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Honors Physics A Physics Toolkit 1 Honors Physics Chapter 1 2 Turn in Contract/Signature Lecture: A Physics Toolkit Q&A Website: http://www.mrlee.altervista.org The Metric System Physics is based on measurement. International System of Units (SI unit) – Created by French scientists in 1795. Two kinds of quantities: – Fundamental (base)quantities: more intuitive – Derived quantities: can be described using fundamental quantities. 3 length, time, mass … Speed = length / time Volume = length3 Density = mass / volume = mass / length3 Units Unit: a measure of the quantity that is defined to be exactly 1.0. Fundamental (base) Unit: unit associated with a fundamental quantity Derived Unit: unit associated with a derived quantity – 4 Combination of fundamental units Units Standard Unit: a unit recognized and accepted by all. – 5 Standard and non-standard are separate from fundamental and derived. Some SI standard base units Quantity Unit Name Unit Symbol Length Time Mass Meter Second kilogram m s kg Prefixes Used With SI Units 6 Prefix nano micro Symbol n Fractions 10-9 10-6 milli centi kilo m c k 10-3 10-2 103 mega giga M G 106 109 1 m 1 106 m 1mm 1 103 m Conversion Factors 1 m = 100 cm so 1m 1 and 100cm 1 100cm 1m Conversion factor: 1m 100cm or Which conversion factor to use? 7 Depends on what we want to cancel. 100cm 1m Example 2.1 km = ____ m Given: 1 km = 1000 m 1km 2.1km 2.1km 1000m Not good, cannot cancel 1000m 2100m 2.1103 m 2.1km 2.1km 1km 8 Practice 12 cm = ____ m 1m 12cm 12cm 0.12m 100cm 9 Chain Conversion 1km 1000m 1m 100cm 1.1 cm = ___ km 1km m 1.1cm 1.1cm 1.1 105 km 100cm 1000m 10 Practice 1km 1000m 1m 100cm 7.1 km = ____ cm 1000m 100cm 7.1km 7.1km 7.1105 cm 1km 1m 11 Still simple? How about… 2 mile/hr = __ m/s mile mile 2 2 hr hr 1600m 1hr 0.89 m 3600 s s mile Chain Conversion 12 1hr 3600s 1mile 1600m When reading the scale, Estimate to 1/10th of the smallest division – – Draw mental 1/10 divisions However, if smallest division is already too small, just estimate to closest smallest division. 1 .5 1 cm 1.3 cm but not 1.33 cm, why? 13 Uncertainty of Measurement All measurements are subject to uncertainties. 14 External influences: temperature, magnetic field Parallax: the apparent shift in the position of an object when viewed from different angles. Uncertainties in measurement cannot be avoided, although we can make it very small by using good experimental skills and apparatus. Uncertainties are not mistakes; mistakes can be avoided. Uncertainty = experimental error Precision Precision: the degree of exactness to which a measurement can be reproduced. The precision of an instrument is limited by the smallest division on the measurement scale. Smaller uncertainty = more precise Larger Uncertainty = less precise – Uncertainty is one-tenth of the smallest division. – 15 Typical meter stick: Smallest division is 1 mm = 0.001 m, uncertainty is 0.1 mm = 0.0001m. A typical meterstick can give a measurement of 0.2345 m, with an uncertainty of 0.0001 m. more precise Accuracy 16 more accurate Accuracy: how close the measurement is to the accepted or true value Accuracy Precision Accepted (true) value is 1.00 m. Measurement #1 is 0.99 m, and Measurement #2 is 1.123 m. – #1 is more accurate: closer to true value ____ – #2 is more precise: uncertainty of 0.001 m ____ (compared to 0.01 m) Significant Figures (Digits) 1. Nonzero digits are always significant. 2. The final zero is significant when there is a decimal point. 3. Zeros between two other significant digits are always significant. 4. Zeros used solely for spacing the decimal point are not significant. Example: 1.002300 7 sig. fig’s 17 0.004005600 7 sig. fig’s 12300 3 sig. fig’s 12300. 