book:chap2:2.6_physics_application_balancing_forces
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
book:chap2:2.6_physics_application_balancing_forces [2021/10/31 17:51] – [2.6.1 Self Test] jv | book:chap2:2.6_physics_application_balancing_forces [2022/04/01 21:00] (current) – jv | ||
---|---|---|---|
Line 1: | Line 1: | ||
+ | [[forcestorques|2. Balancing Forces and Torques]] | ||
+ | * [[ 2.1 Motivation and Outline| 2.1 Motivation and outline: forces are vectors ]] | ||
+ | * [[ 2.2 Sets| 2.2 Sets ]] | ||
+ | * [[ 2.3 Groups| 2.3 Groups ]] | ||
+ | * [[ 2.4 Fields| 2.4 Fields ]] | ||
+ | * [[ 2.5 Vector spaces| 2.5 Vector spaces ]] | ||
+ | * ** 2.6. Physics application: | ||
+ | * [[ 2.7 The inner product | 2.7 The inner product]] | ||
+ | * [[ 2.8 Cartesian coordinates | 2.8 Cartesian coordinates]] | ||
+ | * [[ 2.9 Cross products --- torques| 2.9 Cross products — torques ]] | ||
+ | * [[ 2.10 Worked example Calder' | ||
+ | * [[ 2.11 Problems| 2.11 Problems ]] | ||
+ | * [[ 2.12 Further reading| 2.12 Further reading ]] | ||
+ | |||
+ | ---- | ||
+ | |||
===== 2.6 Physics application: | ===== 2.6 Physics application: | ||
+ | <WRAP group> | ||
<WRAP 120pt left # | <WRAP 120pt left # | ||
{{tug-of-war__NicolayBogdanov.jpg|}}\\ | {{tug-of-war__NicolayBogdanov.jpg|}}\\ | ||
- | Tug of War, Nikolay Bogdanov-Belsky, | + | Tug of War, Nikolay Bogdanov-Belsky, |
- | + | ||
- | {{vector_sums.png}} | + | |
- | Figure 2.10: The left diagrams show two and three forces acting on a ring. To the right it is demonstrated that they add to zero. | + | |
</ | </ | ||
Line 22: | Line 36: | ||
For the ring the sums of the forces are illustrated in the right panels of [[# | For the ring the sums of the forces are illustrated in the right panels of [[# | ||
The ring does not move when they add to zero. | The ring does not move when they add to zero. | ||
+ | </ | ||
+ | |||
+ | <WRAP group> | ||
+ | <WRAP 120pt left # | ||
+ | {{vector_sums.png}} | ||
+ | Figure 2.10: The left diagrams show two and three forces acting on a ring. To the right it is demonstrated that they add to zero. | ||
+ | </ | ||
<WRAP box round # | <WRAP box round # | ||
Line 35: | Line 56: | ||
We come back to this point in [[book: | We come back to this point in [[book: | ||
</ | </ | ||
+ | </ | ||
+ | |||
+ | <WRAP group> | ||
+ | <WRAP 120pt left # | ||
+ | {{ : | ||
+ | Figure 2.11: For a person balancing on a slackline, the gravitational force $\mathbf F_d$ (d for down) | ||
+ | is balanced by forces $\mathbf F_l$ and $\mathbf F_r$ along the line that pull towards the left and right, respectively. See [[# | ||
+ | </ | ||
<WRAP box round # | <WRAP box round # | ||
Line 45: | Line 74: | ||
These forces become huge when the slackline runs almost horizontally. | These forces become huge when the slackline runs almost horizontally. | ||
Every now a then a careless slackliner roots out a tree or fells a pillar. | Every now a then a careless slackliner roots out a tree or fells a pillar. | ||
+ | </ | ||
</ | </ | ||
- | <WRAP 120pt left # | + | <WRAP goup> |
- | {{./ | + | <WRAP 120pt left # |
- | Figure 2.11: For a person balancing on a slackline, the gravitational force $\mathbf F_d$ (d for down) | + | |
- | is balanced by forces $\mathbf F_l$ and $\mathbf F_r$ along the line that pull towards the left and right, respectively. See [[# | + | |
{{free_body_static_friction.png}}\\ | {{free_body_static_friction.png}}\\ | ||
{{PhyPhoxStaticFriction.JPG}}\\ | {{PhyPhoxStaticFriction.JPG}}\\ | ||
Line 58: | Line 85: | ||
i.e., $\mu \simeq 0.5$. | i.e., $\mu \simeq 0.5$. | ||
Using [[https:// | Using [[https:// | ||
- | </ | + | </ |
<WRAP box round> **Example 2.20:** <wrap em> | <WRAP box round> **Example 2.20:** <wrap em> | ||
