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Chapter 1: Measurements

Chapter 1: Measurements. By: Dr. Aziz Shawabkeh Birzeit University Email: Shawabka@birzeit.edu course web page: home.birzeit.edu/physics/aziz/ph141. Measurements. Outline: Standards of Length, Mass and Time Systems of Units Scientific Notation Dimensional Analysis

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Chapter 1: Measurements

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  1. Chapter 1: Measurements By: Dr. Aziz Shawabkeh Birzeit University Email: Shawabka@birzeit.edu course web page: home.birzeit.edu/physics/aziz/ph141 Physics 141

  2. Measurements • Outline: • Standards of Length, Mass and Time • Systems of Units • Scientific Notation • Dimensional Analysis • Conversion of Units • Order of Magnitude Calculations Physics 141

  3. Standards (basic units) : • Length (L) • mass (M) • time (t) • electric current (I) • temperature (T) Physics 141

  4. SI units (used mostly in physics) length: meter (m), mass: kilogram (kg), time: second (s) British engineering system: length: foot (ft) mass: slug (sl) time: second (s) Systems of Units Physics 141

  5. It is convenient to express large or small numbers in scientific notation: 5,000 = 5 x 10 3 .0004 = 4 x 10 - 4 Scientific Notation Physics 141

  6. Physics 141

  7. Dimensional analysis • The Dimension is the qualitative nature of a physical quantity (length, mass, time). Square brackets [ ] denote the dimension or units of a physical quantity  Physics 141

  8. Dimensional analysis: Continue Physics 141

  9. Dimensional analysis: Continue • can be used to derive or check formulas by treating dimensions as algebraic quantities. • Quantities can be added or subtracted only if they have the same dimensions, • quantities on two sides of an equation must have the same dimensions. Physics 141

  10. Conversion of Units • Units can be treated as algebraic quantities. For example, we can use the conversion factor 1 in = 2.54 cm to rewrite 10 inches in centimeters. 10 in = 10 in (2.54 cm /1 in) = 25.4 cm Physics 141

  11. Example: • The diameter of the earth, measured at the equator, is 7930 mi. Express the diameter a) in meters and b) in kilometers. Use scientific notation when expressing your answers. Solution: a)  d= 7930 mi x  ( 1609 m/1.0 mi ) = 1.28 x 107m b) d= 1.28 x 107 m x  (1 km/1.0 x 103 m) = 1.28 x 104 km Physics 141

  12. Order of Magnitude Calculations An order of magnitude calculation is an estimate at various inputs to obtain a result that is usually reliable to within a factor of 10. Specifically, to get the order of magnitude of a given quantity, we round off to the closest power of 10 (example: 75 kg 102 kg). Physics 141

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