MEASUREMENT Unit Conversions

Today's Objectives 1) Importance of unit conversions 2) Parts of a measurement 3) Units in equations 4) Documenting unit conversions 2

Are Units important? 3

Are Units important? "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." http://mars.jpl.nasa.gov/msp98/orbiter/ 4

A. SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

A. SI Prefix Conversions Symbol Factor mega- M 106 kilo- k 103 BASE UNIT --- 100 deci- d 10-1 move left move right centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12

A. SI Prefix Conversions 0.2 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km 32 45,000 0.0805

A. SI Prefix Conversions = 532 m = _______ km 0.532 NUMBER UNIT NUMBER UNIT

B. Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out

B. Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

B. Dimensional Analysis Lining up conversion factors: = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

B. Dimensional Analysis How many milliliters are in 1.00 quart of milk? qt mL 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL 

B. Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb cm3 1.5 lb 1 kg 2.2 lb 1000 g 1 kg 1 cm3 19.3 g = 35 cm3

B. Dimensional Analysis How many liters of water would fill a container that measures 75.0 in3? in3 L 75.0 in3 (2.54 cm)3 (1 in)3 1 L 1000 cm3 = 1.23 L

B. Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in 8.0 cm 1 in 2.54 cm = 3.1 in

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

B. Dimensional Analysis 7) A piece of wire is 1.3 m long. How many 1.5 cm pieces can be cut from this wire? m pieces 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces

Chemical Herbicide Spill Line Mole Method - Example Problem: The permeability of sand is 1.0x10-4cm/s. If a chemical herbicide is dumped on a sandy soil, how long (in hours) will it take for the contaminant to reach the well 150 feet away. Diagram: Herbicide 150 feet Well Permeability of Sand = 1.0x10-4 cm/s t = Time (hours) 1.0x10-4 cm/s = __?__ ft/hr 10

Chemical Herbicide Spill Factor Label Method - Example Theory: Permeability = Distance/Time Assumptions: Sand has constant permeability in area Herbicide moves per permeability of sand Solution: 10-4 cm s 11

Chemical Herbicide Spill Line Mole Method - Example Theory: Permeability = Distance/Time Assumptions: Sand has constant permeability in area Herbicide moves per permeability of sand Solution: 1.0x10-4 cm 1 in 1 ft 60 s 60 min s 2.54 cm 12 in 1 min 1 hr = 0.011811 ft/hr 12

Chemical Herbicide Spill Line Mole Method - Example Solution: Permeability = 0.011811 ft/hr Time = Distance / Permeability t = 150 ft OR t = 150 ft hr 0.011811 ft/hr 0.011811 ft t = 12700 hours = 13000 hours How many years is that? t = 12700 hr 1 day 1 yr = 1.4 yr 24 hr 365 day 13

As an individual, solve... Water Tower Problem Problem Statement: Your home town is growing so rapidly that another water tower is necessary to meet the needs of the community. Civil and environmental engineers predict that the water tower will need to hold 1.00 x 10.06 kilograms of water. The engineers also estimate the density of the water to be 999 kilograms per cubic meter. If this tower is 50.0 meters high and spherical, what volume (gal) of water will the tower hold and what will the diameter (ft) of the tower have to be? 14

Diagram: Theory: Assumptions: • mass of water = 1.00 x 106 kg • density of water = 999 kg/m3 • tower height = 50.0 m ? volume of water (L) • ? diameter (ft) • Theory: 4 Volume of a sphere r3 3 23 3 V diameter 2 r www.algonquin.org/pw.htm 4 Assumptions: • tower is spherical 15

Solution: 1.00 x106 kg 1 m3 1000 L volume of water = = 1.00 x 106 L 4 23 3 V r3 diameter 2 r Volume of a sphere 3 4 1.00 x 106 L 0.035315 ft3 volume of water = = 3.53 x 104 ft3 1 L 23 3 3.53 x 104 ft3 diameter 2 r 40.7 ft 4 16

http://en.wikipedia.org/wiki/Golf Golf Ball Design Minimum allowed diameter of a golf ball is 42.67mm Maximum Mass = 45.93g The surface usually has a pattern of 300-400 dimples designed to improve the ball's aerodynamics. The method of construction and materials greatly affect the ball's playing characteristics such as distance, trajectory, spin and feel. Have a two-, three-, or four-layer design constructed from various synthetic materials Harder materials, such as Surlyn, usually result in the ball's traveling longer distances, Softer covers, such as Balata, tend to generate higher spin, more "feel" and greater stopping potential. Golf balls are separated into three groups depending on their construction: two-, three-, or four-piece covers. 17

Golf Ball Design Minimum allowed diameter of a golf ball is 42.67mm http://en.wikipedia.org/wiki/Golf Golf Ball Design Minimum allowed diameter of a golf ball is 42.67mm Assuming a golf ball has a spherical shape What is the golf ball diameter in inches? What is the volume of a golf ball in cubic centimeters and cubic inches? Maximum Mass = 45.93g What is the mass of a golf ball in pounds? What is the density of a golf ball in g/cm3 and lb/in3? 18

Golf Shafts Golf shafts are what connects the grip to the golf head The profile of the golf shaft is circular in shape and is usually thicker at the grip end than at the club head end. Any strong and light material may be used to make the golf shaft. Almost all shafts today are made of either graphite or tempered steel The shaft is a tapered tube made of metal (usually steel), or graphite fiber. The shaft is roughly 1/2 inch in diameter (12 mm) near the grip and between 35 to 45 inches (89-115 cm) in length. 19

Golf Shafts Almost all shafts today are made of either graphite or tempered steel Graphite: 2.09-2.23 g/cm3 Steel: 7,861.093 kg/m³ (0.284 lb/in³) How much would the shaft of a golf club weigh in pounds if it were constructed from graphite or steel? Assume: Shaft Diameter = 1/2 inch and solid Shaft Length = 40 inches Why would you choose a graphite club over a steel club or vice versa? What is tempered steel? 20