Inquiry Science Another type of super-Model Dimensional Analysis Inquiry Science Another type of super-Model

First, let’s talk about dimensions First, let’s talk about dimensions. Every physical property has dimensions—you may call them “units”.   For example, we can measure Temperature in Celsius Fahrenheit Kelvin Another example is pressure. There’s a lot of ways we measure the units of pressure. psi (pounds per square inch) psf (pounds per square foot) mm HG (millimeters of Mercury) N / m2 (Newtons per square meter) Pascal

“Kill The Units” – courtesy of Mr. Hagler It is very, very useful to have the math ability to convert from one unit to another. For instance, if you measure something in feet, it might be useful to how far that is in miles!   Example 1: Graham built and launched a rocket. It flew 6,500 feet. How far is that in miles, if 1 mile = 5280 feet? 6500 feet miles 6500 feet * 𝟏 𝒎𝒊𝒍𝒆𝒔 𝟓𝟐𝟖𝟎 𝒇𝒆𝒆𝒕 miles 6500 feet * 𝟏 𝟓𝟐𝟖𝟎 𝒎𝒊𝒍𝒆𝒔 𝒇𝒆𝒆𝒕 miles 6500 * 𝟏 𝟓𝟐𝟖𝟎 miles 1.23 miles

Find the number of minutes she was in free-fall. Example 2: Hope went sky diving. Once she left the airplane she was in free-fall for 53 seconds. Then the parachute was pulled and she floated under the chute for 325 seconds. Find the number of minutes she was in free-fall. Find the number of minutes she floated under the chute. Find the number of HOURS she was in the air total! 53 sec * 1 minute = .88 minutes 60 sec 324 sec * 1 minute = 5.4 minutes 60 sec 5.4 + .88 minutes total = 6.28 minutes 6.28 minutes * 1 hour = .105 hour 60 min

Bryan rode his bike 0.2 miles/minute. Example 3: Maureen and Bryan rode their bikes to the river. Maureen rode her bike 63360 feet/hour. Bryan rode his bike 0.2 miles/minute. Convert Maureen’s speed to miles/hour. Convert Bryan’s speed to miles/hour. Who is faster? 63360 ft * 1 mile = 12 mi/hour hour 5280 feet .2 mile * 60 min = 12 mi/hour min 1 hour They’re the same! 

Homework Assignment Dimensional Analysis Worksheet Tomorrow… we’ll connect this back to our Periodic Table work!

Dimensional Analysis Day Two

Warm Ups Convert 20 miles per hour into feet per second. Miles feet hour second 29.3 There are 7 squinchies in a quirtle. There are 15 mombos in 4 droons. Convert 83 squinchies / mombo into quirtles / droon. 83 squinchies quirtles mombo droon 44.46

Converting square or cubic units Sometimes, we need to convert “square” units. For instance, if you want to spread mulch in your garden, and measure it to be 12’ x 10’, the total area of the garden is 12 * 10 = 120 square feet. We write this as 120 ft2 . You want the mulch to be 6” (1/2 foot) deep. So, we need 60 ft3 of mulch. But Home Depot only sells mulch in bags that are 1 yd3. Convert 60 ft3 into yd3. How many bags of mulch must you buy? 60 ft3 = yd3

In-Class Assignment Energy is measured in calories and also in Joules. When one gram of gasoline burns in a car's engine, the amount of energy given off is approximately 1.03 x 104 calories. Express 1.03 x 104 calories in joules (J). (Use 1 cal = 4.184 J) 2. The pressure reading from a barometer is 742 mm Hg. Express this reading in kilopascals, kPa. (Use 760 mm Hg = 1.013 x 105 Pa)

3. The average student is in class 330 min/day. a. How many hours/day is the average student in class? You should know what conversion factors you will need!   b. How many seconds is the average student in class per week? 4. Oprah weighs approximately 160 lbs. The human body is approximately 60% water by mass. You can write this as a conversion factor: 60 lb water / 100 lb body mass. (Does this make sense?) Using that conversion factor, how many pounds of water are in Oprah's body? (This is a rough estimate, since it also depends on body fat).

5. Because your 18 year-old friend never learned dimensional analysis, he started working at a fast food restaurant wrapping hamburgers. Every 3 hours he wraps 350 hamburgers. He works 8 hours per day. He works 5 days a week. He gets paid every 2 weeks with a salary of $440.34 (after taxes).   Approximately how many hamburgers will he have to wrap to make his first one million dollars? b. How much time will it take to wrap all the hamburgers [from part a]? Express the time in years. and that he works with the same efficiency every day. Round your answer to the nearest year. Assume that he will work 40 weeks out of the year. c. How old will he be when he makes his first million?

6. A child is entered into the hospital after ingesting 12 aspirin tablets. The Merck Index indicates that kidney failure can occur if as little as 3 grams is ingested, and may be fatal if as much as 10 grams is eaten. If each aspirin tablet contains 300 mg of aspirin, how much aspirin (in grams) has the child ingested? One mg = 100 grams. Convert 43 km/sec into centimeters per hour. There are 1000 meters in a kilometer. There are 100 centimeters in a meter.

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