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## Conversions

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**Steps to Fool Proof Conversions**• Write what you want to convert with unit • Add a multiplication sign • Draw a horizontal line • Whatever unit you don’t want goes on the opposite side of the line from where it was written • Place whatever unit you do want on the other side of the horizontal line • Add the conversion factor • A 1 goes beside the prefix if you are using conversion factors**Measurements**• Every measurement is wrong! • To a certain degree • Examples: • Your Birthday • Height**Measurement**• Every measurement has a degree of uncertainty • The uncertainty is based on: • The measuring device • The skill of the measurer**Ways to indicate How Accurate a Number Is**• Tolerance Intervals • Percent Error • Significant Digits**Tolerance Intervals**Tolerance is the greatest range of variation that can be allowed 25 0.5 would be between 24.51 to 25.49 25 0.05 would be between 24.951 to 25.049 25 0.005 would be between 24.9951 to 25.0049**Tolerance Intervals**• Used on blueprints and in machining to indicate accuracy**Activity: Tolerance a Part**Design a square piece with a square hole through it’s centre. Key Dimensions: • How must the length of the piece be toleranced • How big must the square hole through the piece be to accommodate the square peg Criteria: • The square piece must sit inside a container that was toleranced 20m lm on each side • The square peg is dimensioned 2m 0.1m**Percent Error**• Indicates a percentage that the value may be out by**Sample Problem**• You buy an 8 foot 2x4. You measure the board to be 94.5 inches long. What is the percentage error for the length of the board? • 12 inches = 1 foot**Significant Digits**The accuracy is determined by the right most digit 25 would be between 24.51 to 25.49 25.0 would be between 24.951 to 25.049 25.00 would be between 24.9951 to 25.0049**Significant Digits: Uses the number of digits in the number**to express the uncertainty of the number • 1 x 101 is less accurate than 12 • 12 is less accurate than 12.0 • 12.0 is less accurate than 12.00**Rules for Significant Digits**• All non-zero digits are significant • All zeros contained between non-zero digits are significant • i.e. 207 – 3sd • All trailing zeros to the right of a decimal are significant • i.e. 3.000 – 4sd**When are zeroes not significant?**• All leading zeros to the left of the first non-zero digit are not significant • i.e. 0.00058 – 2 sd**Exact numbers have infinite significant digits**• How many cars do I have? 1**Examples**a.) 125.9 b.) 230 c.) 0.00658 d.) 500.3**Examples:**a.) 125.9 - 4 s.d. b.) 230 - 3 s.d. c.) 0.00658 - 3 s.d. d.) 500.3 - 4 s.d.**Defining Cylindricity - Extra**• http://www.youtube.com/watch?v=ZuECC8RMZ40**Interchangeable Parts**• Muskets were originally designed by expert gun smiths who made one gun at a time • If it broke and needed servicing, the gun would have to be sent back to an expert gunsmith**Early US Attempts**• In 1801, Eli Whitney built ten guns from the same parts, disassembled all of them in front of congress and then reassembled them from a pile of parts • The concept was great but each part was still handmade by skilled craftsmen**Changes that Allowed Interchangeability**• New machines (lathes, mills, etc) • Development of jigs to control the path of the tool and fixtures to hold the piece in place • Blocks and gauges to determine the accuracy of the finished parts**How to Improve Accuracy**• Improve the measuring instrument • The smaller the unit on the measuring device, the more precise the measurement • Know how to measure • Always look straight down on the measuring device**How to Improve Accuracy**• Repeat • Measure several times to get a good average value • “Measure twice, cut once” • Measure under controlled conditions • Objects can shrink or expand based on measuring conditions**Why wouldn’t you make everything very, very accurate?**• Cost • Waste of time • Not needed • The more accurate a measurement must be, the more it costs to do so**Bibliography**• Britton. "Geometric Dimensioning and Tolerancing." Lecture. http://synthetica.eng.uci.edu/~mccarthy/mechanicaldesign101/GDandT.pdf. 1 Feb. 2013**Adding and Subtracting**• Use the lowest number of decimal places from the numbers given in the problem • 2.35 + 7.669 = 10.019 • According to the rule, we can only keep 2 decimal places = 10.02**12.875 – 8.3 =**20.876 – 5 =**Multiplying and Dividing**• Use the lowest number of significant digits form the numbers given in the problem 3.4 x 2.35 = 7.99 2SD 3SD = 2 SD = 8.0**780 / 23 =**200.600 x 0.0012 =**Scientific Notation**• Used to express numbers with the proper number of significant digits • 1.32 x 1010 (3 s.d) • Only one digit to the left of the decimal place • Only leave the number of sig digs you want in the numerical portion**Finding the exponent**• Every time you move the decimal to the left, the exponent goes up 1 • Every time you move the decimal to the right, the exponent goes down 1 • 3,567,000,000 (with 3 SD) • 0.000,000,000,056,0 (with 3 SD)**In this course,**• The number of significant digits in your answer should be the same as the lowest number of significant digits in the question • Ex: If each students has 0.50 cents and there are 100 students, how much money do they have?