book:chap1:1.4_problems
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book:chap1:1.4_problems [2021/10/25 23:00] – jv | book:chap1:1.4_problems [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 ]] | ||
+ | |||
+ | ---- | ||
+ | |||
===== 1.4 Problems ===== | ===== 1.4 Problems ===== | ||
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- 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 $m=200\text{g}$, | + | - 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. | ||
</ | </ | ||
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** 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