5 sig. fig’s Practice: How many significant figures are there in a) b) c) d) e) f) 18 123000 1.23000 0.001230 0.0120020 1.0 0.10 3 6 4 6 2 2 Operation with measurements 19 In general, no final result should be “more precise” than the original data from which it was derived. Addition and subtraction with measurements The sum or difference of two measurements is precise to the same number of digits after the decimal point as the one with the least number of digits after the decimal point. Example: 16.26 + 4.2 = 20.46 =20.5 20 Which number has the least digits after the DP? 4.2 Precise to how many digits after the DP? 1 So the final answer should be rounded-off (up or down) to how many digits after the DP? 1 Practice: 1) 2) 3) 4) 1) 2) 3) 4) 21 23.109 + 2.13 = ____ 12.7 + 3.31 = ____ 12.7 + 3.35 = ____ 12. + 3.3= ____ 23.109 + 2.13 = 25.239 = 25.24 12.7+3.31 = 16.01 = 16.0 12.7+3.35 = 16.05 = 16.1 12. + 3.3 = 15.3 = 15. Must keep this 0. Keep the decimal pt. Multiplication and Division with measurements The product or quotient has the same number of significant digits as the measurement with the least number of significant digits. Example: 2.33 4.5 = 10.485 =10. Which number has the least number of sig. figs? 4.5 How many sig figs does it have? So the final answer should be rounded-off (up or down) to how many sig figs? 22 2 2 Practice: 2.33/3.0 = ___ 2.33 / 3.0 = 0.7766667 = 0.78 2 sig figs 23 What about exact numbers? Exact numbers have infinite number of sig. figs. If 2 is an exact number, then 2.33 / 2 = __ 2.33 / 2 = 1.165 = 1.17 Note: 2.33 has the least number of sig. figs: 3 24 Scientific Notation Whenever it becomes awkward to say a number, use scientific notation. M 10n 1 <= |M| < 10 n: exponent (positive, zero, or negative integer) Example: 23000 = 2.3 104 25 0.00032 = 3.2 10-4 4 times to the left 4 times to the right Practice 26 8.6 × 105 860000 = _________ 1.02 × 10-5 0.0000102 = ________ 3 × 107 30000000 = ________ 0.0000003 = ________ 3 × 10-7 Arithmetic Operations in Scientific Notation Adding and subtracting with like exponents Adding and subtracting with unlike exponents Adding and subtracting with unlike units Multiplication using scientific notation Division using scientific notation Use calculator. Skip to Slide 36 27 Adding and subtracting with like exponents Add or subtract the values of M and keep the same n. Example: 2 105 m + 3 105 m = (2 + 3) 105 m = 5 105 m 5.3 104 m – 2.1 104 m = (5.3 – 2.1) 104 m = 3.2 104 m 28 Practice: 2 2 3 10 m 6 10 m ___ 2 2 3 10 m 6 10 m 3 6 102 m 2 9 10 m 29 Adding and subtracting with unlike exponents 1. 2. 30 First make the exponents the same. Then add or subtract. 2.0 103 m + 5 102 m = 2.0 103 m + 0.5 103 m = (2.0 + 0.5) 103 m = 2.5 103 m Practice: 3 10 m 6.0 10 m ___ 6 7 3 106 m 6.0 107 m 0.3 10 m 6.0 10 m 7 0.3 6.0 107 m 6.3 107 m 31 7 10 3 106 3 106 10 3 10 106 0.3 107 10 Adding and subtracting with unlike units 1. 2. 3. Convert to common unit Make the components the same Add or subtract Example: 2.10 m + 3 cm = 2.10 m + 0.03 m = 2.13 m 32 Multiplication using scientific notation 1. 2. 3. 33 Multiply the values of M Add the exponents Units are multiplied (3 104 kg) (2 105 m) = (3 2) 104+5 (kgm) = 6 109 kg×m Practice: 2 10 m 5 10 m ___ 3 5 3 5 35 2 10 m 5 10 m 2 5 10 mm 10 108 m 2 1 109 m 2 34 Division using scientific notation 1. 2. 3. Divide the values of M. Subtract the exponent of the divisor from the exponent of the dividend. Divide the unit of the divisor from the unit of the dividend. 6 106 m 6 6 ( 2) m 8m 10 2 10 s 3 102 s 3 s 35 Displaying Data Table Graph 36 Independent variable: manipulated Dependent variable: responding Table Title or description Variables (quantities) Unit (either after variables or each value) Table 1: Displacement and speed of cart at different times 37 Time (s) Displacement (m) Speed 1.0 2.4 2.4 m/s 2.1 4.9 2.3 m/s 3.1 7.6 2.2 cm/s Graph Title or description Labels Units Scales 38 Independent variable on horizontal axis Dependent variable on vertical axis Horizontal and vertical can be different Graph Example Velocity of falling block at different time 14 12 Velocity (m/s) 10 8 6 4 2 0 0 2 4 Time (s) 39 6 8 Linear Relationship y mx b y1 m: slope m 40 y rise run y2 y1 x 2 x1 b: y-intercept Direct Relationship: b x2 x1 y2 y mx x Inverse Relationship a y x Hyperbola 6 5 4 3 2 1 0 0 41 1 2 3 4 5