AP Physics Chapter 1 Measurement AP Physics Turn in Contract/Signature Lecture Q
Zarubin, Lora, Food & Wine Editor has reference to this Academic Journal, PHwiki organized this Journal AP Physics Chapter 1 Measurement AP Physics Turn in Contract/Signature Lecture Q&A Website: http://www.mrlee.altervista.org Measurement in addition to Units Physics is based on measurement. International System of Units (SI unit) Fundamental (base)quantities: more intuitive Derived quantities: can be described using fundamental quantities. length, time, mass Speed = length / time Volume = length3 Density = mass / volume = mass / length3 Two kinds of quantities: Created by French scientists in 1795.
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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 (secondary) Unit: unit associated with a derived quantity Combination of fundamental units St in addition to ard Units St in addition to ard Unit: a unit recognized in addition to accepted by all. St in addition to ard: a reference to which all other examples of the quantity are compared. St in addition to ard in addition to non-st in addition to ard are separate from fundamental in addition to derived. Some SI st in addition to ard base units Length St in addition to ard unit: meter (m) St in addition to ard meter bar: International Bureau of Weights in addition to Measures near Paris Secondary st in addition to ards: duplicates In 1983: The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. Other (nonst in addition to ard) units: cm, km, ft, mile,
Time St in addition to ard unit: second (s) One second is the time taken by 9,192,631,770 vibrations of the light (of a specified wavelength) emitted by a cesium-133 atom. Other nonst in addition to ard units: min, hr, day, Mass St in addition to ard unit: kilogram (kg) St in addition to ard kilogram cylinder: International Bureau of Weights in addition to Measures near Paris Other nonst in addition to ard units: g, Lb, ounce, ton, Atomic mass unit (amu, u) 1 u = 1.6605402 10-27 kg Changing Unit: Conversion Factors Conversion factor: a ratio of units that is equal to one. in addition to So two conversion factors: in addition to
A few equalities (conversion Factors) to remember 1 m = 100 cm 1 inch = 2.54 cm 1 mile = 1.6 km 1 hr = 60 min 1 min = 60 s 1 hr = 3600 s Question Two conversion factors from each identity, but which one to use Depends on the unit we want to cancel. If the unit we want to cancel is on the top with the numerator, then as long as the conversion factor we must put that unit at the bottom with the denominator. If the unit we want to cancel is at the bottom with the denominator, then as long as the conversion factor we must put that unit on the top with the numerator. Example: 5 min = – s
Practice: Convert 12.3 m to cm Chain-link Conversion Convert: 2 hr = – s Practice: 12 m = – inch
Still simple How about 2 mile/hr = – m/s Chain Conversion More practice: 5 inch2 = — cm2 When reading the scale, Estimate to 1/10th of the smallest division 6.3 cm Draw mental 1/10 divisions However, if smallest division is already too small, just estimate to closest smallest division.
Uncertainty of Measurement All measurements are subject to uncertainties. Uncertainties in measurement cannot be avoided, although we can make it very small. Uncertainties are not mistakes; mistakes can be avoided. Uncertainty External influences: temperature, magnetic field Parallax: the apparent shift in the position of an object when viewed from various angles. 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. Uncertainty is one-tenth of the smallest division. Last digit of measurement is uncertain, the measurement can be anywhere within ± one increment of last digit. Meter stick: smallest division = 1 mm = 0.001 m uncertainty is 0.0001 m 1.2345m: 1.2344m -1.2346m 3 digits after decimal pt 4 digits after decimal pt Uncertainty in addition to Precision What is the uncertainty of the meterstick 0.0001m What is the precision of the meterstick 0.001m How precise is the meterstick 0.001m estimate certain certain Sometimes, when not strictly: precision = uncertainty Both the uncertainty in addition to precision of a meterstick is 0.0001m
Uncertainty in addition to Precision What is the uncertainty in addition to precision of 1.234 Uncertainty = 0.001 Precision = 0.01 or 0.001 (loosely) More precise = smaller uncertainty Which is more precise, 12.34 or 2.345 12.34: uncertainty = 0.01 2.345: uncertainty = 0.001 So, 2.345 is more precise. Accuracy Accuracy: how well the result agrees with an accepted or true value Accuracy in addition to Precision are two separate issues. Example Accepted (true) value is 1.00 m. Measurement 1 is 1.01 m, in addition to Measurement 2 is 1.200 m. Which one is more accurate 1, closer to true value. Which one is more precise 2, precise to 0.001m, compared to 0.01m of 1
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 as long as spacing the decimal point are not significant. Example: 1.002300 0.004005600 7 sig. figs 7 sig. figs 12300 3 sig. figs Practice: How many significant figures are there in 123000 1.23000 0.001230 0.0120020 1.0 0.10 Operation with measurements In general, no final result should be more precise than the original data from which it was derived. Too vague.
Addition in addition to subtraction with Sig. Figs The sum or difference of two measurements is only as precise as the least precise one. Example: 16.26 + 4.2 = 20.46 Which number is least precise 4.2 Precise to how many digits after the decimal pt 1 So the final answer should be rounded-off (up or down) to how many digits after the decimal pt 1 =20.5 Practice: 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 Must keep this 0. 3) 12.7+3.35 = 16.05 = 16.1 4) 12. + 3.3 = 15.3 = 15. Keep the decimal pt. Multiplication in addition to Division with Sig. Figs The number of significant digits in a product or quotient is the number in the measurement with the least number of significant digits Example: 2.33 5.5 = 12.815 Which number has the least number of sig. figs 5.5 How many sig figs 2 So the final answer should be rounded-off (up or down) to how many sig figs 2 =13.
Dimensional Analysis [x] = dimension of quantity x When angle in unit of radian 1 AU 1 pc 1 1 ly = distance traveled by light in one year HW 57 Conversion factor to convert
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