Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

User Tools

Site Tools


book:chap1:1.4_problems

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision
Previous revision
book:chap1:1.4_problems [2021/10/25 23:00] jvbook:chap1:1.4_problems [2022/04/01 19:28] (current) jv
Line 1: Line 1:
 +[[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 ]]
 +
 +----
 +
 ===== 1.4 Problems ===== ===== 1.4 Problems =====
  
Line 7: Line 16:
   -  How does the initial velocity $v_0$ impact the distance $W$ of a thrown object (stone, ball, or shot) or a jump?   -  How does the initial velocity $v_0$ impact the distance $W$ of a thrown object (stone, ball, or shot) or a jump?
   -  How does the initial velocity $v_0$ depend on \\ the force $F$ acting by the responsible muscle \\ the accelerated mass $M$, and \\ the distance $L$ of the path where the acceleration is performed?   -  How does the initial velocity $v_0$ depend on \\ the force $F$ acting by the responsible muscle \\ the accelerated mass $M$, and \\ the distance $L$ of the path where the acceleration is performed?
-  -  Estimate the maximum distance \\ of throwing a stone of mass $m=200\text{g}$, \\ of a standing jump for a human and a grass hopper.+  -  Estimate the maximum distance \\ of throwing a stone of mass $m=200\,\text{g}$, \\ of a standing jump for a human and a grass hopper.
   -  Make an explicit analysis of standing jumps by exploring how their distance scales with the ratio of characteristic sizes (i.e., body length) of the jumper.   -  Make an explicit analysis of standing jumps by exploring how their distance scales with the ratio of characteristic sizes (i.e., body length) of the jumper.
 </WRAP> </WRAP>
Line 16: Line 25:
 ** Water waves ** ** Water waves **
 \\ \\
-The speed of waves on the ocean depends only on their wave length$L$ and the gravitational acceleration $g \simeq 10\text{m/s$^2$}$.+The speed of waves on the ocean depends only on  
 +their wave length $L$ and  
 +the gravitational acceleration $g \simeq 10\,\text{m/s}^2$.
  
   -  How does the speed of the waves depend on $L$ and $g$?   -  How does the speed of the waves depend on $L$ and $g$?
book/chap1/1.4_problems.1635195633.txt.gz · Last modified: 2021/10/25 23:00 by jv