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Motion in One Dimension

Motion in One Dimension. Reminder: Homework due on Wed, August 28 Converting Units Order of magnitude 2.1 Reference Frame 2.2 average Velocity. Reading Significant Figures. Nonzero Digits are always significant Zeros between significant figures are significant. Examples: 409.8 s

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Motion in One Dimension

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  1. Motion in One Dimension • Reminder: Homework due on Wed, August 28 • Converting Units • Order of magnitude • 2.1 Reference Frame • 2.2 average Velocity

  2. Reading Significant Figures • Nonzero Digits are always significant • Zeros between significant figures are significant. • Examples: 409.8 s 0.058700 cm 950.0X 101 mL

  3. Answer • In 409.8 s : all four digits are significant • In 0.058700 cm: the two zeros on the left are not significant, they are used to place a decimal point, the numbers 5,8,7 are significant, and so are the two final zeros. • In 950.0X 101 ml: the final zero is significant since it comes after the decimal point. The zero at its left is also significant since it comes between two other significant digits, so the results is four significant figures.

  4. Adding Significant Figures 67.9 g + 0.002 g + 3.51 g = ? Sum (or difference) can’t be more precise than least precise quantity Answer: 71.4 g When you add or subtract you keep the decimal place of the least precise value.

  5. Multiplying Significant Figures • Distance = velocity x time Velocity = 65.4mph Time = 4.2 hours • Distance=274.7 or 275 or 2.7x102 miles • When you multiply (or divide) you keep the number of significant figures that are equal to the quantity with the smallestnumberof significant figures.

  6. Importance of Units • The 165 million dollars Mars Polar Lander • Units help you figure out equations Speed in mph Density in kg/m3 • Units help you determine the correct solution www.nasa.gov

  7. Units, Standards, and the SI System https://www.nist.gov/si-redefinition/meet-constants

  8. Units, Standards, and the SI System

  9. Units, Standards, and the SI System

  10. Units, Standards, and the SI System

  11. Units, Standards, and the SI System We will be working in the SI system, in which the basic units are kilograms, meters, and seconds. Quantities not in the table are derived quantities, expressed in terms of the base units. Other systems: cgs; units are centimeters, grams, and seconds. British engineering systemhas force instead of mass as one of its basic quantities, which are feet, pounds, and seconds.

  12. Converting units • Problem 11. (I) Write the following as full (decimal) numbers with standard units: (a) 286.6 mm, (b) 35mV, (c) 760 mg, (d) 60.0 ps, (e) 22.5 fm, (f) 2.50 gigavolts.

  13. Converting units Problem 15. (II) What is the conversion factor between (a) ft2 and yd2 (b) m2 and ft2 1yd=3ft and 1m=3.28ft

  14. Converting units Write this in miles/s and miles/hour 30.0 km/h =? 1 km = 0.6214 miles 1 mile=1.6093km How many Us dollars is in 220 Canadian dollars? $220 Canadian Dollars = ? 1 US dollar = 1.31 Canadian dollar

  15. Converting units

  16. Question 1 atm = 1.013 x105 Pa = 14.70 lb/in2 If you want to convert 0.46 atm to Pa you should Multiply 0.46 atm by 14.70 lb/in2 Multiply 0.46 atm by 1.013 x105 Pa Divide 0.46 atm by 14.70 lb/in2 Divide 0.46 atm by 1.013 x105 Pa

  17. Converting units • Multiplying by 1 leaves a quantity unchanged. • “1” can be represented as • Choose form for ‘1’ for which units match.

  18. Prefixes • Prefixes correspond to powers of 10 • Each prefix has a specific name • Each prefix has a specific abbreviation

  19. Prefixes • The prefixes can be used with any base units • They are multipliers of the base unit • Examples: • 1 mm = 10-3 m • 1 mg = 10-3 g

  20. Fundamental and Derived Quantities • In mechanics, three fundamental or base quantitiesare used • Length • Mass • Time • Will also use derived quantities • These are other quantities that can be expressed as a mathematical combination of fundamental quantities

  21. Density • Density is an example of a derivedquantity • It is defined as mass per unit volume • Units are kg/m3

  22. Order of Magnitude: Rapid Estimating 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.

  23. 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!)

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