hwsol1 - Made to Order (of Magnitude) Description: Several...

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Made to Order (of Magnitude) Description: Several unrelated order-of-magnitude calculations. Learning Goal: To be able to make order-of-magnitude calculations. Imagine that a company wants to build a new factory. Such a complex project would involve significant investment in terms of both time and money. Consequently, before construction can start the company asks for an estimate of the total cost. Although estimate figures are not exact, they are still helpful: For instance, if the projected cost is three times the amount of money that the company is willing to spend, the project will be canceled or substantially changed. Individuals make such estimates all the time. For instance, when you need to drive somewhere for a meeting, you can roughly predict how much time you will spend on the road and depart accordingly. Of course, the actual travel time is unlikely to be exactly the same as the estimated one —but it still helps to make an estimate so that you can decide when to leave. Physicists must frequently make such estimates—known as order-of-magnitude calculations —as part of their job. Depending on the results of the estimate, a potentially lengthy and costly research project may be postponed, canceled, or redesigned. Being able to make a quick calculation and get a "ball-park figure" of the expected result is an important skill for a scientist, involving processes such as identifying relevant information, searching for this information, and using your experience or background knowledge. In this problem, you will practice making such order-of-magnitude calculations. It is impossible, of course, to give an accurate answer to this question. However, it is quite possible to find the order of magnitude of the answer. All one needs to do is to use some common sense and, possibly, search for relevant reference information. The calculation can proceed as follows: There are about people on earth. An average adult male weighs, say, 75 ; an average adult female weighs about 60 , and an average child will weigh considerably less than 60 . Figuring roughly one child per adult, we can reasonably say that an average person's mass is about 50 , which gives the total mass of all humans on our planet as
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. Of course, we may be off in our estimates of the average mass or number of people. While it would be unreasonable to say that we know the total mass is , we can be reasonably sure that we have the correct order of magnitude; that is, we have the correct exponent to which the number 10 is raised. In each of the following problems, you will be asked to make similar estimates. Part A How many people could fit into the largest office building in the world? Assume that everybody must be standing on the floor. Round the answer to the nearest power of 10 and then express your answer as the order of magnitude . For instance, if your estimated answer is , enter 5. If your estimated answer is , you should enter 6 (rounding up to the next power of 10).
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This note was uploaded on 05/22/2008 for the course PHYS 2A taught by Professor Hicks during the Winter '07 term at UCSD.

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hwsol1 - Made to Order (of Magnitude) Description: Several...

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