Dimensional Analysis 1 =, Schemes and Mind Maps of Dimensional Analysis

Download Dimensional Analysis 1 = and more Schemes and Mind Maps Dimensional Analysis in PDF only on Docsity! MPC 095 1 Dimensional Analysis Dimensional Analysis Dimensional analysis converts one set of units to another just by multiplying by 1. In mathematics, you can always multiply by 1 and not change the value of a number. Further, if two numbers are equal to each other, then either number divided by the other is also equal to 1. So, 1 = 4 4 = 1 2 2 4 = 100 centimeters 1 meter = 1 pound 16 ounces = 1 hour 60 minutes = 60 minutes 1hour . If 1 mile = 5280 feet, then    1 mile 5280 feet = 1 and     5280 feet 1 mile = 1. These “funny looking ones” are called conversion factors. We can use them to convert from feet to miles or vice versa. For instance, how many feet are there in 17.37 miles? 17.37 miles ×     5280 feet 1 mile = 91713.6 feet. Notice that I multiplied by a conversion factor that made the “miles” in the numerator divide out with the “miles” in the denominator. If I had multiplied by the other conversion factor, the units wouldn’t have divided out, and I would have ended up with 17.37 miles ×    1 mile 5280 feet = 0.003290 (miles)2 feet . The result is equivalent to 17.37 miles, but I wouldn’t have answered the original question. We treat the units of a measurement just the same as we treat the number part of a measurement. If the same unit appears in the numerator and the denominator, the common unit can be divided out; the unit of miles reduced out in the first example. This method of converting units can be used in a string to convert more than one unit. For instance, the speed of a good fastball in professional baseball is about 90 miles per hour. To express this number in feet per second, do the following:     90 miles hour ×    1 hour 3600 seconds ×     5280 feet 1 mile = 132 feet second Notice how the conversion factors were chosen so that the unwanted units divided out, and didn’t multiply each other. We can treat the units just as we would variables in an equation. If we were asked to convert 16.2 ft2 (square feet) to in2 (square inches), we could just square the appropriate conversion factor.     12 in. 1 ft 2 =     12 in. 1 ft ×     12 in. 1 ft =     144 in2 1 ft2 Now we have an appropriate conversion factor to convert square feet to square inches. 16.2 ft2 ×     144 in2 1 ft2 = 2332.8 in2 This same method can be used to convert units of volume such as cubic yards (yd3) and cubic centimeters (cm3). Dimensional analysis can be used to convert any unit to any other appropriate unit. MPC 095 2 Dimensional Analysis Exercises: Use dimensional analysis to convert the following: 1. 7 mi. to yards 2. 234 oz. to tons 3. 11.2 mg to grams 4. 1.35 km to centimeters 5. 9,800,000 mm (millimeters) to miles 6. 4.5 ft2 to square yards 7. 435,000 m2 to square kilometers 8. 8 km2 to square feet 9. 0.0065 km3 to cubic meters 10. 14.62 in3 to cubic centimeters 11. 5,500 cm3 to cubic yards 12. 3.5 mph (miles per hour) to feet per second 13. 185 yd. per min. to miles per hour 14. 153 ft/s (feet per second) to miles per hour 15. 248 mph to meters per second 16. 186,000 mph to kilometers per year 17. 7.50 T/yd2 (tons per square yard) to pounds per square inch 18. 16 ft/s2 to kilometers per hour squared Use dimensional analysis to solve the following: 19. On a recent trip, Jan traveled 260 miles using 8 gallons of gas. How many miles per 1-gallon did she travel? How many yards per 1-ounce? 20. A chair lift at the Divide ski resort in Cold Springs, WY is 4806 feet long and takes 9 minutes. What is the average speed in miles per hour? How many feet per second does the lift travel? 21. A certain laser printer can print 12 pages per minute. Determine this printer’s output in pages per day, and reams per month. (1 ream = 5000 pages) 22. An average human heart beats 60 times per minute. If an average person lives to the age of 75, how many times does the average heart beat in a lifetime? 23. Blood sugar levels are measured in milligrams of glucose per deciliter of blood volume. If a person’s blood sugar level measured 128 mg/dL, how much is this in grams per liter? 24. You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet cost $18 per square yard. How much will the carpet cost? 25. A car travels 14 miles in 15 minutes. How fast is it going in miles per hour? in meters per second?