AP1200_Ch2_OrderOfMagnitude-2007

AP1200_Ch2_OrderOfMagnitude-2007 - AP1200 Foundation...

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AP1200 Foundation Physics Chapter 2: Order of Magnitude 2.1 Rough estimates Very often, whether in daily life or professional work, we need or wish to make quick and rough estimates for a wide variety of quantities. These may be called “guesses”. The main reason for making such guesses is simply that we don’t have detailed information to quickly make precise estimates. For example: How long will it take to cross the city at rush hour? How much salt should I buy to cook during the next month? How much packaging material will I need to wrap gifts to my family? How many people will show up at a ceremony? How much money should I budget to advertise a new product? How well will this new product sell, so I can plan how many products to make? How much time would I need to walk from Hong Kong to Shanghai? What is the volume of the Three Gorges Dam (San Xia Shui Ba)? How much water does the reservoir behind the Three Gorges Dam contain? If global warming melted all ice on Earth, how high would the oceans rise? We may need quick and rough estimates for a variety of reasons: To evaluate whether a trip or visit can be made in a reasonable time To buy home supplies for the future, even when we don’t know how much we will use To make initial comparisons between alternative commercial strategies To give interesting information in informal conversations To evaluate whether a line of action is worth pursuing To check that a calculation is roughly correct Often, a quick and rough estimate will be followed by a more precise estimate: however, more work will usually be needed to obtain the higher precision, because it will be necessary to find or calculate more precise data. In general, we can think of a succession of increasingly precise estimates, each one needing more detailed study than the preceding one. At each stage, we then have a better picture of the situation and can decide whether the plan is still reasonable. Let us look more closely at a simple, practical situation that illustrates the usefulness of rough estimates. When planning a line of action (such as a trip, a commercial strategy or a research project), it is helpful to start with a very rough plan that can be set up quickly: this rough plan may already tell you that the whole idea is bad and should be abandoned, without the need to do a more detailed and time-consuming analysis. To do this we need a rough idea of the magnitudes of the tasks involved.
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Consider this proposition by your friend: he invites you to walk (yes, walk!) from Hong Kong to Shanghai. Your first question may be: can this be done in a reasonable time? If not, you can abandon the idea before doing more planning. To decide this, you need to make a rough estimate of the time needed to walk from Hong Kong to Shanghai. That time can be calculated if you know the rough distance and your rough walking speed. So let’s make very rough guesses for these quantities:
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AP1200_Ch2_OrderOfMagnitude-2007 - AP1200 Foundation...

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