Line 71: | Line 98: | ||
By splitting the gravitational force, $m\mathbf g$ acting on a block on a plane into its components parallel and normal to the surface (gray arrows in [[# | By splitting the gravitational force, $m\mathbf g$ acting on a block on a plane into its components parallel and normal to the surface (gray arrows in [[# | ||
one finds that in the presence of a force balance $m \mathbf g + \mathbf f + \mathbf F_N = \mathbf 0$ | one finds that in the presence of a force balance $m \mathbf g + \mathbf f + \mathbf F_N = \mathbf 0$ | ||
- | one has\\ | + | one has |
\begin{align*} | \begin{align*} | ||
\left . | \left . | ||
Line 87: | Line 114: | ||
When $\theta$ exceeds $\theta_c$ the block starts to slide. | When $\theta$ exceeds $\theta_c$ the block starts to slide. | ||
Hence, one can infer $\gamma$ from measurements of $\theta_c$. | Hence, one can infer $\gamma$ from measurements of $\theta_c$. | ||
+ | </ | ||
</ | </ | ||
Line 93: | Line 121: | ||
<WRAP # | <WRAP # | ||
- | There are three forces acting on the center of mass of a body. In which cases does it stay at rest?\\ | + | There are three forces acting on the center of mass of a body. In which cases does it stay at rest? |
{{ : | {{ : | ||
+ | </ | ||
- | </ | + | ---- |
<WRAP # | <WRAP # | ||
- | Determine the sum of the vectors. In which cases is the resulting vector vertical to the horizontal direction?\\ | + | Determine the sum of the vectors. In which cases is the resulting vector vertical to the horizontal direction? |
- | {{forceSelftest-vectorSum1.pdf}}\\ | + | |
- | {{forceSelftest-vectorSum2.pdf}}\\ | + | {{ : |
- | </ | + | {{ : |
+ | </ | ||
+ | |||
+ | ---- | ||
<WRAP # | <WRAP # | ||
Three Scottish muscleman ((In highland games one still uses Imperial Units. A hundredweight (cwt) amounts to eight stones (stone) that each have a mass of $14$ pounds(lb). A pound-force (lbg) amounts to the gravitational force acting on a pound. One can solve this problem without converting units.)) try to tow a stone with mass $M=20\text{cwt}$ from a field. Each of them gets his own rope, and he can act a maximal force of | Three Scottish muscleman ((In highland games one still uses Imperial Units. A hundredweight (cwt) amounts to eight stones (stone) that each have a mass of $14$ pounds(lb). A pound-force (lbg) amounts to the gravitational force acting on a pound. One can solve this problem without converting units.)) try to tow a stone with mass $M=20\text{cwt}$ from a field. Each of them gets his own rope, and he can act a maximal force of | ||
- | $300\text{lbg}$ as long as the ropes run in directions that differ by at least $30^\circ$\\ | + | $300\text{lbg}$ as long as the ropes run in directions that differ by at least $30^\circ$ |
- Sketch the forces acting on the stone and their sum. By which ratio is the force exerted by three men larger than that of a single man? | - Sketch the forces acting on the stone and their sum. By which ratio is the force exerted by three men larger than that of a single man? | ||
- The stone counteracts the pulling of the men by a static friction force $\mu M g$, where $g$ is the gravitational acceleration. What is the maximum value that the friction coefficient $\mu$ may take when the men can move the stone? | - The stone counteracts the pulling of the men by a static friction force $\mu M g$, where $g$ is the gravitational acceleration. What is the maximum value that the friction coefficient $\mu$ may take when the men can move the stone? | ||
- | </ | + | </ |
~~DISCUSSION|Questions, | ~~DISCUSSION|Questions, |
book/chap2/2.6_physics_application_balancing_forces.1635699083.txt.gz · Last modified: 2021/10/31 17:51 by jv