Chapter 1 Introduction, Measurement, Estimating

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Chapter 1 Introduction, Measurement, Estimating

Kidd, Kristine, Food Editor has reference to this Academic Journal, PHwiki organized this Journal Chapter 1 Physics as long as Scientists & Engineers, with Modern Physics, 4th edition Giancoli Chapter 1 Introduction, Measurement, Estimating Units of Chapter 1 The Nature of Science Models, Theories, & Laws Measurement & Uncertainty; Significant Figures (reviewed in lab) Units, St in addition to ards, & the SI System Converting Units Order of Magnitude: Rapid Estimating Dimensions in addition to Dimensional Analysis

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The Scientific Method Feynman: How not to be fooled . Observing Trends, Patterns, Singular Events Asking Questions What When Where How in addition to WHY Researching prior explanations & models Developing Testable Hypothesis The Scientific Method Creating Experiments to TEST Hypothesis There is always uncertainty in every measurement, in every result. Building a model is an experiment. Analyzing results Anticipate sources of error Refine or Discard Hypothesis Develop further tests & Repeat! Compare results w/ existing theories The Scientific Method Sharing preliminary results Submit a paper to peer-reviewed journal Ask colleagues as long as input Present at conferences Discuss, Debate, Defend results Seeking independent confirmation Revising Theories Publishing

1-1 The Nature of Science Observation: important first step toward scientific theory; requires imagination to tell what is important Theories: created to explain observations; will make predictions Further Observations will tell if the prediction is accurate, in addition to the cycle goes on. No theory can be absolutely verified, although a theory can be proven false. 1-1 The Nature of Science How does a new theory get accepted Predictions agree better with data Explains a greater range of phenomena Example: Aristotle believed that objects would return to a state of rest once put in motion. Galileo realized that an object put in motion would stay in motion until some as long as ce stopped it. 1-1 The Nature of Science The principles of physics are used in many practical applications, including construction. Communication between architects in addition to engineers is essential if disaster is to be avoided.

1-2 Models, Theories, in addition to Laws Models: useful to help underst in addition to phenomena. creates mental pictures, but must be careful to also underst in addition to limits of model not take it too seriously Example: model bay bridge turnbuckle to estimate whether it can withst in addition to load A theory is detailed; gives testable predictions. Example: Theory of Damped Harmonic Oscillators 1-2 Models, Theories, in addition to Laws A law is a brief description of how nature behaves in a broad set of circumstances. Ex: Hooke’s Law as long as simple harmonic oscillators A principle is similar to a law, but applies to a narrower range of phenomena. Ex: Principle of Hydrostatic Equilibrium 1-3 Measurement in addition to Uncertainty; Significant Figures No measurement is exact; there is always some uncertainty due to limited instrument accuracy in addition to difficulty reading results. The photograph to the left illustrates this – it would be difficult to measure the width of this board more accurately than ± 1 mm.

1-3 Measurement in addition to Uncertainty; Significant Figures Estimated uncertainty written “ ± ” ex. 8.8 ± 0.1 cm. Percent uncertainty: ratio of uncertainty to measured value, multiplied by 100: 1-3 Measurement in addition to Uncertainty; Significant Figures Number of significant figures = number of “reliably known digits” in a number. Often possible to tell of significant figures by the way the number is written: 23.21 cm = four significant figures. 0.062 cm = two significant figures (initial zeroes don’t count). 80 km is ambiguous—it could have one or two sig figs. If it has three, it should be written 80.0 km. 1-3 Measurement in addition to Uncertainty; Significant Figures When multiplying or dividing numbers, or using functions, result has as many sig figs as term with fewest. ex: 11.3 cm x 6.8 cm = 77 cm. When adding or subtracting, answer is no more precise than least precise number used. ex: 1.213 + 2 = 3, not 3.213!

1-3 Measurement in addition to Uncertainty; Significant Figures Calculators will not give right of sig figs; usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). top image: result of 2.0/3.0. bottom image: result of 2.5 x 3.2. 1-3 Measurement in addition to Uncertainty; Significant Figures Conceptual Example 1-1: Significant figures. Using a protractor, you measure an angle to be 30°. (a) How many significant figures should you quote in this measurement (b) Use a calculator to find the cosine of the angle you measured. 1-3 Measurement in addition to Uncertainty; Significant Figures Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown. For example, we cannot tell how many significant figures the number 36,900 has. However, if we write 3.69 x 104, we know it has three; if we write 3.690 x 104, it has four. Much of physics involves approximations; these can affect the precision of a measurement also.

1-3 Accuracy vs. Precision Accuracy is how close a measurement comes to the true value. ex. Acceleration of Earth’s gravity = 9.81 m/sec2 Your experiment produces 10 ± 1m/sec2 You were accurate, but not super “precise” Precision is the repeatability of the measurement using the same instrument. ex. Your experiment produces 8.334 m/sec2 You were precise, but not very accurate! 1-5 Converting Units Unit conversions involve a conversion factor. Example: 1 in. = 2.54 cm. Equivalent to: 1 = 2.54 cm/in. Measured length = 21.5 inches, converted to centimeters How many sig figs are appropriate here 1-5 Converting Units Example 1-2: The 8000-m peaks. The 14 tallest peaks in the world are referred to as “eight-thous in addition to ers,” meaning their summits are over 8000 m above sea level. What is the elevation, in feet, of an elevation of 8000 m

1-5 Converting Units 1 m = 3.281 feet 8000 m = 2.6248 E04 or 26,248 feet. “8000 m” has only 1 significant digit! Round the answer up to 30,000 ft! Rather rough! 30,000 – 26,248 = 3,752 3,752/26,248 = 14.3% high! 1-6 Order of Magnitude: Rapid Estimating Quick way to estimate calculated quantity: – round off all numbers to one significant figure in addition to then calculate. – result should be right order of magnitude; expressed by rounding off to nearest power of 10. 1-6 Order of Magnitude: Rapid Estimating Example 1-5: Volume of a lake. Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, in addition to you guess it has an average depth of about 10 m.

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1-6 Order of Magnitude: Rapid Estimating Example 1-6: Thickness of a page. Estimate the thickness of a page of your textbook. (Hint: you don’t need one of these!) 1-6 Order of Magnitude: Rapid Estimating Example 1-7: Height by triangulation. Estimate the height of the building shown by “triangulation,” with the help of a bus-stop pole in addition to a friend. (See how useful the diagram is!) 1-7 Dimensions in addition to Dimensional Analysis Dimensions of a quantity are the base units that make it up; they are generally written using square brackets. Example: Speed = distance/time Dimensions of speed: [L/T] Quantities that are being added or subtracted must have the same dimensions. In addition, a quantity calculated as the solution to a problem should have the correct dimensions.

1-7 Dimensions in addition to Dimensional Analysis Dimensional analysis is the checking of dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions. Example: Is this the correct equation as long as velocity Check the dimensions: Wrong! 1-6 Order of Magnitude: Rapid Estimating Example 1-8: Estimating the radius of Earth. If you have ever been on the shore of a large lake, you may have noticed that you cannot see the beaches, piers, or rocks at water level across the lake on the opposite shore. The lake seems to bulge out between you in addition to the opposite shore—a good clue that the Earth is round. 1-6 Order of Magnitude: Rapid Estimating Ex 1-8: Estimating the radius of Earth. Climb a stepladder & discover when your eyes are 10 ft (3.0 m) above the water, you can just see the rocks at water level on the opposite shore. From a map, you estimate the distance to the opposite shore as d 6.1 km. Use h = 3.0 m to estimate the radius R of the Earth.

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