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# Universal Units

Universal Units. Instructor Slides. Force and Weight. Mass, Force and Weight. Mass Dimension representing how much Units [=] grams Force Based on Newton’s Second Law: force = mass * acceleration Units [=] newtons Weight weight = mass * gravity Units [=] newtons. w = m g. Massland.

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## Universal Units

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1. Universal Units Thinking Like an Engineer 2e Instructor Slides

2. Force and Weight Thinking Like an Engineer 2e

3. Mass, Force and Weight • Mass • Dimension representing how much • Units [=] grams • Force • Based on Newton’s Second Law: force = mass * acceleration • Units [=] newtons • Weight • weight = mass * gravity • Units [=] newtons Thinking Like an Engineer 2e w = m g

4. Massland kg lbm ton slug w = m g Welcome to Units World! Thinking Like an Engineer 2e Forceville dyne N lbf kip

5. Example Units_1 What is the weight of a 5 kilogram bowling ball in units of newtons? • 0.5 N • 5 N • 50 N Answer: C 50 N = 5.1 kg Thinking Like an Engineer 2e

6. Example Units_1: Answer • What is the weight of a 5 kilogram bowling ball in units of newtons? Thinking Like an Engineer 2e

7. Example Units_2 The weight of a TI-30 X calculator on earth is 0.25 pounds-force. What is the mass of the TI-30 X calculator on the International Space Station expressed in units of grams? (iClicker format: Xg) Thinking Like an Engineer 2e

8. Example Units_2: Answer Thinking Like an Engineer 2e

9. Density Thinking Like an Engineer 2e

10. Density is shown as Greek letter rho, r Density = mass (m) of an object divided by the volume (V) the object occupies Density (r) Thinking Like an Engineer 2e

11. Specific Gravity (SG) • Relation between density of object & density of water • SG is dimensionless & unitless • Can be used in ANY unit system depending on choice of density of water units Thinking Like an Engineer 2e

12. Density Values to Know • Density of water: • 1000 kg / m3 • 1 g / cm3 • 62.4 lbm / ft3 • 1.94 slug / ft3 Thinking Like an Engineer 2e

13. Example Units_3 • What is the specific gravity of bromine (Br2)? (iClicker format: XX.XX) • The density of bromine is 3,120 kg / m3 • Assume density of water = 1000 kg / m3 S G = density bromine / density water = (3120 kg / m3) / (1000 kg / m3) = 3.12 Thinking Like an Engineer 2e

14. Example Units_4 • Which of the following quantities has the highest density? (A) Fluid A = SG of 0.787 (B) Fluid B = 1.025 g / cc (C) Fluid C = 1,350 kg / m3 (D) Fluid D = 75 lbm / ft3 Answer: C Fluid C (SG = 1.35) Thinking Like an Engineer 2e

15. Example Units_5 • Which is the mass of water in a volume of one cubic foot? (A) 62.4 kg (B) 1.94 kg (C) 28.3 g (D) 28.3 kg Answer: D 28.3 kg Thinking Like an Engineer 2e

16. Example Units_6 • How many newtons does two liters of bromine (Br2) weigh? (iClicker format: XXN) • Density of bromine (Br2) = 3,120 kg/m3 Answer: 61 N Thinking Like an Engineer 2e

17. Example Units_7 • What is the mass of one gallon of bromine (Br2) in units of pounds-mass? (iClicker format: XXlbm) • Density of bromine (Br2) = 3,120 kg/m3 Answer: 26 lbm Thinking Like an Engineer 2e

18. Temperature Thinking Like an Engineer 2e

19. Temperature Fahrenheit (1686 – 1736) Two Relative Scales • (SI) Celsius [ºC] • (AES, USCS) Fahrenheit [ºF] Two Absolute Scales • (SI) Kelvin [K] • (AES, USCS) Rankine [ºR] Thinking Like an Engineer 2e

20. Relating R to F T [R] = T [F] + 460 1 F ≡ 1 R Converting Temperature Relating K to C T [K] = T [C] + 273 1 C ≡ 1 K Relating F to C T [F] = 1.8 T [C] + 32 1 C ≡ 1.8 F Thinking Like an Engineer 2e

21. Temperature values to know • Boiling point of water 100 °C = 212 °F • Freezing point of water 0 °C = 32 °F • Room temperature 21 °C = 70 °F • Absolute zero 0 K = -273 °C 0 °R = -460 °F Thinking Like an Engineer 2e

22. Example Units_8 • The Mars Phoenix lander touched down in the Martian Arctic in 2008. The lowest temperature recorded by Phoenix is -97.7 degrees Celsius. • What is this temperature expressed in units of degrees Rankine? (iClicker format: XXR) Answer: Range of 315.5 – 316.1 °R Thinking Like an Engineer 2e

23. Example Units_9 • Which of the following quantities is the highest temperature? (A) -150 °F (B) -150 °C (C) 150 K (D) 150 °R Answer: A = -150 °F -150 °C = -238 °F 150 K = -189.7 °F 150 °R = -309 °F Thinking Like an Engineer 2e

24. Example Units_10 • Which of the following is the highest value? (A) 5 kg / °C (B) 5 lbm / °F (C) 3 kg / K (D) 3 lbm / °R Answer: A = 5 kg /°C 3 kg /K = 3 kg /°C 5 lbm /°F = 4 kg /°C 3 lbm /°R = 2.45 kg /°C Thinking Like an Engineer 2e

25. Pressure Thinking Like an Engineer 2e

26. Pressure • Pressure is force distributed over an area. • In SI units [=] pascal Thinking Like an Engineer 2e

27. Massland Pressure Island ft H2O in Hg mm Hg bar psi kg lbm ton Pa slug w = m g atm P = F / A dyne Forceville N lbf kip

