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CHAPTER 8

CHAPTER 8. Dimensions, Units, and Error. Objectives. Sections. Understand the difference between a unit and dimensions Convert quantities between the different systems of measurement Understand the types of error in a measurement Express large numbers in scientific notation.

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CHAPTER 8

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  1. CHAPTER 8 Dimensions, Units, and Error

  2. Objectives Sections Understand the difference between a unit and dimensions Convert quantities between the different systems of measurement Understand the types of error in a measurement Express large numbers in scientific notation 8.1 Introduction 8.2 Dimensions and Units 8.3 Conversion between Different Units 8.4 Errors and Accuracy 8.5 Significant Digits 8.6 Summary

  3. Basic Units and Dimensions • Unit is the basic quantity in a given system of measurement • yard, meter, inch • Some units can be a combination of different basic units • Example: Unit of force depends on the choice of the units of mass and acceleration • Dimension describes the quantity in terms of Mass, Length, Time and Temperature without specifying any unit. Example:

  4. Basic Units and Dimensions…2 • One of the fundamental tenet for any physically valid equation is that dimensions on either side of the equation should be identical. Now F=ma=kx. Now to get the units of stiffness k, • In fact dimensional analysis is used to check any proposed equation is valid or not. • Groups of quantities can be combined in a manner that the group becomes dimensionless and they oftentimes represent very important fundamental quantities.

  5. 8.2 Systems and Measurement • There are three major systems of measurement • They are • BGS (British Gravitational System) • EES (English Engineering System) • SI System (The current worldwide standard) BGS • Here force (not mass), feet (for length) and second (time) are the fundamental units. • Since, ,mass is derived unit.

  6. Systems of Measurement…2 • The unit of mass is a slug • Since weight is a force acting on mass of 1 slug A body with a mass of 1 slug has a weight of 32.174 lb.

  7. Systems and Measurement…3 EES • Here the unit of mass is defined such that weight is 1 lbf • Mass is 1 lbm • For this system use SI • SI is the metric system. Fundamental units are grams (weight), cm ( length), and seconds (time).

  8. Conversion of • FPSSI Force 1 lb = 4.4482 N Mass 1 slug = 14.5938 kg Length 1 ft = 0.3048 m Conversion between Units • We are faced with converting a quantity from one system to another. Use the logic that units should cancel on both sides Example:

  9. Comparison of Units in BGS, EES, and SI

  10. Order of 10 in metric system

  11. Errors and Accuracy • Every quantity is measure in some form or another • Accuracy is defined as the difference between true value and measured value • All measurements contain error • Error has two parts • Bias error-inherent in the measurement systems. E.g. graduation in a tape • Precision error- Error that arises due to lack of repeatability. Arises due to operator or environmental conditions

  12. CHAPTER 8..concludes Dimensions, Units, and Error

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