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Unit Conversions and Dimensional Analysis Measurements in physics - SI Standards (fundamental units) Fundamental units: length – meter (m) time – second (s) mass - kilogram (kg) temperature - kelvin (K) current – ampere (A) luminous Intensity - candela (cd) Amount of substance – mole (mol) – 6.02 x 1023 Derived units: combinations of fundamental units speed (v) = distance/time units: m/s acceleration (a) = velocity / time units: m/s/s = m/s2 force (F) = mass x acceleration units: kgm/s2 = N (Newton) energy (E) = force x distance units: kgm2/s2 = Nm = J (Joule) charge (Q) = current x time units: As = C (Coulomb) 1.3 The Role of Units in Problem Solving THE CONVERSION OF UNITS 1 ft = 0.3048 m 1 mi = 1.609 km 1 hp = 746 W 1 liter = 10-3 m3 1.3 The Role of Units in Problem Solving Example 1 The World’s Highest Waterfall The highest waterfall in the world is Angel Falls in Venezuela, with a total drop of 979.0 m. Express this drop in feet. Since 3.281 feet = 1 meter, it follows that (3.281 feet)/(1 meter) = 1 3.281 feet Length 979.0 meters 3212 feet 1 meter 1.3 The Role of Units in Problem Solving 1.3 The Role of Units in Problem Solving A typical bacterium has a mass of about 2.0 fg. Express this measurement in terms of grams and kilograms. We know 1 fg = 10-15 g and 1 kg = 103 g 11015 g 2 1015 g (2.0 fg ) 1 fg (2 10 15 1kg 18 2.0 10 kg g ) 3 110 g 1.3 The Role of Units in Problem Solving Reasoning Strategy: Converting Between Units 1. In all calculations, write down the units explicitly. 2. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically. 3. Use the conversion factors located on the page facing the inside cover. Be guided by the fact that multiplying or dividing an equation by a factor of 1 does not alter the equation. 1.3 The Role of Units in Problem Solving Example 2 Interstate Speed Limit Express the speed limit of 65 miles/hour in terms of meters/second. Use 5280 feet = 1 mile and 3600 seconds = 1 hour and 3.281 feet = 1 meter. feet miles miles 5280 feet 1 hour Speed 65 1 65 95 hour hour mile 3600 s second feet feet 1 meter meters Speed 95 1 95 29 second second second 3.281 feet 1.3 The Role of Units in Problem Solving DIMENSIONAL ANALYSIS [L] = length [M] = mass [T] = time Is the following equation dimensionally correct? x vt 1 2 2 L 2 L T LT T 1.3 The Role of Units in Problem Solving Is the following equation dimensionally correct? x vt L L T L T