#### Transcript DIMENSIONAL ANALYSIS

DIMENSIONAL ANALYSIS - Convert a given result from one system of units to another - Unit factor method Ex 1) A pin measuring 2.85 cm in length. What is its length in inches? O Need an equivalence statement 2.54cm = 1in O Divide both sides by 2.54cm O Unit Factor 1𝑖𝑛 1= 2.54𝑐𝑚 O Multiply any expression by this unit factor and it will not change its value Ex 1) A pin measuring 2.85 cm in length. What is its length in inches? O Pin is 2.85cm need to multiply by the unit factor 1𝑖𝑛 2.85𝑖𝑛 2.85𝑐𝑚 𝑥 = = 1.12𝑖𝑛 2.54𝑐𝑚 2.54 Ex 2) A pencil is 7.00 in long. What is the length in cm? O Convert in cm O Need equivalence statement 2.54cm = 1in O Unit Factor 2.54𝑐𝑚 1𝑖𝑛 2.54𝑐𝑚 7.00𝑖𝑛 𝑥 = 7𝑥2.54𝑐𝑚 = 17.8𝑐𝑚 1𝑖𝑛 DIMENSIONAL ANALYSIS O Unit factors can be derived from each equivalence statement 2.54cm = 1in O 2 unit factors 2.54𝑐𝑚 1𝑖𝑛 and 1𝑖𝑛 2.54𝑐𝑚 DIMENSIONAL ANALYSIS 2.54𝑐𝑚 1𝑖𝑛 and 1𝑖𝑛 2.54𝑐𝑚 O How to choose – look at direction of required change O in cm (need to cancel in – goes in denominator) 2.54𝑐𝑚 1𝑖𝑛 O cm in (need to cancel cm – goes in denominator) 1𝑖𝑛 2.54𝑐𝑚 Ex 3) You want to order a bicycle with a 25.5in frame, but the sizes in the catalog are given only in cm. What size should you order? 2.54𝑐𝑚 25.5𝑖𝑛 𝑥 = 7𝑥2.54𝑐𝑚 = 64.8𝑐𝑚 1𝑖𝑛 Ex 3) A student entered a 10.0-km run. How long is the run in miles? O km mi O Equivalence statement 1m = 1.094yd O Strategy first km m yards mi O Equivalence statements: 1km = 1000m 1m = 1.094 yd 1760yd = 1 mi Ex 3) A student entered a 10.0-km run. How long is the run in miles? O km m 10.0𝑘𝑚 𝑥 1000𝑚 = 1.00𝑥104 𝑚 1𝑘𝑚 Ex 3) A student entered a 10.0-km run. How long is the run in miles? O m yd 1.00𝑥104 𝑚 𝑥 1.094𝑦𝑑 = 1.094𝑥104 yd 1𝑚 Ex 3) A student entered a 10.0-km run. How long is the run in miles? O yd mi 1.094𝑥104 yd 𝑥 1 𝑚𝑖 = 6.216𝑚𝑖 = 6.22𝑚𝑖 1760𝑦𝑑 O Original 10.0 which has 3 sig figs so you want 3 sig figs in your answer Ex 3) A student entered a 10.0-km run. How long is the run in miles? O Can combine all conversions into one step 10.0km 𝑥 1000𝑚 1.094𝑦𝑑 1𝑚𝑖 𝑥 𝑥 = 6.22 𝑚𝑖 1𝑘𝑚 1𝑚 1760𝑦𝑑 DO NOW Ex 4) If