Dimensional Analysis Day 1

Are Units important? 3

"The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units in a segment of ground-based, navigation- related mission software, as NASA has previously announced," said Arthur Stephenson, chairman of the Mars Climate Orbiter Mission Failure Investigation Board. "The failure review board has identified other significant factors that allowed this error to be born, and then let it linger and propagate to the point where it resulted in a major error in our understanding of the spacecraft's path as it approached Mars." 4

Travel to Korea US Dollar Won

A physical quantity must include: Number + Unit + Unit

Calculation Corner: Unit Conversion 1 dollar = won $ won $1

Calculation Corner: Unit Conversion $ won $1 “Conversion factors” 3 dollar 3 dollar won won 1 dollar 1 dollar = won ( ( ) ) ( ( ) )

A 10k run is 10 Kilometers. If 1 meter = yards, use dimensional analysis to find the length of the race in miles. ( hint: 1mi = 1760yds) applicable conversion factors: equality: 10 km x  1 m = yds ______1.904 yds 1 m We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. ______ 1 km 1000m () ___ 1 km 1000 m 6.2 mi ) 1 m 1.094yds (( ) ______ 1 mi 1760yds ______1 mi 1760yds

A car travels a distance of 100feet in about 2.8 seconds. What is the velocity of the car in miles per hour? applicable conversion factors: 100 feet 2.8sec  ______60 sec 1 min Again, the units must cancel. ______ 1 hr 60 min () ______ 24mph 60 sec 1 min ______ 5280 feet 1 mi ______ 1 hr 60 min () ______ () 5280 feet 1 mi

How many feet is inches? applicable conversion factors: equality: or X ft in = 1 ft = 12 in ______1 ft 12 in Again, the units must cancel. () ____ 3.28 ft 1 ft 12 in ______ 1 ft 12 in

Scott found a rare video game on an online auction site priced at 35 Australian dollars. If the exchange rate is $1 US = $1.24 in Australian, find the cost of the video game in US dollars. Round to the nearest cent. $35 A 1  $28.22 US () ____ $1.24 A $1 US

How many seconds is 4.38 days? = 1 h 60 min24 h 1 d1 min 60 s ____ ()() () _____ 4.38 d x 378,432 s

Try: Dimensional Analysis How many milliliters are in 1.00 quart of milk? 1.00 qt 1 L qt = 946 mL qtmL 1000 mL 1 L 

Try: Dimensional Analysis 6) Taft football needs 550 cm for a 1st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.0 yd cmyd 1 ft 12 in 1 yd 3 ft

Try: Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm1 in 2.54 cm = 3.1 in cmin

Simple Math with Conversion Factors Day 2

Measured dimensions of a rectangle: Find area of rectangle. A = L. W = (9.70 cm)(4.25 cm) length (L) = 9.70 cm width (W) = 4.25 cm L W = Example Problem 41.2cm 2

Convert 41.2 cm 2 to m cm 1 m () ______ X m 2 = 41.2 cm 2 X m 2 = 41.2 cm. cm Recall that…41.2 cm 2 = 41.2 cm. cm 100 cm 1 m () ______ X m 2 = 41.2 cm 2 =0.412 m 2 =0.412 cm. m WRONG! () ______ 100 cm 1 m = m 2 () ______ 100 cm 1 m 2 = m 2

Measured dimensions of a rectangular solid: Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L. W. H = (15.2 cm)(3.7 cm)(8.6 cm) =480cm 3

Convert to m 3. X m 3 = 480 cm 3 = m cm 1 m 3 () _____ X m 3 = 480 cm 3 = X m 3 = cm 1 m () _____ 100 cm 1 m () _____ 100 cm 1 m () _____ = or cm. cm. cm 1 m cm ( ) _________ x m 3 or 3 2 cm

Measured dimensions of a rectangular solid: Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L. W. H = (0.152 m)(0.037 m)(0.086 m) = m m m m Convert to m 3...

Try: Dimensional Analysis How many liters of water would fill a container that measures 75.0 in 3 ? 75.0 in 3 (2.34 cm) 3 (1 in) 3 = 1.23 L in 3 L 1 L 1000 cm 3

Try: 1.You want to buy 100 U.S. Dollars Candadian dollars. If the exchange rate is 1 Can$ = 0.65 US$, how much will it cost? # Can$= 100 US$x 1 Can$ 0.65 US$ = Can$

Try: 3.There are 12 inches in a foot, inches in a centimeter, and 3 feet in a yard. How many cm are in one yard? # cm= 1 ydx 3 ft 1 yd = cm x 12 in 1 ft x 1 cm in

Challenge :Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. lbcm lb 1 kg 2.2 lb = 35 cm g 1 kg 1 cm g