Report

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 1 1= 2.54 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 1 2.85 2.85 = = 1.12 2.54 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 2.54 1 2.54 7.00 = 72.54 = 17.8 1 DIMENSIONAL ANALYSIS O Unit factors can be derived from each equivalence statement 2.54cm = 1in O 2 unit factors 2.54 1 and 1 2.54 DIMENSIONAL ANALYSIS 2.54 1 and 1 2.54 O How to choose – look at direction of required change O in cm (need to cancel in – goes in denominator) 2.54 1 O cm in (need to cancel cm – goes in denominator) 1 2.54 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? 2.54 25.5 = 72.54 = 64.8 1 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 10.0 1000 = 1.00104 1 Ex 3) A student entered a 10.0-km run. How long is the run in miles? O m yd 1.00104 1.094 = 1.094104 yd 1 Ex 3) A student entered a 10.0-km run. How long is the run in miles? O yd mi 1.094104 yd 1 = 6.216 = 6.22 1760 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 1000 1.094 1 = 6.22 1 1 1760 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 435.6 115 = 5.22104 1 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 2.5 = 250 1 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 500.0 1760 1 1 = 804.7 1 1.094 1000 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 1 1 60 60 103 1.6093 1 1 ℎ = 1.15103 /ℎ 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 5280 1ℎ 1 50 = 70/ ℎ 1 60 1 Ex 9) Convert 22.50 gal/min to L/s O gal L ; min sec O Equivalence statement 1 gal = 3.7854L 3.7854 1 22.50 = 1.41953 = 1.420 / 1 60 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 1 1 60 = 0.984 /ℎ 2.54 24 ℎ 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 5 1 = 1.6 1 100 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 1 60 60 15.2 = 54.7 /ℎ 1000 1 1 ℎ 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 2.54 110−2 1 1 60 60 . 510 1 1 1000 110−3 1 1ℎ = 46.6 /ℎ