a woman has a mass 115lb, what is her mass in grams? O lb g O Equivalence Statement 1lb = 453.6g 435.6𝑔 115𝑙𝑏 𝑥 = 5.22𝑥104 𝑔 1𝑙𝑏 Ex 5) If a woman has a mass 115lb, what is her mass in grams? O dollar cents O Equivalence Statement 1 dollar = 100 cents 100 𝑐𝑒𝑛𝑡 2.5 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 𝑥 = 250 𝑐𝑒𝑛𝑡𝑠 1 𝑑𝑜𝑙𝑙𝑎𝑟 Ex 6) Determine the length of a 500.0 mi automobile race in km O mi yd m km O Equivalence statements – 1mi = 1760yd 1m = 1.094yd 1km = 1000m 500.0𝑚𝑖 𝑥 1760𝑦𝑑 1𝑚 1𝑘𝑚 𝑥 𝑥 = 804.7𝑘𝑚 1𝑚𝑖 1.094𝑦𝑑 1000𝑚 Ex 7) The average speed of a nitrogen molecule in air at 25C is 515m/s. Convert this speed to miles per hour O m/s km/s mi/s mi/min mi/hr O Equivalence statements – 1km = 103 1mi = 1.6093km 60s = 1min 60min = 1hr 15 𝑚 𝑠 𝑥 1𝑘𝑚 1𝑚𝑖 60𝑠 60𝑚𝑖𝑛 𝑥 𝑥 𝑥 103 𝑚 1.6093𝑘𝑚 1𝑚𝑖𝑛 1 ℎ𝑟 = 1.15𝑥103 𝑚𝑖/ℎ𝑟 Ex 8) If you are going 50 mi/hr, how many feet/sec are your going? O mi ft ; hr min sec O Equivalence statement 5280 ft=1mi 𝑚𝑖 5280𝑓𝑡 1ℎ𝑟 1𝑚𝑖𝑛 50 𝑥 𝑥 𝑥 = 70𝑓𝑡/𝑠𝑒𝑐 ℎ𝑟 1𝑚𝑖 60𝑚𝑖𝑛 1𝑠𝑒𝑐 Ex 9) Convert 22.50 gal/min to L/s O gal L ; min sec O Equivalence statement 1 gal = 3.7854L 𝑔𝑎𝑙 3.7854𝐿 1𝑚𝑖𝑛 22.50 𝑥 𝑥 = 1.41953 = 1.420 𝐿/𝑠 𝑚𝑖𝑛 1𝑔𝑎𝑙 60𝑠 Ex 10)Bamboo can grow up to 60.0 cm/day. Calculate this growth rate in inches per hour O cm in ; day hr O Equivalence statement 1 in = 2.54 cm 𝑐𝑚 1 𝑖𝑛 1 𝑑𝑎𝑦 60 𝑥 𝑥 = 0.984 𝑖𝑛/ℎ𝑟 𝑑𝑎𝑦 2.54 𝑐𝑚 24 ℎ𝑟 Ex 11)How much bleach (bl) would you need to make a quart of 5% bleach solution (bls)? – (refer to brightstorm youtube video for this question if you get confused) O qt oz ; need 5% bls O Equivalence statement 1 qt = 32 oz 5oz bs = 5% Bleach 100 oz bls = 100 % bleach solution 32 𝑜𝑧 𝑏𝑙𝑠 5 𝑜𝑧 𝑏𝑙 1 𝑞𝑡 𝑏𝑙𝑠 𝑥 𝑥 = 1.6 𝑜𝑧 𝑏𝑙 1 𝑞𝑡 𝑏𝑙𝑠 100 𝑜𝑧 𝑏𝑙𝑠 Ex 12) A bumblebee flies with a ground speed of 15.2 m/s. Calculate its speed in km/hr O m km ; s min hr O Equivalence statement 𝑚 1 𝑘𝑚 60 𝑠 60 𝑚𝑖𝑛 15.2 𝑥 𝑥 𝑥 = 54.7 𝑘𝑚/ℎ𝑟 𝑠 1000 𝑚 1 𝑚𝑖𝑛 1 ℎ𝑟 Ex 13) Convert 0.510 in/ms to km/hr O in cm m km; ms s min hr O Equivalence statement 1 in = 2.54cm 𝑖𝑛 2.54𝑐𝑚 1𝑥10−2 𝑚 1𝑘𝑚 1𝑚𝑠 60𝑠 60𝑚𝑖𝑛 . 510 𝑥 𝑥 𝑥 𝑥 𝑥 𝑥 𝑚𝑠 1𝑖𝑛 1𝑐𝑚 1000𝑚 1𝑥10−3 𝑠 1𝑚𝑖𝑛 1ℎ𝑟 = 46.6 𝑘𝑚/ℎ𝑟