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Sec 2.5.2 The Method of Conversion Factors Sample

Sec 2.5.2 The Method of Conversion Factors Sample - 30 The...

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30 The Silicon Web: Physics for the Internet Age Units for other quantities will be introduced as needed throughtout the book. An important part of learning about science and technology is learning how to cal- culate physical quantities in real-life situations. This is useful in everything from esti- mating your home heating bill to understanding how computer circuits work. Here we will study a systematic method for calculating quantities involving units. Consider a car traveling with speed equal to S . The formula for the distance ( D ) trav- eled in a certain time ( t ) by the car is: D = S . t , where the dot means “times.” Common sense tells us that if the car’s speed is 100 kilometers per hour (100 km/hr), and the car travels for 2 hours, the distance it covers is 200 km. That is, D = (100 km/hr) . (2 hr) = 200 km There are several equivalent ways to write 100 kilometers per hour: 100 100 km per hr = 100 km/hr = 100 km hr km h = r The word “per” acts like division ( ÷ ) for the units. Let us analyze the distance calculation in more detail: D S t = = = (100 km per hr) (2hr)  100 km hr      2 hr 200 km     = The hr unit appears both in the numerator and the denominator and it therefore cancels, just as in ordinary fractions involving numbers or variables; for example, a b b a =   Notice also that we must use values of the speed and time that are compatible, so that the unit of time (hours) will cancel properly, as in the above example. If instead we were to give the time in minutes (120 min) and put this into the formula, we would get D S t = = 100 120 km hr min = 1200 km min hr Written this way, the minutes and hours units do not cancel, and we get a result that is hard to interpret. To remedy this, we need to use the following method. 2.5.2 The Method of Conversion Factors In the preceding example, we were left with the awkward units min/hr, which we want to eliminate. We know that there are 60 minutes per hour; this means that there are 1/60 hour per minute. Another way to say this is that 60 minutes equals 1 hour, or 60 min = 1 hr. This means that 60 min divided by 1 hr equals 1. 60 1 min 1 hr CF = In this equation, the “1” on the right-hand side has no units. This quantity is called a conversion factor , and we write “CF” near the bottom of the bracket to remind us. It is also true that 1 hr divided by 60 minutes equals 1: 1 1 hr 60 min CF = TAF-K10173-08-1107-002.indd 30 TAF-K10173-08-1107-002.indd 30 4/24/09 9:18:49 PM 4/24/09 9:18:49 PM
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Mathematics 31 We can multiply any quantity by any conversion factor without changing the quanti- ty’s value. Consider a simple example: What does 3 hours equal in minutes?
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