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5. The Do the Math! example on page 412 of your textbook shows the technique of unit conversion, called dimensional analysis, which indicates whether to multiply or divide when converting one quantity to another. The example converts Calories per day to watts. The conversion factors used in the example are (1 day) / (24 hours), (1 hour) / (3600 seconds), and (4184 joules) / (1 Calorie). The Calorie here is the "big" Calorie, commonly used in rating foods. Note carefully how the units cancel just as numbers do when multiplying fractions. We will use this technique to solve the following: How many joules of energy are transferred per day at the rate of 1 watt? We know that 1 W is equal to 1 J/s. So 1 J 36008 24 K J/d 1 8 1 k 1 d Note in this case that (1 ])/ (1 s) is multiplied by (3600 s) / (1 h) rather than by (1 h)/(3600 s). This way, the units s cancel. The same is true for units h. So 1 J is multiplied by 3600, since there are 3600 seconds in 1 hour, and again by 24, because there are 24 hours in 1 day. These numbers appear only in the numerators, so they are simply multiplied. We multiply the numerators and divide by the denominators. In this case we see only the numerical values of 1 appear in the demoninators. a. By dimensional analysis convert 50 calories per hour (small calories) to joules per day. 50 cal J X h X 1 h d ca b. Try this one: How many joules will a 100-watt bulb give off in 4 hours? 100 W x 4h = J x 4 h x S S h c. This one puts you more on your own: Find the number of joules given off by a 4-W bulb in a night light that burns continously for one month (1 mo). 4 W x 1 mo = 4 J 1 s * 1 mo x 6. On a certain planet the unit of heat energy is called the OOH, where 1 OOH = 3 calories, and the unit of time is called the AAH, where 1 AAH = 12.56 seconds. By dimensional analysis show that 1 watt = 1 OOH/AAH. CONCEPTUAL PHYSICS