183_notes:model_of_solids

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183_notes:model_of_solids [2021/02/18 20:33] – [Modeling tension microscopically] stumptyl183_notes:model_of_solids [2021/03/13 19:29] (current) – [Modeling tension microscopically] stumptyl
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 ===== Matter & Models of Solids ===== ===== Matter & Models of Solids =====
  
-Until now, you have read (primarily) about forces that result from the gravitational interaction in both its [[183_notes:gravitation|exact]] and [[183_notes:localg|approximate]] forms. The exception thus far has been the [[183_notes:springmotion|spring force]], which, until now, you took as just another of likely many possible forces. As it turns out //the main types of force that you are concerned about in mechanics are the gravitational force and the electric force.// In fact, the spring force is the result of electrical interactions in matter. As you will read, all contact forces (like the spring force) result from the compression or extension of solid materials, which are themselves compressions or extensions of the bonds between atoms in the material (electrical interactions). In these notes, you read about how we model these compressions and extensions, and how those interactions give rise to another contact force -- tension. +Until now, you have read (primarily) about forces that result from the gravitational interaction in both its [[183_notes:gravitation|exact]] and [[183_notes:localg|approximate]] forms. The exception thus far has been the [[183_notes:springmotion|spring force]], which, until now, you took as just another of likely many possible forces. As it turns out //the main types of force that you are concerned about in mechanics are the gravitational force and the electric force.// In fact, the spring force is the result of electrical interactions in matter. As you will read, all contact forces (like the spring force) result from the compression or extension of solid materials, which are themselves compressions or extensions of the bonds between atoms in the material (electrical interactions). **In these notes, you read about how we model these compressions and extensions, and how those interactions give rise to another contact force -- tension. 
 +**
 ==== Lecture Video ==== ==== Lecture Video ====
  
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 All matter is made up of atoms, which (as you know) are in turn made up of a dense positively charge nucleus (with a $\sim1\times10^{-15}m$ radius) and a sparse, negatively charged electron cloud (with a $\sim1\times10^{-10}m$ radius). The interaction between atoms is due primarily to the charges in the atoms. We observe that when two atoms are near each other, the long range electrical forces cause them to attract, but only up to a point. When atoms are pushed too close together, they begin to repel each other. All matter is made up of atoms, which (as you know) are in turn made up of a dense positively charge nucleus (with a $\sim1\times10^{-15}m$ radius) and a sparse, negatively charged electron cloud (with a $\sim1\times10^{-10}m$ radius). The interaction between atoms is due primarily to the charges in the atoms. We observe that when two atoms are near each other, the long range electrical forces cause them to attract, but only up to a point. When atoms are pushed too close together, they begin to repel each other.
  
-[{{ 183_notes:mi3e_04-003.png?200|Extending or compressing the ends of ball-spring system.}}]+[{{ 183_notes:horizontal_springsystems_compression.png?200|Extending or compressing the ends of ball-spring system.}}]
 These observations are not unlike those we observe with two ends of a spring (Figure to the right). Pulling the ends apart (past the springs relaxed length) stretches the spring, which results in a force by the spring "inward" to restore it to its relaxed length. Pushing the ends together (past the relaxed length) compresses the spring, which results in a force by the spring "outward" to restore it to its relaxed length.  These observations are not unlike those we observe with two ends of a spring (Figure to the right). Pulling the ends apart (past the springs relaxed length) stretches the spring, which results in a force by the spring "inward" to restore it to its relaxed length. Pushing the ends together (past the relaxed length) compresses the spring, which results in a force by the spring "outward" to restore it to its relaxed length. 
  
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 ==== Tension ==== ==== Tension ====
  
-[{{ 183_notes:mi3e_04-008.png?50|Free body diagram for the ball}}]+[{{  183_notes:phy_freebody_3.png?50|Free body diagram for the ball}}]
  
  
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 ==== Modeling tension microscopically ==== ==== Modeling tension microscopically ====
  
-[{{ 183_notes:mi3e_04-009.png?100|Each bond extends the same amount.}}]+[{{ 183_notes:vertical_parallel_springsystem.png?100|Each bond extends the same amount.}}]
  
 Consider a very thin wire that is one atom thick. In this case, you can observe what happens to each bond in the wire when a heavy ball is attached to the end of the wire (Figure to the left). **In this case, each bond is "stretched" by roughly the same amount. This is the model to consider when you think "the tension is the same throughout the wire."** Consider a very thin wire that is one atom thick. In this case, you can observe what happens to each bond in the wire when a heavy ball is attached to the end of the wire (Figure to the left). **In this case, each bond is "stretched" by roughly the same amount. This is the model to consider when you think "the tension is the same throughout the wire."**
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