28. Pressure values to know • Standard atmospheric pressure = 1 atm • 1 atm 14.7 lbf per square inch [psi]  101,325 pascals [Pa] Thinking Like an Engineer 2e

29. Example Units_11 • Which of the following is the highest value? (A) 5 atm (B) 5 bar (C) 50,000 Pa (D) 50 psi Answer: A = 5 atm 5 bar = 4.93 atm 50,000 Pa = 0.493 atm 50 psi = 3.4 atm Thinking Like an Engineer 2e

30. Hydrostatic Pressure • Weight of a fluid pushing down on an object. • Pascal’s Law Thinking Like an Engineer 2e

31. Sum of: Hydrostatic Pressure Surface Pressure Total Pressure Ptotal = Psurface+ Phydro = Psurface+ ρg H Thinking Like an Engineer 2e

32. Example Units_12 • The hull of seaQuest Deep Submergence Vehicle (DSV) is rated to withstand a hydrostatic pressure of 90 Megapascals. • If sea water has a specific gravity of 1.03, how deep (in units of kilometers) can seaQuest DSV descend before reaching this pressure limit?? (iClicker format: X.Xkm) Answer: 8.9 km Thinking Like an Engineer 2e

33. Example Units_12: Answer Thinking Like an Engineer 2e

34. Example Units_13 • In the year 2027, Titan Submersible Explorer (TSE) lands on a lake of methane (specific gravity = 0.415) and submerges to a depth of 40 meters to explore the bottom of the lake. • The surface pressure on Titan is 21.3 pounds-force per square inch (psi) and the acceleration due to gravity is 1.35 meters per second squared. • What is the total pressure on the TSE at that depth in units of kilopascals? (iClicker format: XkPa) Answer: 169 kPa Thinking Like an Engineer 2e

35. Example Units_13: Answer • Hydrostatic = (Density) (Gravity) (Height) • Surface Pressure • Total Pressure = Hydrostatic + Surface Thinking Like an Engineer 2e

36. Gas Pressure Thinking Like an Engineer 2e

37. Ideal Gas Law • An ideal gas occupies a volume of 22.4 L under “standard conditions” • Pressure 1 atm • Temperature 273 K • Amount 1 mole • R = Ideal gas constant Temperature MUST be in ABSOLUTE units at all times! Thinking Like an Engineer 2e

38. Example Units_14 • 21 grams of nitrogen (N2) is placed in an 8 liter container. • The pressure gauge on the container reads 2.25 atmospheres. • What is the temperature in units of kelvin in the container? (iClicker format: XXXK) Answer: T = 292 K Thinking Like an Engineer 2e

39. Example Units_14: Answer P V = n R T or T = (P V) / (n R) Thinking Like an Engineer 2e

40. Example Units_15 • An ideal gas, kept in a 5 liter container at 300 Kelvin, exhibits a pressure of 2 atmospheres. • If the volume of the container is decreased to 2.5 liters, but the temperature remains the same, what isthe pressure in the second container compared to the first container? (A) Higher (B) Lower (C) Same Answer: A = Higher Thinking Like an Engineer 2e

41. Energy Thinking Like an Engineer 2e

42. Energy • Abstract, conserved quantity; can shift forms • Study 4 types • Work: Energy of exerting a force over a distance • Potential: Energy of position • Kinetic: Energy of motion • Thermal: Energy of change in temperature Thinking Like an Engineer 2e Q = m CpDT Work = F x PE = m g H KE = ½ m v2

43. Energy as… • Work, Kinetic, Potential • SI units [=] joule • Heat • British Thermal Unit (BTU) • Heat to raise temp of 1 lbm water by 1 ºF • calorie • Heat to raise temp of 1 g water by 1 ºC 1 J ≡ (1 N) (1 m) Thinking Like an Engineer 2e

44. Massland Pressure Island atm Q = m CpΔT w = m g P = F / A N Forceville W = F x PE = m g H KE = ½ m v2 E = P V BTU Energy City Pa kg cal J

45. Example Units_16 • Which of the following quantities has the highest energy? (A) 1 J (B) 1 BTU (C) 1 cal (D) 1 ft lbf Answer: B = 1 BTU 1 BTU = 1,054 J = 252 cal = 777 ft lbf Thinking Like an Engineer 2e

46. Example Units_17 • If it requires 5,650 joules of energy to lift a mass 15 feet into the air, what is the weight of that mass in units of newtons? (iClicker format: XN) Answer: w = 1,236.2 N Thinking Like an Engineer 2e

47. Example Units_17: Answer W = 1236.4 N Thinking Like an Engineer 2e

48. Example Units_18 • In the Space Shuttle Columbia accident, it has been estimated by the review board that a piece of foam insulation, with a mass of 1.67 pounds-mass, caused the damage to the shuttle tiles which caused the explosion upon reentry. • It has been simulated that velocity of the piece of foam relative to the shuttle was 545 miles per hour upon impact. • How much energy was transferred to the shuttle in the impact, in units of joules, assuming all the energy is transferred from the foam to the shuttle? (iClicker format: XJ) Answer: 22494 J Thinking Like an Engineer 2e

49. Example Units_18: Answer Thinking Like an Engineer 2e

50. Example Units_19 • A cup of coffee with a mass of 58 grams is heated from 70 degrees Fahrenheit to 125 degrees Fahrenheit. • If coffee has a specific heat of 4 joules per gram kelvin, how much energy in units of joules is required to heat the coffee? (iClicker format: XJ) Answer: 7089 J Thinking Like an Engineer 2e

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