PreClass Notes: Chapter 1 From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc. Narration and extra little notes by Jason Harlow, University of Toronto This video is meant for University of Toronto students taking PHY131. 2012 Pearson Education, Inc. Slide 1-1 Outline 1.1 The different realms of physics, and their applications in both natural and technological systems 1.2 The SI unit system 1.3 How to express and manipulate numbers in physics calculations Scientific notation Accuracy and significant figures Making quick estimates 1.4 A universal strategy for solving physics problems The DVD player is a metaphor for all of physics R.Wolfson 2012 Pearson Education, Inc. Slide 1-2 1
The SI Unit System Quantity Unit Standard Length Meter Length of the path traveled by light in 1/299,792,458 second Time Second Time required for 9,192,631,770 periods of radiation emitted by cesium atoms Mass Kilogram Platinum cylinder in International Bureau of Weights and Measures, Paris 2012 Pearson Education, Inc. Slide 1-3 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. 2012 Pearson Education, Inc. Slide 1-4 2
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: 2012 Pearson Education, Inc. Slide 1-5 SI Prefixes These are the standard SI prefixes for indicating powers of 10. 2012 Pearson Education, Inc. Slide 1-6 3
These are the only prefixes used in this class. 2012 Pearson Education, Inc. Slide 1-7 Converting Units Example Appendix C of your text says that 1 ft = 0.3048 m. The height of Dubai s Burj Khalifa (the world s tallest structure) is 2717 ft. How tall is this in m?? 2012 Pearson Education, Inc. Slide 1-8 4
Units Matter: A Bad Day on Mars In September 1999, the Mars Climate Orbiter was destroyed when the spacecraft passed through Mars s atmosphere and burned up. NASA identified the root cause as failure to convert the English units one team used to specify rocket thrust to the SI units another team expected. This was a $125-million mistake! 2012 Pearson Education, Inc. Slide 1-9 Significant Figures The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written: 23.21 cm has four significant figures. 0.062 cm has two significant figures (the initial zeroes don t count). 80 km is ambiguous it could have one or two significant figures. If it has three, it should be written 80.0 km. 2012 Pearson Education, Inc. Slide 1-10 5
Rules for Significant Figures When multiplying or dividing numbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures. Example: 11.3 cm x 6.8 cm = 76.84 cm 2 77 cm 2. When adding or subtracting, the answer is no more accurate than the least accurate number used. Example: 11.3 cm - 6.894 cm = 4.406 cm = 4.4 cm 2012 Pearson Education, Inc. Slide 1-11 Significant Figures Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). The top calculator shows the result of 2.0/3.0. If this is your final answer, you should round it to 0.67. The bottom calculator shows the result of 2.5 x 3.2. If this is your final answer, you should write it as 8.0. 2012 Pearson Education, Inc. Slide 1-12 6
Scientific Notation and 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 3.690 x 10 4, it has four. Much of physics involves approximations; these can affect the precision of a measurement also. 2012 Pearson Education, Inc. Slide 1-13 GOT IT? How many significant figures are in the number 0.041 10 9? A. 1 B. 2 C. 3 D. 4 E. 5 2012 Pearson Education, Inc. Slide 1-14 7
GOT IT? How many significant figures are in the number 10.041 10 9? A. 1 B. 2 C. 3 D. 4 E. 5 2012 Pearson Education, Inc. Slide 1-15 Estimation A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Diagrams are also very useful in making estimations. 2012 Pearson Education, Inc. Slide 1-16 8
Estimation 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. 2012 Pearson Education, Inc. Slide 1-17 A Strategy for Problem Solving The IDEA strategy consists of four broad steps. IDEA is not a cookbook but rather a general framework to organizing your path to the solution of a problem. The four IDEA steps are INTERPRET DEVELOP EVALUATE ASSESS 2012 Pearson Education, Inc. Slide 1-18 9
INTERPRET Step I: Interpret and Identify Interpret what the problem is asking. Identify the applicable concepts and principles. Identify the players in the situation. 2012 Pearson Education, Inc. Slide 1-19 DEVELOP Step D: Draw a Diagram, Determine relevant equations, Develop a plan Draw a diagram showing the situation. The diagram need not be neat, but it should be labeled and indicate objects, forces and other physical entities. Determine the relevant equations namely, those that contain the quantities you re given in the problem as well as the unknowns you re solving for. Develop a plan that might include calculating intermediate quantities, finding values in a table, or even solving a preliminary problem whose answer you need in order to get your final result. 2012 Pearson Education, Inc. Slide 1-20 10
EVALUATE Step E: Execute your plan, Evaluate the final answer Physics problems often have numerical or symbolic answers, and you need to evaluate your answer. In this step you execute your plan, going in sequence through the steps you ve developed in step D. Use algebra, trigonometry, or calculus, as needed, to solve your equations. It s a good idea to keep all numerical quantities, whether known or not, in symbolic form as you work through the solution of your problem. At the end you can plug in numbers and work the arithmetic to evaluate the numerical answer, if the problem calls for one. 2012 Pearson Education, Inc. Slide 1-21 ASSESS Step A: Assess your Answer Look at your answer and think about whether or not it makes sense. Is the answer roughly what you might have guessed in the first place? Are the units correct? Does the answer work in obvious special cases, like perhaps turning off gravity or making an object s mass zero or infinite? If you think your answer doesn t make sense, go back and look for mistakes you can correct. 2012 Pearson Education, Inc. Slide 1-22 11