Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

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book:chap1:1.3_order-of-magnitude_guesses [2021/10/25 22:55] jvbook:chap1:1.3_order-of-magnitude_guesses [2022/04/01 19:28] (current) jv
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 +[[basics| 1. Basic Principles]]
 +  * [[ 1.1 Basic notions of mechanics ]]
 +  * [[ 1.2 Dimensional analysis ]]
 +  * ** 1.3 Order-of-magnitude guesses **
 +  * [[ 1.4 Problems ]]
 +  * [[ 1.5  Further reading ]]
 +
 +----
 +
 ===== 1.3 Order-of-magnitude guesses ===== ===== 1.3 Order-of-magnitude guesses =====
  
 Many physical quantities take a value close to one Many physical quantities take a value close to one
-when they are expressed in their ``natural'' dimensionless units.+when they are expressed in their natural” dimensionless units.
 When the choice is unique, then clearly it is also natural. When the choice is unique, then clearly it is also natural.
 Otherwise, the appropriate choice is a matter of experience. Otherwise, the appropriate choice is a matter of experience.
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 (see [[#fig_pendulum-omg|Figure 1.3]]). (see [[#fig_pendulum-omg|Figure 1.3]]).
 \\ \\
-As discussed in \Example{pendulum-nodimthe dimensionless time unit for this problem is $\sqrt{L/g}$. +As discussed in [[book:chap1:1.2_dimensional_analysis#bsp_pendulum-nodim|Example 1.8]] the time unit for this problem is $\sqrt{L/g}$. 
-Hence we estimate that the period $T$ of the pendulum is of the order of+Hencewe estimate that the period $T$ of the pendulum is of the order of
 $ $
 T \simeq \sqrt{L/g}  T \simeq \sqrt{L/g} 
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 </WRAP> </WRAP>
  
-<WRAP box round>**Example 1.11** <wrap em>The speed of Tsunami waves</wrap> \\ +<WRAP box round #Tsunami-speed-omg>**Example 1.11** <wrap em>The speed of Tsunami waves</wrap> \\ 
 A Tsunami wave is a water wave that is generated by an earth quake or an underwater land slide. A Tsunami wave is a water wave that is generated by an earth quake or an underwater land slide.
 Typical wave lengths are of an order of magnitude $\lambda = 100\,\text{km}$. Typical wave lengths are of an order of magnitude $\lambda = 100\,\text{km}$.
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 You put these books into bookshelves with seven boards in each shelf. You put these books into bookshelves with seven boards in each shelf.
 How many meters of bookshelves will you need to store your data on paper? How many meters of bookshelves will you need to store your data on paper?
 +</WRAP>
  
 ~~DISCUSSION|Questions, Remarks, and Suggestions~~ ~~DISCUSSION|Questions, Remarks, and Suggestions~~
  
book/chap1/1.3_order-of-magnitude_guesses.1635195356.txt.gz · Last modified: 2021/10/25 22:55 by jv