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MEASUREMENT

Understand the significance of unit conversions, parts of a measurement, units in equations, documenting conversions, SI prefix conversions, and dimensional analysis examples. Learn why units are crucial and avoid errors like the Mars Climate Orbiter mission.

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MEASUREMENT

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  1. MEASUREMENT Unit Conversions

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

  3. Are Units important? 3

  4. 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

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

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

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

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

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

  10. 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.

  11. 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

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

  13. lb cm3 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. 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

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

  15. cm in B. 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 cm 1 in 2.54 cm = 3.1 in

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

  17. m pieces 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? 1 piece 1.5 cm 100 cm 1 m 1.3 m = 86 pieces

  18. 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: 150 feet Herbicide Well Permeability of Sand = 1.0x10-4 cm/s t = Time (hours) 1.0x10-4 cm/s = __?__ ft/hr 10

  19. 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

  20. 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 in 1 ft 60 s 60 min 1.0x10-4 cm s 2.54 cm 12 in 1 min 1 hr = 0.011811 ft/hr 12

  21. 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

  22. 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

  23. Diagram: • 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 r3 Volume of a sphere 3 233 V 2 r diameter www.algonquin.org/pw.htm 4 Assumptions: • tower is spherical 15

  24. Solution: 1.00 x106kg 1000 L 1 m3 volume of water = = 1.00 x 106 L 1 m3 999 kg 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. Roentgen

  30. Roentgen • Named after Wilhelm C. Roentgen • (thus the abbr... is capital “R”) • Pronounced rent’gen with a hard “g” • Limitations • only applies to photons • only applies in air • only applies to energies less than 3 MeV

  31. rad

  32. rad • 1 rad = 1 Roentgen

  33. rem

  34. rem • The unit of dose equivalent for any type of ionizing radiation absorbed by body tissue in terms of estimated biological effect - Unit of dose equivalent • Dose in health record is in units of rem • 1 rem = 1 Roentgen • Roentgen Equivalent Man

  35. Quality Factor (Q) The specific value that accounts for the ability of different types of ionizing radiation to cause varying degrees of biological damage • X-rays, gamma rays, & beta particles 1 • Neutrons & High energy protons 10 • Alpha Particles 20

  36. Curie (Ci) • Radiation hazard does not solely depend on the activity. It also depends on the type of decay (alpha, beta, photon, etc.) • Named in honor of Pierre Curie

  37. SI Radiation Protection Units • Becquerel (Bq) for Curie • 1 Ci = 3.7 x 1010 Bq • Gray (Gy) for rad • 1 Gy = 100 rad • Sievert (Sv) for rem • 1 Sv = 100 rem

  38. Unit Analysis BASE UNIT CONVERSION TABLE Unit Unit Conversion 1 Bq 2.7 x 10-11 Ci 1 Ci 3.7 x 1010 Bq 1 Bq 1 dis/sec 1 dis/sec 2.7 x 10-11 Ci 1 Ci 3.7 x 1010 dis/sec

  39. Unit Analysis (Con’t.) BASE UNIT CONVERSION TABLE Unit Unit Conversion 1 rem 0.01 Sv 1 Sv 100 rem 1 rad 0.01 Gy 1 Gy 100 rad 1 R 2.58 x 10-4 C/kg 1 meter 3.28 ft (39.37in)

  40. Summary • Radiation Protection unit definitions (including SI units) • Unit Prefixes • Unit conversions

  41. Old Terms • Roentgen-Based on the quantity of electrical charges produced in air by X or Gamma photons 1R=2 billion pr • RAD-Radiation Absorbed Dose is the work energy resulting from the absorption of one ROENTGEN or 6.24 E5 Mev

  42. More Old Terms • REM-Roentgen Equivalent Mammal is equal to the absorbed does in RADS multiplied by a quality factor • Quality Factors • Beta = 1 • Gamma & X ray photons = 1 • Alpha = 10 • Neutrons = 20

  43. New Terms sort of International Units have replaced the RAD and REM GRAY (Gy) = 100 RAD SIEVERT (Sv) = 100 REM Same Quality Factors apply to the Sv

  44. Units of Radioactivity • Curie (Ci) = 2.22 E12 dpm or 3.7E10 dps • Becquerel (Bq) = 1 dps • Maximum Dose/year = 5 REM or 50 mSv • Maximum Dose/year for Declared Pregnant Woman & Minors= 0.5 REM or 5 mSv

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