Bellringer 1-1 Suppose a rectangular sheet of steel is measured to be 2.50 m wide and 3.2 m long. What is the area of the sheet? A. 8 m 2 B. 8.0 m 2 C m 2 D m 2 E m 2 Copyright © 2009 Pearson Education, Inc.

Robotics Team Interest meeting Thursday, August 13 th during Zero Block in Room for more informationhttp://bestinc.org Copyright © 2009 Pearson Education, Inc.

Unit 1.1 Introduction, Measurement, Estimating

Copyright © 2009 Pearson Education, Inc. The Scientific Method Feynman: How not to be fooled…. Observing –Trends, Patterns, Singular Events Asking Questions –What? When? Where? How? … and WHY? –Researching prior explanations & models Developing Testable Hypothesis

Copyright © 2009 Pearson Education, Inc. 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

Copyright © 2009 Pearson Education, Inc. The Scientific Method Sharing preliminary results –Submit a paper to peer-reviewed journal –Ask colleagues for input –Present at conferences –Discuss, Debate, Defend results Seeking independent confirmation Revising Theories Publishing

Copyright © 2009 Pearson Education, Inc. 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, and the cycle goes on. No theory can be absolutely verified, although a theory can be proven false.

Copyright © 2009 Pearson Education, Inc. 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 force stopped it.

Copyright © 2009 Pearson Education, Inc. The Nature of Science The principles of physics are used in many practical applications, including construction. Communication between architects and engineers is essential if disaster is to be avoided.

Copyright © 2009 Pearson Education, Inc. Models, Theories, and Laws Models: useful to help understand phenomena. creates mental pictures, but must be careful to also understand limits of model not take it too seriously Example: model bay bridge turnbuckle to estimate whether it can withstand load… A theory is detailed; gives testable predictions. Example: Theory of Damped Harmonic Oscillators

Copyright © 2009 Pearson Education, Inc. Models, Theories, and Laws A law is a brief description of how nature behaves in a broad set of circumstances. Ex: Hooke’s Law for simple harmonic oscillators A principle is similar to a law, but applies to a narrower range of phenomena. Ex: Principle of Hydrostatic Equilibrium

Think about it….. A friend asks to borrow your precious diamond for a day to show her family. You are a bit worried, so you carefully have your diamond weighed on a scale which reads 8.17 grams. The scale’s accuracy is claimed to be ±0.05 gram. The next day you weigh the returned diamond again, getting 8.09 grams. Is this your diamond? Copyright © 2009 Pearson Education, Inc.

Lab Activity Sig Fig and Measurement Lab Copyright © 2009 Pearson Education, Inc.

Bellringer “Questions” section of handout. Copyright © 2009 Pearson Education, Inc.

Measurement and Uncertainty; Significant Figures No measurement is exact; there is always some uncertainty due to limited instrument accuracy and 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.

Copyright © 2009 Pearson Education, Inc. Measurement and Uncertainty; Significant Figures Estimated uncertainty written “ ± ” ex.8.8 ± 0.1 cm. Percent uncertainty: ratio of uncertainty to measured value, multiplied by 100:

Copyright © 2009 Pearson Education, Inc. Measurement and 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: cm = four significant figures 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.

Copyright © 2009 Pearson Education, Inc. Measurement and 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: = 3, not 3.213!

Copyright © 2009 Pearson Education, Inc. Measurement and 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.

Copyright © 2009 Pearson Education, Inc. Measurement and Uncertainty; Significant Figures Conceptual Example: 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.

Copyright © 2009 Pearson Education, Inc. Measurement and 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 10 4, we know it has three; if we write x 10 4, it has four. Much of physics involves approximations; these can affect the precision of a measurement also.

Copyright © 2009 Pearson Education, Inc. Accuracy vs. Precision Accuracy is how close a measurement comes to the true value. ex. Acceleration of Earth’s gravity = 9.81 m/sec 2 Your experiment produces 10 ± 1m/sec 2 You were accurate, but not super “precise” Precision is the repeatability of the measurement using the same instrument. ex. Your experiment produces m/sec 2 You were precise, but not very accurate!

Copyright © 2009 Pearson Education, Inc. 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?

Copyright © 2009 Pearson Education, Inc. Converting Units Example Problem: The 8000-m peaks. The 14 tallest peaks in the world are referred to as “eight- thousanders,” meaning their summits are over 8000 m above sea level. What is the elevation, in feet, of an elevation of 8000 m?

Copyright © 2009 Pearson Education, Inc. Converting Units 1 m = feet 8000 m = 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!

Copyright © 2009 Pearson Education, Inc. Order of Magnitude: Rapid Estimating Quick way to estimate calculated quantity: - round off all numbers to one significant figure and then calculate. - result should be right order of magnitude; expressed by rounding off to nearest power of 10.

Copyright © 2009 Pearson Education, Inc. Order of Magnitude: Rapid Estimating Example Problem: Volume of a lake. Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, and you guess it has an average depth of about 10 m.

Copyright © 2009 Pearson Education, Inc. Order of Magnitude: Rapid Estimating Example Problem: Thickness of a page. Estimate the thickness of a page of your textbook. (Hint: you don’t need one of these!)

Copyright © 2009 Pearson Education, Inc. Order of Magnitude: Rapid Estimating Example Problem: Height by triangulation. Estimate the height of the building shown by “triangulation,” with the help of a bus-stop pole and a friend. (See how useful the diagram is!)

Copyright © 2009 Pearson Education, Inc. Dimensions and 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.

Copyright © 2009 Pearson Education, Inc. Dimensions and 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 for velocity? Check the dimensions: Wrong!

Copyright © 2009 Pearson Education, Inc. Order of Magnitude: Rapid Estimating Example Problem: 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 and the opposite shore—a good clue that the Earth is round.

Copyright © 2009 Pearson Education, Inc. Order of Magnitude: Rapid Estimating Ex cont’d: 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.