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Measurement and Problem Solving in Physics

An introduction to the concept of measurement in physics, including the SI units of length, mass, and time. Also covers unit conversions and significant figures.

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Measurement and Problem Solving in Physics

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  1. Chapter 1 Measurement and Problem Solving August 19 SI unites and the metric system 1.2 SI Units of Length, Mass, and Time Physics studies the laws of the motion of the world.Physics describes the nature through measurement. All measurements are expressed in units.Standard units are established by a government or an international organization.There are two major systems of units: metric and British(mainly used by the U.S.). Physics has adopted the SI units (International system of units, French Systéme Internationale d’Unités), which is based on the metric system. The units of length, mass, and time: Length, mass, and time are fundamental quantities in mechanics. The SI unit of length is the meter. The original definition of a meter used the size of the earth. From north pole to the equator is 10 000 km. Modern definition of a meter is the distance that light travels in vacuum in 1/299 792 458 s.

  2. The SI unit of mass is the kilogram. The original definition of a kilogram was the mass of one liter of water. Currently the standard kilogram is a platinum-iridium cylinder kept at the French Bureau of Weights and Measures. The SI unit of time is the second. The original definition of a second, of course, was from a solar day. Modern definition of a second is 9 192 631 770 oscillations of the radiation from the cesium-133 atom. Thumb rule: The distance from ground to your belt is about one meter. The mass of two bottles of drinking water is about one kilogram. Relations between the SI units and the British units:

  3. Importance of using units: When you are writing a physical quantity, never forget its unit, whether it is in the middle of your calculation or it is the final result. Seven base units of the SI: In addition to length, mass, and time, base units in the SI system include electric current, temperature, amount of substance, and luminous intensity. These seven units are believed to be able to describe all phenomena in nature.

  4. 1.3 More about the Metric System In the metric system, units of the same type of quantity are related by factors of 10. Here are some common prefixes:

  5. Read: Ch1: 1-3 Homework: Ch1: E (means Exercise)7 Due: August 30

  6. August 21 Unit conversion and significant figures • 1.4 Unit Analysis • A powerful way to pre-check your calculations is to use unit analysis. • For an equation to stand true, not only must the numerical values on both sides of an equation be equal, the units must be equal as well. • Only two quantities of similar units can be added or subtracted. • Example 1.2: Checking Dimensions: Unit Analysis • Additional Example: A student finds that the surface area of a cylinder is • Can this equation be true?

  7. 1.5 Unit Conversions • A conversion factor expresses two equal quantities in different units in a ratio form which always equals to one. • Unit conversion: • Example: 65 mile/hr= ?meter/second. • Method 1: Multiply or divide by a conversion factor. Method 2: Direct substitution.

  8. 1.6 Significant figures • Calculations contain two types of numbers: exact numbers and measured numbers. • The significant figures in a measurement usually include some digits that are known with certainty, plus one digit that is uncertain.Example: the thickness of our text is 39.4 mm. Here 39 mm is thought to be certain, and 0.4 mm is estimated. • The significant figures in a given number start from the first non-zero digit and ends at the last digit (no matter it is zero or not). • Example: 39.4 has three significant figures, while 0.3940 has four. • Rules of significant figures in calculations: • 1. When multiplying and dividing quantities, leave as many significant figures in the answer as there are in the given quantity with the least number of significant figures. • 2. When adding or subtracting quantities, leave the same number of decimal places (rounded) in the answer as there are in the given quantity with the least number of decimal places. • Example 1.7:Using Significant Figures in Multiplication and Division: Rounding Applications • Example 1.8:Using Significant Figures in Addition and Subtraction: Application of Rules

  9. Read: Ch1: 4-7 Homework: Ch1: E9,26,43,45,47 Due: August 30

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