Transcript Document
Measurements We need numbers in order to accurately take measurements • When executing the scientific method we must perform experiments measurements data • Express measurements using units • International System of Units (SI) aka: Metric system (meters, grams, seconds) • English units (feet, slugs, seconds) Unfortunately American students must learn both systems! • Units allow us to describe things numerically • Measurement standards – a fixed and reproducible value for the purpose of taking accurate measurements How do we know the length of a meter, yard? • Egyptians, cubit • King Louis XIV, foot • Distance from equator to north pole 1/10,000,000, meter, from Greek metron for “measure” • Modern standard, distance light,travels in 1/299,792,458 s Distance from Earth to nearest large galaxy One light year Radius of Earth Height of person Diameter of a period in a sentence Diameter of a hydrogen atom Diameter of a proton 1022 m 1016 m 106 m 2m 10-4 m 10-10 m 10-15 m The mass of things • Mass is the amount of matter an object contains – different than, something's weight! • Mass is measured in kilograms, grams, milligrams, etc… • How do we know the mass of a kilogram? – the kilogram is defined to be the mass of a cylinder of platinum-iridium kept at the international Bureau of Weights and Measures • Quart of milk ~ 1 kg Typical Masses Milk Way Galaxy 4 10 41 kg Earth 6 10 24 kg Space Shuttle 2 10 6 kg Elephant 5400 kg Automobile 1200 kg Human 70 kg Baseball 0.15 kg Honeybee 1.5 10 –4 kg Bacteria 10 –15 kg Hydrogen Atom 1.67 10 –27 kg Electron 9.11 10 –31 kg The time of things • Define time? Even though we all have a sense of what time is, it’s difficult to give a good definition for it. • In scientific work we need to know: When did it happen? How long did it take? • How do we know the time of a second? - originally defined in terms of a fraction of the average day (1 second = 1/86,400 of an average day) - currently defined in terms of the frequency of radiation emitted from a cesium atom (called an atomic clock) Typical Times Age of the universe 5 10 17 s Age of the Earth 1.3 10 17 s Existence of Humans 6 10 13 s Human Lifetime 2 10 9 s One Year 3 10 7 s One Day 8.6 10 4 s Time between heartbeats 0.8 s Human reaction time 0.1 s One cycle of an AM radio wave 10 –6 s One cycle of a visible light wave 10 –15 s Converting Units of Measurement – Dimensional Analysis • It is often the case that we must convert from one set of units to another. • Suppose we want to convert 316 ft to its equivalent in meters 1 km 1000 meters 0.62 mile 1 km 12 inches 1 foot 5280 feet 2.54 cm 100 cm 1 mile 1 inch 1 meter these cancel ! Example: How many kilometers is 50,000 inches? 50,000 inches 1 foot 12 inches 1 mile 5280 feet 1 kilometer 0 . 62 mile 1x 1 x 1 50,000 kilometers 1.27 kilometers 12 x 5280x 0.62 left with the units we want ! The order that you apply the conversions makes no difference in the end! Converting Units of Measurement – Dimensional Analysis 1 km 1000 meters 0.62 mile 1 km 12 inches 1 foot 5280 feet 2.54 cm 100 cm 1 mile 1 inch 1 meter If I run 10 m/s in a school zone posted 20 miles/hour, am I speeding? Here we must convert two things: meters to miles, and seconds to hours 1 kilometers 0.62 miles 10 m / s 1 kilometer 1000 meters 22.3 mph YES ! SLOWDOWN 3600 sec 1 hour Conversions are a breeze with the metric system because it is based on powers of 10! Converting Units of Measurement – Dimensional Analysis 1 km 1000 meters 0.62 mile 1 km 12 inches 1 foot 5280 feet 2.54 cm 100 cm 1 mile 1 inch 1 meter Converting higher order units If I have a house with 2,000 ft2 how many m2 does this correspond to? 1 m = 3.28 ft Notice these powers match! 2 2,000 ft 2 1 meter 2 185 . 9 m 3.28 ft Converting Units of Measurement – Dimensional Analysis Prefix Power Examples Kilo- 1000, 103 Kilometer, Kiloliter, Kilogram Hecto- 100, 102 Hectometer,Hectoliter,Hectogram Deca- 10, 101 Decameter,Decaliter,Decagram m, l, gr 1, 100 meter,liter,gram Deci- 0.1, 10-1 Decimeter,Deciliter,Decigram Centi- 0.01, 10-2 Centimeter,Centiliter,Centigram Milli- 0.001, 10-3 Millimeter,Milliliter,Milligram What if I had 10 milliliters and needed to convert this to kiloliters? 10 mL 1L 1 kL 0.00001kL 1 105 kL 1000mL 1000 L There’s a cooler way to do it and it involves my friend Hector! Converting Units of Measurement – Dimensional Analysis Prefix Power Examples Kilo- 1000, 103 Kilometer, Kiloliter, Kilogram Kind Hecto- 100, 102 Hectometer,Hectoliter,Hectogram Hector Deca- 10, 101 Decameter,Decaliter,Decagram Decked m, l, gr 1, 100 meter,liter,gram Mr. Deci- 0.1, 10-1 Decimeter,Deciliter,Decigram Deci Centi- 0.01, 10-2 Centimeter,Centiliter,Centigram Cinema Milli- 0.001, 10-3 Millimeter,Milliliter,Milligram Monday Kind Hector Decked Mr. Deci at the Cinema on Monday. KHDMDCM Each word represents one of the powers of ten in the metric system!! Converting Units of Measurement – Dimensional Analysis KHDMDCM So let’s look at how this works using the example we just did. What if I had 10 milliliters and needed to convert this to kiloliters? KHDMDCM 10.0 mL = ?? kL KHDMDCM Notice that I had to move over 6 letters to get to the “K” (or Kilo). So this corresponds to the number (and direction) of spaces I have to move my decimal! 10.0 mL = 0.00001 kL Let’s try another example! Converting Units of Measurement – Dimensional Analysis 1 km 1000 meters 0.62 mile 1 km 12 inches 1 foot 5280 feet 2.54 cm 100 cm 1 mile 1 inch 1 meter We can use converting units to solve some neat problems. How about this. If I know that a stack of 1,000 - $1 bills is = 1 inch in height Could I jump over $1,000,000? Where would we start? 1,000,000 dollars 1 inch 1000 dollars 1,000,000 dollars 1 inch 1000 dollars ??? 1 ft 83 ft 12 inches If I could jump this high I would be in the NBA!! Look this stuff is even useful for everyday life!! CAN YOU BELIEVE IT!! 7-inch and 14-inch pizzas ($4.95, $13.95) How much bigger is the 14-inch and which is the better buy? Area of a circle = r2 7-inch Area = 153.9 inch2 14-inch Area = 615.7 inch2 Best Buy? (Price per inch2) 7-inch $ 4.95/153.9 inch2 0.03 $/inch2 14-inch $ 13.95/615.7 inch2 0.02 $/inch2 Dimensional Analysis • Any valid physical formula must be dimensionally consistent – each term must have the same dimensions From the table: Distance = velocity × time Velocity = acceleration × time Energy = mass × (velocity)2