Physics Notes (Unit Conversion, Accuracy & Precision, Error in Measurements)

Lesson 1: CONVERSION OF UNIT, ACCURACY & PRECISION, ERRORS IN MEASUREMENT ACCURACY & PRECISION CONVERSION OF UNIT What is Conversion of Units? • • Accuracy: • A unit conversion is a changing of one unit to another. Ex: ( km to m, kg to g, kl to L) Describes how close a measured value is to the actual (true) value. Ex: What is more accurate when measuring a book that has a true length of 17.0 cm? • What is a Metric Unit? • • • • Metric unit are the universally accepted units around the world (except US). They are the easiest to convert. Based Units (meter, litters, grams) – all other metric units are based off of these. Ex. (km is based on meter, kL is based on liter, kg is based on grams) Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm Accuracy: • Common Metric Units (Prefixes) • • • • • • mega - M kilo - k centi -c milli – m micro - µ nano – n • Describes how closely measurements are to each other and how carefully measurements were made. Ex: which is more precise? 18.2, 18.4, 18.35 17.9, 18.3, 18.85 16.8, 17.2, 19.44 Metric Conversion Factors ERRORS IN MEASUREMENT 1km = 1000m 1kg = 100 g 1kL =1000L 100cm = 1m 100cg = 1g 1000cl =1000L 1000mm = 1m 1000mg = 1g 1000mL = 1L 10mm = 1cm 10mg = 1cg 10mL = 1cL Errors • • The difference between the measurement value and the actual value. The uncertainty in reading a measurement. How do Errors Arise? 1 min = 60 sec 5280 ft = 1 mile 60 min = 1 hr 12 in = 1 ft 24 hrs = 1 day 1 mile = 1600 m Errors occurs due to (a) choice of instrument and (b) techniques of measurement. Types Of Error: 1 in = 2.543 cm 3 ft = 1 yard (𝐹𝑎ℎ𝑟𝑒𝑛ℎ𝑒𝑖𝑔ℎ𝑡)𝐹 = • 1. Systematic Error • • (9 × 𝐶) + 32 5 5 × (𝑓 − 32) (𝐶𝑒𝑙𝑠𝑖𝑢𝑠)𝐶 = 9 (𝐾𝑒𝑙𝑣𝑖𝑛)𝐾 = 𝐶 + 273 (𝐶𝑒𝑙𝑠𝑖𝑢𝑠)𝐶 = = 𝐾 − 273 • • Arises due to defect in the measuring device Readings are above or below the true value by fixed amount Causes: There’s something wrong with the instrument or its data handling system The instruments is wrongly used by the experimenter Types: • • • Personal Error – Errors for which the individual analysist is responsible and are not connected with and method or procedure. Instrumental Error – Measuring device has faulty calibration or used under inappropriate conditions. External Error – Due to external properties like temperature, pressure and air flow. Nicole Matthew Leonard a. b. 2. Random Error • • • • • Consistent, repeatable error associated with faulty equipment or a flawed experiment design. You measured the same thing multiple times, your measurements are scattered around the true value. Sources: Natural Variation in real world or Experimental Contexts Imprecise or unreliable measurement instruments Individual differences between participants or units Lesson 1: SAMPLE PROBLEMS I. IDENTIFICATION Trial 1 35.4g 31.8g 39.2g his Accuracy and precision. III. CONVERSION OF UNITS 1. 2. 3. 4. 5. How many meters are in 252mm? How much water in mL would 5.25 mg of copper displace? d(Cu) = 11.53 g/mL How many Kelvins are in -15.5 C ֯ ? How many liters are in 2.52 × 104 ? A car travels 23 km in 15 minutes. How fast going in meters per second? ANSWERS KEYS: I. IDENTIFICATION 1. Metric Units _________2. The process of changing one unit to another. 2. Metric Unit Conversion _________3. The degree to which a process or instrumental will repeat the same value. 3. Random Error _________4. The uncertainty in reading a measurement. 5. External error II. ANALYZATION 1. 2. John measurement the mass of a rock and finds it to be 12.21 kg. he states that his measurement is both accurate and precise. For what two reasons is his statement incorrect? Three students have made multiple measurement of the solubility of sodium chloride (in g of NaCl per 100 g of water). Their results are summarized in the table below. The correct value for the solubility of sodium chloride is 35.9 g. Trial 3 35.7g 41.5g 38.9g Which student’s measurements have high precision but low accuracy? Calculate the average of Matthew’s three measurements. Comment on _________1. These are universal accepted unit. _________5. Difference in temperature, increase/decrease pressure and air flow are what type of error? Trial 2 36.1g 34.1g 39.3g 4. Error II. ANALYZATION 1. First, John doesn’t know the true value(measurement) of the rock for him to say that it’s accurate. Secomd, he only measures the mass of rock once, therefore he can’t say that it’s precise. a. Leonard’s measurements is high in precision but low in accuracy. b. 31.8g + 34.1g + 41.5g = 35.8g Matthew’s measurements are accurate but imprecise. II. ANALYZATION 1. 0.252 m 3. 257.5K 2. 0.000453 4. 25.2L 5. 25.56 m/s