Theoretical Mechanics IPSP

Jürgen Vollmer, Universität Leipzig

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book:chap2:2.6_physics_application_balancing_forces

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book:chap2:2.6_physics_application_balancing_forces [2021/10/31 18:23] jvbook:chap2:2.6_physics_application_balancing_forces [2022/04/01 21:00] (current) jv
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 +[[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: balancing forces **
 +  * [[  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's mobiles| 2.10 Worked example: Calder's mobiles ]]
 +  * [[ 2.11 Problems| 2.11 Problems ]]
 +  * [[ 2.12 Further reading| 2.12 Further reading ]]
 +
 +----
 +
 ===== 2.6 Physics application: balancing forces ===== ===== 2.6 Physics application: balancing forces =====
  
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 <WRAP #quest_forceSelftest-rest > Problem 2.14: ** Particles at rest **\\ <WRAP #quest_forceSelftest-rest > Problem 2.14: ** Particles at rest **\\
-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? 
 {{ :book:chap2:forceselftest-rest.png?direct&600 |}} {{ :book:chap2:forceselftest-rest.png?direct&600 |}}
 +</WRAP>
  
-</WRAP>\\+----
  
 <WRAP #quest_forceSelftest-vectorSum >Problem 2.15: ** Graphical sum of vectors **\\ <WRAP #quest_forceSelftest-vectorSum >Problem 2.15: ** Graphical sum of vectors **\\
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 {{ :book:chap2:forceselftest-vectorsum1.png?direct&600 |}} {{ :book:chap2:forceselftest-vectorsum1.png?direct&600 |}}
 {{ :book:chap2:forceselftest-vectorsum2.png?direct&600 |}} {{ :book:chap2:forceselftest-vectorsum2.png?direct&600 |}}
-</WRAP>\\+</WRAP> 
 + 
 +----
  
 <WRAP #quest_forceSelftest-Muskelprotz >Problem 2.16: ** Towing a stone **\\ <WRAP #quest_forceSelftest-Muskelprotz >Problem 2.16: ** Towing a stone **\\
 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?
-</WRAP>\\+</WRAP>
  
 ~~DISCUSSION|Questions, Remarks, and Suggestions~~ ~~DISCUSSION|Questions, Remarks, and Suggestions~~
book/chap2/2.6_physics_application_balancing_forces.1635701036.txt.gz · Last modified: 2021/10/31 18:23 by jv