb. = 1.10 ton 1 lb = 454 g = 0.454 Kg 1 ton = 2000lb = 908 Kg = 0.908 mt 13 1.05 Dimensional Analysis and Calculations
More Conversion factors... 14 1.05 Dimensional Analysis and Calculations
Exercise on Dimensional Analysis Suppose the exchange rate for the yen is 77 Yen / $1.00. If gold at the Tokyo exchange is 140K Yen an ounce, how much will 50.0 gram cost in euro. (453.9 gram = 1.00 lb., 16 oz. = 1.0 lb..) $3.2K or 2.2 15 1.05 Dimensional Analysis and Calculations
Exercise 16 1.05 Dimensional Analysis and Calculations
II Accuracy, Precision & Significant Figures Exception to significant figure rules: These type of numbers contain unlimited significant figures (do not influence the number of significant figures in the final answer). Number of Tallies, i.e., 5 fingers, 176 students. *Definition of numbers - i.e., Exactly 1 m = 100 cm, or 1 in = 2.54 cm Power of 10 in exponential notation i.e., 10 6 but practical to express numbers as 10 6.4 (exponential calc) *Define conversion versus measured conversion. 17 1.05 Dimensional Analysis and Calculations
Conversion factors: Measured versus defined One last important note: -Conversion factor comes in two forms, the first are conversion factors from definitions. Examples are, 60 min = 1 hr, 100cm = 1m, 5280 ft = 1 mile, 1 gal = 3.785 L, 100 pennies = $1.00. -Other conversion factors are based on measured values. 65.0 mph (65.0 mi = 1 hr), $10/hr (10 $ = 1 hr), 0.76Euro/$ (0.76 euro = 1.00$) -Measured conversion factors do have defined significant figures unlike defined conversion factors that have infinite number of significant figures. Thus in the problem; If a runner for 139.9 minutes at 11 mph, how far will the runner travel in miles? The answer is rounded to two significant figures. 139.9 min 1 hr 60 min 11 mi 1 hr = 25.6483 mi = 26 mi 18 1.05 Dimensional Analysis and Calculations
Exercise Answer the following using dimensional analysis. 1 How many kilograms in 250.5 lb? 2 How long in centimeter is a 30.5-inch waist? 3a An SUV requires 20.5 gallons of gasoline (gas) for a full tank. How many ml of gas is needed for a full tank of gasoline? 3b If gasoline has a density of 0.85 grams per ml, what is the mass of this volume of gas? 4. How fast is a car moving in cm / sec if its speedometer is reading 65.00 mph? 5. How many pennies are needed (1.95 cm diameter) to stretch from the earth to the sun? It takes 8.00 minutes and 20.0 seconds for light to travel from the sun to the earth traveling at 186,282 mi/sec. 19 1.05 Dimensional Analysis and Calculations