Units and Dimensions

Units and Dimensions PowerPoint PPT Presentation


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Objectives. Know the difference between units and dimensionsUnderstand the SI, USCS, and AES systems of unitsKnow the SI prefixes from nano- to giga-Understand and apply the concept of dimensional homogeneity. Units

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Units and Dimensions

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1. Units and Dimensions Class 6.2 This is truly a joint class between the instructors. This may seem like a lot of slides for half of a class, but over half of them are quick lists that do not require much discussion. The supplements fundamentalSI.ppt and gcderived.ppt are linked on the web, so students can access them that way. Also, in an attempt to keep the students on task and avoid them doing the class exercises in advance, many of the numerical/unit values in the last two pairs exercises have been replaces with ‘?’ in the student version.This is truly a joint class between the instructors. This may seem like a lot of slides for half of a class, but over half of them are quick lists that do not require much discussion. The supplements fundamentalSI.ppt and gcderived.ppt are linked on the web, so students can access them that way. Also, in an attempt to keep the students on task and avoid them doing the class exercises in advance, many of the numerical/unit values in the last two pairs exercises have been replaces with ‘?’ in the student version.

2. Objectives Know the difference between units and dimensions Understand the SI, USCS, and AES systems of units Know the SI prefixes from nano- to giga- Understand and apply the concept of dimensional homogeneity

3. Units & Dimensions A system of units is described by: a set of fundamental dimensions from which all other dimensions may be derived, and a set of base units.

4. Dimensions

5. Base Units

6. The International System of Units (SI)

7. What are these things? See fundamentalSI.ppt for information about these 'things'

8. SI Prefixes

9. Supplementary SI Dimensions

10. SI System of Units Force = (mass) (acceleration)

11. SI System of Units: Force Force = ma = Newton = N

12. SI System of Units: Work/Energy Work/ Energy = Force X Distance = N.m = Joule = J

13. SI System of Units: Power Power = Work / Time = Watt = W

14. SI System of Units: Stress/Pressure Pressure = Force / Area = Pascal = Pa

15. U.S. Customary System of Units (USCS)

16. USCS: Force = (mass)*(acceleration)

17. American Engineering System of Units (AES)

18. American Engineering System Note, there is a problem when we use the same unit (“pound”, meaning lbf and lbm) to describe two different dimensions. Newton's Second Law: F = ma ? 1 lbf = 1 lbm ft/s2 ??? NO!!! Must have consistency of units.

19. Consistency of Units Principle of consistency of units: units on the left side of an equation must be the same as those on the right side of an equation dimensional homogeneity

20. AES and Newton’s Law Must maintain dimensional homogeneity: Now we have lbf = lbf See gcderived.ppt for the derivation of gc

21. Units What do students in ENGR 111 need to know about these system of Units? See Units.doc

22. “Typical” Units Conversion Converting Between Foot and Meter To convert from foot to meter, multiply by 3.048* E-01 To convert from foot to meter, multiply by (3.048* E-01)-1

23. Thought Item Concerning the previous slide, which of the following is true? a. There are exactly 0.3048 m/ft. b. There are exactly 0.3048 ft/m. c. Neither a not b. Hint: Think about this physically..

24. Pairs Exercise (5 min.) Suppose you needed a metric drawing of the front view of a 6’x6’x6’ box. At a scale of 1:10, would it fit on an A size sheet of paper (portrait or landscape) with ¼” margins? Did you need to do unit conversion? How long would you draw each side on the metric drawing?

25. Another Type of Units Conversion The force of wind acting on a body can be computed by the formula: F = 0.00256 Cd V2 A where: F = wind force in lbf , Cd= drag coefficient (no units), V = wind velocity in miles per hour and A = projected area in ft2 Is this dimensionally homogeneous? What are the units of 0.00256? More in Class 9.2

26. Reality Check... Are units really important? Is checking your work and your team’s work really important? Mars Lander (ABC news) Mars Lander (NASA)

27. Assignment #10 INDIVIDUAL ASSIGNMENT Due: Foundations: 13.1, 13.2

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